Wavefront sensing reveals optical coherence.
Stoklasa, B; Motka, L; Rehacek, J; Hradil, Z; Sánchez-Soto, L L
2014-01-01
Wavefront sensing is a set of techniques providing efficient means to ascertain the shape of an optical wavefront or its deviation from an ideal reference. Owing to its wide dynamical range and high optical efficiency, the Shack-Hartmann wavefront sensor is nowadays the most widely used of these sensors. Here we show that it actually performs a simultaneous measurement of position and angular spectrum of the incident radiation and, therefore, when combined with tomographic techniques previously developed for quantum information processing, the Shack-Hartmann wavefront sensor can be instrumental in reconstructing the complete coherence properties of the signal. We confirm these predictions with an experimental characterization of partially coherent vortex beams, a case that cannot be treated with the standard tools. This seems to indicate that classical methods employed hitherto do not fully exploit the potential of the registered data.
Wavefront Sensing via High Speed DSP
Smith, J. Scott; Dean, Bruce
2004-01-01
Future light-weighted and segmented primary mirror systems require active optical control to maintain mirror positioning and figure to within nanometer tolerances. Current image-based wavefront sensing approaches rely on post-processing techniques to return an estimate of the aberrated optical wavefront with accuracies to the nanometer level. But the lag times between wavefront sensing, and then control, contributes to a significant latency in the wavefront sensing implementation. In this analysis we demonstrate accelerated image-based wavefront sensing performance using multiple digital signal processors (DSP's). The computational architecture is discussed as well as the heritage leading to the approach.
Compressive wavefront sensing with weak values.
Howland, Gregory A; Lum, Daniel J; Howell, John C
2014-08-11
We demonstrate a wavefront sensor that unites weak measurement and the compressive-sensing, single-pixel camera. Using a high-resolution spatial light modulator (SLM) as a variable waveplate, we weakly couple an optical field's transverse-position and polarization degrees of freedom. By placing random, binary patterns on the SLM, polarization serves as a meter for directly measuring random projections of the wavefront's real and imaginary components. Compressive-sensing optimization techniques can then recover the wavefront. We acquire high quality, 256 × 256 pixel images of the wavefront from only 10,000 projections. Photon-counting detectors give sub-picowatt sensitivity.
Complex wavefront sensing with a plenoptic sensor
Wu, Chensheng; Ko, Jonathan; Davis, Christopher C.
2016-09-01
There are many techniques to achieve basic wavefront sensing tasks in the weak atmospheric turbulence regime. However, in strong and deep turbulence situations, the complexity of a propagating wavefront increases significantly. Typically, beam breakup will happen and various portions of the beam will randomly interfere with each other. Consequently, some conventional techniques for wavefront sensing turn out to be inaccurate and misleading. For example, a Shack-Hartmann sensor will be confused by multi-spot/zero-spot result in some cells. The curvature sensor will be affected by random interference patterns for both the image acquired before the focal plane and the image acquired after the focal plane. We propose the use of a plenoptic sensor to solve complex wavefront sensing problems. In fact, our results show that even for multiple beams (their wavelengths can be the same) passing through the same turbulent channel, the plenoptic sensor can reconstruct the turbulence-induced distortion accurately. In this paper, we will demonstrate the plenoptic mapping principle to analyze and reconstruct the complex wavefront of a distorted laser beam.
Asymmetric cryptography based on wavefront sensing.
Peng, Xiang; Wei, Hengzheng; Zhang, Peng
2006-12-15
A system of asymmetric cryptography based on wavefront sensing (ACWS) is proposed for the first time to our knowledge. One of the most significant features of the asymmetric cryptography is that a trapdoor one-way function is required and constructed by analogy to wavefront sensing, in which the public key may be derived from optical parameters, such as the wavelength or the focal length, while the private key may be obtained from a kind of regular point array. The ciphertext is generated by the encoded wavefront and represented with an irregular array. In such an ACWS system, the encryption key is not identical to the decryption key, which is another important feature of an asymmetric cryptographic system. The processes of asymmetric encryption and decryption are formulized mathematically and demonstrated with a set of numerical experiments.
Refractive error sensing from wavefront slopes.
Navarro, Rafael
2010-01-01
The problem of measuring the objective refractive error with an aberrometer has shown to be more elusive than expected. Here, the formalism of differential geometry is applied to develop a theoretical framework of refractive error sensing. At each point of the pupil, the local refractive error is given by the wavefront curvature, which is a 2 × 2 symmetric matrix, whose elements are directly related to sphere, cylinder, and axis. Aberrometers usually measure the local gradient of the wavefront. Then refractive error sensing consists of differentiating the gradient, instead of integrating as in wavefront sensing. A statistical approach is proposed to pass from the local to the global (clinically meaningful) refractive error, in which the best correction is assumed to be the maximum likelihood estimation. In the practical implementation, this corresponds to the mode of the joint histogram of the 3 different elements of the curvature matrix. Results obtained both in computer simulations and with real data provide a close agreement and consistency with the main optical image quality metrics such as the Strehl ratio.
Implementation of a Wavefront-Sensing Algorithm
Smith, Jeffrey S.; Dean, Bruce; Aronstein, David
2013-01-01
A computer program has been written as a unique implementation of an image-based wavefront-sensing algorithm reported in "Iterative-Transform Phase Retrieval Using Adaptive Diversity" (GSC-14879-1), NASA Tech Briefs, Vol. 31, No. 4 (April 2007), page 32. This software was originally intended for application to the James Webb Space Telescope, but is also applicable to other segmented-mirror telescopes. The software is capable of determining optical-wavefront information using, as input, a variable number of irradiance measurements collected in defocus planes about the best focal position. The software also uses input of the geometrical definition of the telescope exit pupil (otherwise denoted the pupil mask) to identify the locations of the segments of the primary telescope mirror. From the irradiance data and mask information, the software calculates an estimate of the optical wavefront (a measure of performance) of the telescope generally and across each primary mirror segment specifically. The software is capable of generating irradiance data, wavefront estimates, and basis functions for the full telescope and for each primary-mirror segment. Optionally, each of these pieces of information can be measured or computed outside of the software and incorporated during execution of the software.
High order dark wavefront sensing simulations
Ragazzoni, Roberto; Farinato, Jacopo; Viotto, Valentina; Bergomi, Maria; Dima, Marco; Magrin, Demetrio; Marafatto, Luca; Greggio, Davide; Carolo, Elena; Vassallo, Daniele
2016-01-01
Dark wavefront sensing takes shape following quantum mechanics concepts in which one is able to "see" an object in one path of a two-arm interferometer using an as low as desired amount of light actually "hitting" the occulting object. A theoretical way to achieve such a goal, but in the realm of wavefront sensing, is represented by a combination of two unequal beams interferometer sharing the same incoming light, and whose difference in path length is continuously adjusted in order to show different signals for different signs of the incoming perturbation. Furthermore, in order to obtain this in white light, the path difference should be properly adjusted vs the wavelength used. While we incidentally describe how this could be achieved in a true optomechanical setup, we focus our attention to the simulation of a hypothetical "perfect" dark wavefront sensor of this kind in which white light compensation is accomplished in a perfect manner and the gain is selectable in a numerical fashion. Although this would ...
Phase error correction in wavefront curvature sensing via phase retrieval
DEFF Research Database (Denmark)
Almoro, Percival; Hanson, Steen Grüner
2008-01-01
Wavefront curvature sensing with phase error correction system is carried out using phase retrieval based on a partially-developed volume speckle field. Various wavefronts are reconstructed: planar, spherical, cylindrical, and a wavefront passing through the side of a bare optical fiber. Spurious...
Wavefront-sensing-based autofocusing in microscopy
Xu, Jing; Tian, Xiaolin; Meng, Xin; Kong, Yan; Gao, Shumei; Cui, Haoyang; Liu, Fei; Xue, Liang; Liu, Cheng; Wang, Shouyu
2017-08-01
Massive image acquisition is required along the optical axis in the classical image-analysis-based autofocus method, which significantly decreases autofocus efficiency. A wavefront-sensing-based autofocus technique is proposed to increase the speed of autofocusing and obtain high localization accuracy. Intensities at different planes along the optical axis can be computed numerically after extracting the wavefront at defocus position with the help of the transport-of-intensity equation method. According to the focus criterion, the focal plane can then be determined, and after sample shifting to this plane, the in-focus image can be recorded. The proposed approach allows for fast, precise focus detection with fewer image acquisitions compared to classical image-analysis-based autofocus techniques, and it can be applied in commercial microscopes only with an extra illumination filter.
Wavefront Compensation Segmented Mirror Sensing and Control
Redding, David C.; Lou, John Z.; Kissil, Andrew; Bradford, Charles M.; Woody, David; Padin, Stephen
2012-01-01
The primary mirror of very large submillimeter-wave telescopes will necessarily be segmented into many separate mirror panels. These panels must be continuously co-phased to keep the telescope wavefront error less than a small fraction of a wavelength, to ten microns RMS (root mean square) or less. This performance must be maintained continuously across the full aperture of the telescope, in all pointing conditions, and in a variable thermal environment. A wavefront compensation segmented mirror sensing and control system, consisting of optical edge sensors, Wavefront Compensation Estimator/Controller Soft ware, and segment position actuators is proposed. Optical edge sensors are placed two per each segment-to-segment edge to continuously measure changes in segment state. Segment position actuators (three per segment) are used to move the panels. A computer control system uses the edge sensor measurements to estimate the state of all of the segments and to predict the wavefront error; segment actuator commands are computed that minimize the wavefront error. Translational or rotational motions of one segment relative to the other cause lateral displacement of the light beam, which is measured by the imaging sensor. For high accuracy, the collimator uses a shaped mask, such as one or more slits, so that the light beam forms a pattern on the sensor that permits sensing accuracy of better than 0.1 micron in two axes: in the z or local surface normal direction, and in the y direction parallel to the mirror surface and perpendicular to the beam direction. Using a co-aligned pair of sensors, with the location of the detector and collimated light source interchanged, four degrees of freedom can be sensed: transverse x and y displacements, as well as two bending angles (pitch and yaw). In this approach, each optical edge sensor head has a collimator and an imager, placing one sensor head on each side of a segment gap, with two parallel light beams crossing the gap. Two sets
Method and apparatus for wavefront sensing
Bahk, Seung-Whan
2016-08-23
A method of measuring characteristics of a wavefront of an incident beam includes obtaining an interferogram associated with the incident beam passing through a transmission mask and Fourier transforming the interferogram to provide a frequency domain interferogram. The method also includes selecting a subset of harmonics from the frequency domain interferogram, individually inverse Fourier transforming each of the subset of harmonics to provide a set of spatial domain harmonics, and extracting a phase profile from each of the set of spatial domain harmonics. The method further includes removing phase discontinuities in the phase profile, rotating the phase profile, and reconstructing a phase front of the wavefront of the incident beam.
Fast & Furious focal-plane wavefront sensing
Korkiakoski, V.A.; Keller, C.U.; Doelman, N.; Kenworthy, M.; Otten, G.; Verhaegen, M.H.G.
2014-01-01
We present two complementary algorithms suitable for using focal-plane measurements to control a wavefront corrector with an extremely high-spatial resolution. The algorithms use linear approximations to iteratively minimize the aberrations seen by the focal-plane camera. The first algorithm, Fast &
Fast & Furious focal-plane wavefront sensing
Korkiakoski, Visa; Doelman, Niek; Kenworthy, Matthew; Otten, Gilles; Verhaegen, Michel
2014-01-01
We present two complementary algorithms suitable for using focal-plane measurements to control a wavefront corrector with an extremely high spatial resolution. The algorithms use linear approximations to iteratively minimize the aberrations seen by the focal-plane camera. The first algorithm, Fast & Furious (FF), uses a weak-aberration assumption and pupil symmetries to achieve fast wavefront reconstruction. The second algorithm, an extension to FF, can deal with an arbitrary pupil shape; it uses a Gerchberg-Saxton style error reduction to determine the pupil amplitudes. Simulations and experimental results are shown for a spatial light modulator controlling the wavefront with a resolution of 170 x 170 pixels. The algorithms increase the Strehl ratio from ~0.75 to 0.98-0.99, and the intensity of the scattered light is reduced throughout the whole recorded image of 320 x 320 pixels. The remaining wavefront rms error is estimated to be ~0.15 rad with FF and ~0.10 rad with FF-GS.
Comparative study of infrared wavefront sensing solutions for adaptive optics
Plantet, C.; Fusco, T.; Guerineau, N.; Derelle, S.; Robert, C.
2016-07-01
The development of new low-noise infrared detectors, such as RAPID (CEA LETI/Sofradir) or SAPHIRA (Selex), has given the possibility to consider infrared wavefront sensing at low ux. We propose here a comparative study of near infrared (J and H bands) wavefront sensing concepts for mid and high orders estimation on a 8m- class telescope, relying on three existing wavefront sensors: the Shack-Hartmann sensor, the pyramid sensor and the quadri-wave lateral shearing interferometer. We consider several conceptual designs using the RAPID camera, making a trade-off between background flux, optical thickness and compatibility with a compact cryostat integration. We then study their sensitivity to noise in order to compare them in different practical scenarios. The pyramid provides the best performance, with a gain up to 0.5 magnitude, and has an advantageous setup.
UA wavefront control lab: design overview and implementation of new wavefront sensing techniques
Miller, Kelsey; Guyon, Olivier; Codona, Johanan; Knight, Justin; Rodack, Alexander
2015-09-01
We present an overview of the design of a new testbed for studying coronagraphic imaging and wavefront control using a variety of pupil and coronagraph architectures. The testbed is designed to explore optimal use of starlight (including starlight rejected by the coronagraph) for wavefront control, system self-calibration, and point spread function (PSF) calibration. It is also compatible with coronagraph designs for centrally obscured and segmented apertures, and includes shaped or apodized pupils, a range of focal plane masks and Lyot stops of multiple sizes, and an optional PIAA apodizing stage. Starlight is reflected and imaged from the focal plane mask and Lyot stop for low-order wavefront sensing. Both a segmented and a continuous sheet MEMS DM are included to simulate segmented telescope pupils, apply known test phase patterns, and implement a controllable phase apodization coronagraph. The testbed is adaptable and is currently being used to investigate three different techniques: (1) the differential optical transfer function (dOTF), (2) low-order wavefront sensing (LOWFS) with a hybrid-Lyot coronagraph, and (3) linear dark field control (LDFC).
Wavefront Sensing for WFIRST with a Linear Optical Model
Jurling, Alden S.; Content, David A.
2012-01-01
In this paper we develop methods to use a linear optical model to capture the field dependence of wavefront aberrations in a nonlinear optimization-based phase retrieval algorithm for image-based wavefront sensing. The linear optical model is generated from a ray trace model of the system and allows the system state to be described in terms of mechanical alignment parameters rather than wavefront coefficients. This approach allows joint optimization over images taken at different field points and does not require separate convergence of phase retrieval at individual field points. Because the algorithm exploits field diversity, multiple defocused images per field point are not required for robustness. Furthermore, because it is possible to simultaneously fit images of many stars over the field, it is not necessary to use a fixed defocus to achieve adequate signal-to-noise ratio despite having images with high dynamic range. This allows high performance wavefront sensing using in-focus science data. We applied this technique in a simulation model based on the Wide Field Infrared Survey Telescope (WFIRST) Intermediate Design Reference Mission (IDRM) imager using a linear optical model with 25 field points. We demonstrate sub-thousandth-wave wavefront sensing accuracy in the presence of noise and moderate undersampling for both monochromatic and polychromatic images using 25 high-SNR target stars. Using these high-quality wavefront sensing results, we are able to generate upsampled point-spread functions (PSFs) and use them to determine PSF ellipticity to high accuracy in order to reduce the systematic impact of aberrations on the accuracy of galactic ellipticity determination for weak-lensing science.
Wavefront sensing for WFIRST with a linear optical model
Jurling, Alden S.; Content, David A.
2012-09-01
In this paper we develop methods to use a linear optical model to capture the field dependence of wavefront aberrations in a nonlinear optimization-based phase retrieval algorithm for image-based wavefront sensing. The linear optical model is generated from a ray trace model of the system and allows the system state to be described in terms of mechanical alignment parameters rather than wavefront coefficients. This approach allows joint optimization over images taken at different field points and does not require separate convergence of phase retrieval at individual field points. Because the algorithm exploits field diversity, multiple defocused images per field point are not required for robustness. Furthermore, because it is possible to simultaneously fit images of many stars over the field, it is not necessary to use a fixed defocus to achieve adequate signal-to-noise ratio despite having images with high dynamic range. This allows high performance wavefront sensing using in-focus science data. We applied this technique in a simulation model based on the Wide Field Infrared Survey Telescope (WFIRST) Intermediate Design Reference Mission (IDRM) imager using a linear optical model with 25 field points. We demonstrate sub-thousandth-wave wavefront sensing accuracy in the presence of noise and moderate undersampling for both monochromatic and polychromatic images using 25 high-SNR target stars. Using these high-quality wavefront sensing results, we are able to generate upsampled point-spread functions (PSFs) and use them to determine PSF ellipticity to high accuracy in order to reduce the systematic impact of aberrations on the accuracy of galactic ellipticity determination for weak-lensing science.
Wavefront sensing and adaptive control in phased array of fiber collimators
Lachinova, Svetlana L.; Vorontsov, Mikhail A.
2011-03-01
A new wavefront control approach for mitigation of atmospheric turbulence-induced wavefront phase aberrations in coherent fiber-array-based laser beam projection systems is introduced and analyzed. This approach is based on integration of wavefront sensing capabilities directly into the fiber-array transmitter aperture. In the coherent fiber array considered, we assume that each fiber collimator (subaperture) of the array is capable of precompensation of local (onsubaperture) wavefront phase tip and tilt aberrations using controllable rapid displacement of the tip of the delivery fiber at the collimating lens focal plane. In the technique proposed, this tip and tilt phase aberration control is based on maximization of the optical power received through the same fiber collimator using the stochastic parallel gradient descent (SPGD) technique. The coordinates of the fiber tip after the local tip and tilt aberrations are mitigated correspond to the coordinates of the focal-spot centroid of the optical wave backscattered off the target. Similar to a conventional Shack-Hartmann wavefront sensor, phase function over the entire fiber-array aperture can then be retrieved using the coordinates obtained. The piston phases that are required for coherent combining (phase locking) of the outgoing beams at the target plane can be further calculated from the reconstructed wavefront phase. Results of analysis and numerical simulations are presented. Performance of adaptive precompensation of phase aberrations in this laser beam projection system type is compared for various system configurations characterized by the number of fiber collimators and atmospheric turbulence conditions. The wavefront control concept presented can be effectively applied for long-range laser beam projection scenarios for which the time delay related with the double-pass laser beam propagation to the target and back is compared or even exceeds the characteristic time of the atmospheric turbulence change
Modeling on Bessel beam guide star beacon for wavefront sensing
Sun, Quan; Luo, Ruiyao; Yang, Yi; Wu, Wuming; Du, Shaojun; Ning, Yu
2017-06-01
Bessel beam has the advantages of reducing scattering artefacts and increasing the quality of the image and penetration. This paper proposed to generate a guide star by Bessel beam with vortex phase, and to use the beacon with special spot structure to measure the atmosphere turbulence aberrations. With the matching algorithm of measured characteristic spot in each subaperture, the detection accuracy of Hartmann wavefront sensor can be improved. Based on wave optics theory, the modeling of Bessel beam guide star and wavefront sensing system was built. The laser guide star beacon generated by Bessel beam with vortex phase and beacon echo wave measured by Hartmann sensor were both simulated. Compared with the results measured by echo wave from Gauss beam generated guide star beacon, this novel method can reduce the error of wavefront detection and increase the detection accuracy of Hartmann sensor.
Non-iterative adaptive optical microscopy using wavefront sensing
Tao, X.; Azucena, O.; Kubby, J.
2016-03-01
This paper will review the development of wide-field and confocal microscopes with wavefront sensing and adaptive optics for correcting refractive aberrations and compensating scattering when imaging through thick tissues (Drosophila embryos and mouse brain tissue). To make wavefront measurements in biological specimens we have modified the laser guide-star techniques used in astronomy for measuring wavefront aberrations that occur as star light passes through Earth's turbulent atmosphere. Here sodium atoms in Earth's mesosphere, at an altitude of 95 km, are excited to fluoresce at resonance by a high-power sodium laser. The fluorescent light creates a guide-star reference beacon at the top of the atmosphere that can be used for measuring wavefront aberrations that occur as the light passes through the atmosphere. We have developed a related approach for making wavefront measurements in biological specimens using cellular structures labeled with fluorescent proteins as laser guide-stars. An example is a fluorescently labeled centrosome in a fruit fly embryo or neurons and dendrites in mouse brains. Using adaptive optical microscopy we show that the Strehl ratio, the ratio of the peak intensity of an aberrated point source relative to the diffraction limited image, can be improved by an order of magnitude when imaging deeply into live dynamic specimens, enabling near diffraction limited deep tissue imaging.
Revisiting static modulation in pyramid wavefront sensing
Marafatto, L.; Ragazzoni, R.; Vassallo, D.; Bergomi, M.; Biondi, F.; Farinato, J.; Greggio, D.; Magrin, D.; Viotto, V.
2016-07-01
The Pyramid Sensor (PS) is based on the Focault knife-edge test, yielding then, in geometrical approximation, only the sign of the wavefront slope. To provide linear measurements of the wavefront slopes the PS relies on a technique known as modulation, which also plays a central role to improve the linear range of the pyramid WFS, very small in the nonmodulated case. In the main PS using modulation so far, this task is achieved by moving optical components in the WFS, increasing the complexity of the system. An attractive idea to simplify the optical and mechanical design of a pyramid WFS is to work without any dynamic modulation. This concept was only merely described and functionally tested in the framework of MAD, and subsequently, with a holographic diffuser. The latter produce a sort of random distribution of the light coming out from the pupil plane, leading to sort of inefficient modulation, as most of the rays are focused in the central region of the light diffused by such device. The bi-dimensional original grating is, in contrast, producing a well defined deterministic distribution of the light onto a specifically shaped pattern. A crude option has been already discussed as a possibility, and it is here generalized to holographic plates leading to various distribution of lights, including a circle whose diameter would match the required modulation pattern, or more cost effective approaches like the one of a square pattern. These holographic diffusers would exhibit also zero-th and high order patterns and the actual size of the equivalent modulation would be linearly wavelength dependent, leading to colour effects that requires a careful handling in order to properly choose the right amount of equivalent modulation.
Broadband Phase Retrieval for Image-Based Wavefront Sensing
Dean, Bruce H.
2007-01-01
A focus-diverse phase-retrieval algorithm has been shown to perform adequately for the purpose of image-based wavefront sensing when (1) broadband light (typically spanning the visible spectrum) is used in forming the images by use of an optical system under test and (2) the assumption of monochromaticity is applied to the broadband image data. Heretofore, it had been assumed that in order to obtain adequate performance, it is necessary to use narrowband or monochromatic light. Some background information, including definitions of terms and a brief description of pertinent aspects of image-based phase retrieval, is prerequisite to a meaningful summary of the present development. Phase retrieval is a general term used in optics to denote estimation of optical imperfections or aberrations of an optical system under test. The term image-based wavefront sensing refers to a general class of algorithms that recover optical phase information, and phase-retrieval algorithms constitute a subset of this class. In phase retrieval, one utilizes the measured response of the optical system under test to produce a phase estimate. The optical response of the system is defined as the image of a point-source object, which could be a star or a laboratory point source. The phase-retrieval problem is characterized as image-based in the sense that a charge-coupled-device camera, preferably of scientific imaging quality, is used to collect image data where the optical system would normally form an image. In a variant of phase retrieval, denoted phase-diverse phase retrieval [which can include focus-diverse phase retrieval (in which various defocus planes are used)], an additional known aberration (or an equivalent diversity function) is superimposed as an aid in estimating unknown aberrations by use of an image-based wavefront-sensing algorithm. Image-based phase-retrieval differs from such other wavefront-sensing methods, such as interferometry, shearing interferometry, curvature
Common-Path Wavefront Sensing for Advanced Coronagraphs
Wallace, J. Kent; Serabyn, Eugene; Mawet, Dimitri
2012-01-01
Imaging of faint companions around nearby stars is not limited by either intrinsic resolution of a coronagraph/telescope system, nor is it strictly photon limited. Typically, it is both the magnitude and temporal variation of small phase and amplitude errors imparted to the electric field by elements in the optical system which will limit ultimate performance. Adaptive optics systems, particularly those with multiple deformable mirrors, can remove these errors, but they need to be sensed in the final image plane. If the sensing system is before the final image plane, which is typical for most systems, then the non-common path optics between the wavefront sensor and science image plane will lead to un-sensed errors. However, a new generation of high-performance coronagraphs naturally lend themselves to wavefront sensing in the final image plane. These coronagraphs and the wavefront sensing will be discussed, as well as plans for demonstrating this with a high-contrast system on the ground. Such a system will be a key system-level proof for a future space-based coronagraph mission, which will also be discussed.
Hybrid architecture active wavefront sensing and control system, and method
Feinberg, Lee D. (Inventor); Dean, Bruce H. (Inventor); Hyde, Tristram T. (Inventor)
2011-01-01
According to various embodiments, provided herein is an optical system and method that can be configured to perform image analysis. The optical system can comprise a telescope assembly and one or more hybrid instruments. The one or more hybrid instruments can be configured to receive image data from the telescope assembly and perform a fine guidance operation and a wavefront sensing operation, simultaneously, on the image data received from the telescope assembly.
Preparing for JWST wavefront sensing and control operations
Perrin, Marshall D.; Acton, D. Scott; Lajoie, Charles-Philippe; Knight, J. Scott; Lallo, Matthew D.; Allen, Marsha; Baggett, Wayne; Barker, Elizabeth; Comeau, Thomas; Coppock, Eric; Dean, Bruce H.; Hartig, George; Hayden, William L.; Jordan, Margaret; Jurling, Alden; Kulp, Trey; Long, Joseph; McElwain, Michael W.; Meza, Luis; Nelan, Edmund P.; Soummer, Remi; Stansberry, John; Stark, Christopher; Telfer, Randal; Welsh, Andria L.; Zielinski, Thomas P.; Zimmerman, Neil T.
2016-07-01
The James Webb Space Telescopes segmented primary and deployable secondary mirrors will be actively con- trolled to achieve optical alignment through a complex series of steps that will extend across several months during the observatory's commissioning. This process will require an intricate interplay between individual wavefront sensing and control tasks, instrument-level checkout and commissioning, and observatory-level calibrations, which involves many subsystems across both the observatory and the ground system. Furthermore, commissioning will often exercise observatory capabilities under atypical circumstances, such as fine guiding with unstacked or defocused images, or planning targeted observations in the presence of substantial time-variable offsets to the telescope line of sight. Coordination for this process across the JWST partnership has been conducted through the Wavefront Sensing and Control Operations Working Group. We describe at a high level the activities of this group and the resulting detailed commissioning operations plans, supporting software tools development, and ongoing preparations activities at the Science and Operations Center. For each major step in JWST's wavefront sensing and control, we also explain the changes and additions that were needed to turn an initial operations concept into a flight-ready plan with proven tools. These efforts are leading to a robust and well-tested process and preparing the team for an efficient and successful commissioning of JWSTs active telescope.
Coronagraph-Integrated Wavefront Sensing with a Sparse Aperture Mask
Subedi, Hari; Kasdin, N Jeremy; Cavanagh, Kathleen; Riggs, A J Eldorado
2015-01-01
Stellar coronagraph performance is highly sensitive to optical aberrations. In order to effectively suppress starlight for exoplanet imaging applications, low-order wavefront aberrations entering a coronagraph such as tip-tilt, defocus and coma must be determined and compensated. Previous authors have established the utility of pupil-plane masks (both non-redundant/sparse-aperture and generally asymmetric aperture masks) for wavefront sensing. Here we show how a sparse aperture mask (SAM) can be integrated with a coronagraph to measure low-order, differential phase aberrations. Starlight rejected by the coronagraph's focal plane stop is collimated to a relay pupil, where the mask forms an interference fringe pattern on a subsequent detector. Our numerical Fourier propagation models show that the information encoded in the fringe intensity distortions is sufficient to accurately discriminate and estimate Zernike phase modes extending from tip-tilt up to radial degree $n=5$, with amplitude up to $\\lambda/20$ RM...
Curvature Wavefront Sensing for the Large Synoptic Survey Telescope
Xin, Bo; Liang, Ming; Chandrasekharan, Srinivasan; Angeli, George; Shipsey, Ian
2015-01-01
The Large Synoptic Survey Telescope (LSST) will use an active optics system (AOS) to maintain alignment and surface figure on its three large mirrors. Corrective actions fed to the LSST AOS are determined from information derived from 4 curvature wavefront sensors located at the corners of the focal plane. Each wavefront sensor is a split detector such that the halves are 1mm on either side of focus. In this paper we describe the extensions to published curvature wavefront sensing algorithms needed to address challenges presented by the LSST, namely the large central obscuration, the fast f/1.23 beam, off-axis pupil distortions, and vignetting at the sensor locations. We also describe corrections needed for the split sensors and the effects from the angular separation of different stars providing the intra- and extra-focal images. Lastly, we present simulations that demonstrate convergence, linearity, and negligible noise when compared to atmospheric effects when the algorithm extensions are applied to the LS...
System and Method for Null-Lens Wavefront Sensing
Hill, Peter C. (Inventor); Thompson, Patrick L. (Inventor); Aronstein, David L. (Inventor); Bolcar, Matthew R. (Inventor); Smith, Jeffrey S. (Inventor)
2015-01-01
A method of measuring aberrations in a null-lens including assembly and alignment aberrations. The null-lens may be used for measuring aberrations in an aspheric optic with the null-lens. Light propagates from the aspheric optic location through the null-lens, while sweeping a detector through the null-lens focal plane. Image data being is collected at locations about said focal plane. Light is simulated propagating to the collection locations for each collected image. Null-lens aberrations may extracted, e.g., applying image-based wavefront-sensing to collected images and simulation results. The null-lens aberrations improve accuracy in measuring aspheric optic aberrations.
Wavefront sensing based on phase contrast theory and coherent optical processing
Lei, Huang; Qi, Bian; Chenlu, Zhou; Tenghao, Li; Mali, Gong
2016-07-01
A novel wavefront sensing method based on phase contrast theory and coherent optical processing is proposed. The wavefront gradient field in the object plane is modulated into intensity distribution in a gang of patterns, making high-density detection available. By applying the method, we have also designed a wavefront sensor. It consists of a classical coherent optical processing system, a CCD detector array, two pieces of orthogonal composite sinusoidal gratings, and a mechanical structure that can perform real-time linear positioning. The simulation results prove and demonstrate the validity of the method and the sensor in high-precision measurement of the wavefront gradient field.
Focal plane wave-front sensing algorithm for high-contrast imaging
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
High-contrast imaging provided by a coronagraph is critical for the direction imaging of the Earth-like planet orbiting its bright parent star.A major limitation for such direct imaging is the speckle noise that is induced from the wave-front error of an optical system.We derive an algorithm for the wave-front measurement directly from 3 focal plane images.The 3 images are achieved through a deformable mirror to provide specific phases for the optics system.We introduce an extra amplitude modulation on one deformable mirror configuration to create an uncorrelated wave-front,which is a critical procedure for wave-front sensing.The simulation shows that the reconstructed wave-front is consistent with the original wave-front theoretically,which indicates that such an algorithm is a promising technique for the wave-front measurement for the high-contrast imaging.
All-digital wavefront sensing for structured light beams.
Dudley, Angela; Milione, Giovanni; Alfano, Robert R; Forbes, Andrew
2014-06-02
We present a new all-digital technique to extract the wavefront of a structured light beam. Our method employs non-homogeneous polarization optics together with dynamic, digital holograms written to a spatial light modulator to measure the phase relationship between orthogonal polarization states in real-time, thereby accessing the wavefront information. Importantly, we show how this can be applied to measuring the wavefront of propagating light fields, over extended distances, without any moving components. We illustrate the versatility of the tool by measuring propagating optical vortices, Bessel, Airy and speckle fields. The comparison of the extracted and programmed wavefronts yields excellent agreement.
Stochastic sensing through covalent interactions
Bayley, Hagan; Shin, Seong-Ho; Luchian, Tudor; Cheley, Stephen
2013-03-26
A system and method for stochastic sensing in which the analyte covalently bonds to the sensor element or an adaptor element. If such bonding is irreversible, the bond may be broken by a chemical reagent. The sensor element may be a protein, such as the engineered P.sub.SH type or .alpha.HL protein pore. The analyte may be any reactive analyte, including chemical weapons, environmental toxins and pharmaceuticals. The analyte covalently bonds to the sensor element to produce a detectable signal. Possible signals include change in electrical current, change in force, and change in fluorescence. Detection of the signal allows identification of the analyte and determination of its concentration in a sample solution. Multiple analytes present in the same solution may be detected.
Pupil phase discontinuity measurement: comparison of different wavefront sensing concepts
El Hadi, K.; Sauvage, J.-F.; Dohlen, K.; Fusco, T.; Neichel, B.; Marchis, F.; N'Diaye, M.
2016-07-01
The Laboratoire d'Astrophysique de Marseille is involved in the preparation of the E-ELT instrumentation framework: In particular, an ESO-EELT M1 mirror segment (1.5 m) has been demonstrated and different wavefront sensing (WFS) concepts among which Pyramid, Zernike phase mask sensor (ZELDA), Phase diversity or still NL Curvature) are also investigated. Segmented mirrors are widely used today in diverse domains: fiber coupling, laser beam shaping, microscopy or retina imaging. If, these mirrors offer a solution to realize important monolithic sizes for giant telescopes in astronomy, they also raise the problem of segments cophasing and measurement of phase discontinuities. In this work, we aim to investigate a suitable WFS approach for pupil phase discontinuity measurement. Coupling a segmented PTT mirror (Iris AO) with four different WFS (Shack-Hartmann, Quadriwave Lateral Shearing Interferometer, Pyramid and Zernike Phase Mask), we study their sensitivity to segmented pupil: in particular, segment phasing, stability, saturation, flat, or still the addressing mode are then performed and compared.
Prototype pipeline for LSST wavefront sensing and reconstruction
Claver, Charles F.; Chandrasekharan, Srinivasan; Liang, Ming; Xin, Bo; Alagoz, Enver; Arndt, Kirk; Shipsey, Ian P.
2012-09-01
The Large Synoptic Survey Telescope (LSST) uses an Active Optics System (AOS) to maintain system alignment and surface figure on its three large mirrors. Corrective actions fed to the LSST AOS are determined from 4 curvature based wavefront sensors located on the corners of the inscribed square within the 3.5 degree field of view. Each wavefront sensor is a split detector such that the halves are 1mm on either side of focus. In this paper we describe the development of the Active Optics Pipeline prototype that simulates processing the raw image data from the wavefront sensors through to wavefront estimation on to the active optics corrective actions. We also describe various wavefront estimation algorithms under development for the LSST active optics system. The algorithms proposed are comprised of the Zernike compensation routine which improve the accuracy of the wavefront estimate. Algorithm development has been aided by a bench top optical simulator which we also describe. The current software prototype combines MATLAB modules for image processing, tomographic reconstruction, atmospheric turbulence and Zemax for optical ray-tracing to simulate the closed loop behavior of the LSST AOS. We describe the overall simulation model and results for image processing using simulated images and initial results of the wavefront estimation algorithms.
Angle-sensitive pixel design for wavefront sensing
Zheng, Guoan
2013-01-01
Conventional image sensors are only responsive to the intensity variation of the incoming light wave. By encoding the wavefront information into the balanced detection scheme, we demonstrate an image sensor pixel design that is capable to detect both the local intensity and wavefront information simultaneously. With the full compatibility to the CMOS fabrication process, the proposed pixel design can benefit a variety of applications, including phase microscopy, lensless imaging and machine vision.
Wavefront sensing in a partially illuminated, rotating pupil
Bertram, Thomas; Kumar Radhakrishnan Santhakumari, Kalyan; Marafatto, Luca; Arcidiacono, Carmelo; Berwein, Jürgen; Ragazzoni, Roberto; Herbst, Thomas M.
2014-08-01
LINC-NIRVANA is the near-infrared interferometric imaging camera for the Large Binocular Telescope. Once operational, it will provide an unprecedented combination of angular resolution, sensitivity, and field of view. Its pyramid-based layer-oriented MCAO systems are conjugated to the ground layer and to an additional layer in the upper atmosphere. The Groundlayer Wavefront Sensor optically coadds the light of up to 12 reference stars in the pupil, the Highlayer Wavefront Sensor optically combines the light of up to 8 reference stars in its metapupil. Each Wavefront Sensor has its own associated field derotator. It introduces a dependency of the sensor-actuator relation on the angle of the field derotator, which requires regular updates of the reconstructor in closed loop. In addition, the Highlayer Wavefront Sensor has to be able to reconstruct the incoming wavefronts by analyzing an only partially illuminated metapupil. The distribution of illuminated subapertures depends on the distribution of reference stars. For each pointing, a specific reconstruction matrix has to be generated, which only considers the illuminated subapertures. In this contribution we will present the concept of LINC-NIRVANA's wavefront reconstruction mechanism and report on laboratory and on-sky tests.
Optical differentiation wavefront sensing with binary pixelated transmission filters.
Qiao, J; Mulhollan, Z; Dorrer, C
2016-05-02
Sensors measuring the spatial phase of optical waves are widely used in optics. The optical differentiation wavefront sensor (ODWS) reconstructs the wavefront of an optical wave from wavefront slope measurements obtained by inducing linear field-transmission gradients in the far-field. Its dynamic range and sensitivity can be adjusted simply by changing the gradient slope. We numerically and experimentally demonstrate the possibility of implementing the spatially varying transmission gradient using distributions of small pixels that are either transparent or opaque. Binary pixelated filters are achromatic and can be fabricated with high accuracy at relatively low cost using commercial lithography techniques. We study the impact of the noise resulting from pixelation and binarization of the far-field filter for various test wavefronts and sensor parameters. The induced wavefront error is approximately inversely proportional to the pixel size. For an ODWS with dynamic range of 100 rad/mm over a 1-cm pupil, the error is smaller than λ/15 for a wide range of test wavefronts when using 2.5-μm pixels. We experimentally demonstrate the accuracy and consistency of a first-generation ODWS based on binary pixelated filters.
Wavefront sensing with all-digital Stokes measurements
CSIR Research Space (South Africa)
Dudley, Angela L
2014-09-25
Full Text Available . INTRODUCTION The quest for efficient and precise measurement techniques of the phase (or wavefront) of an optical field has led to some conventional, state-of-the-art methods, ranging from ray tracing [1], pyramid sensors [2], interferometers [3, 4...] on our SLM, to construct an adjustment-free, computer-controlled measurement scheme. We illustrate the robustness of our technique by measuring the wavefront of a variety of static and propagating optical fields such as vortex, Bessel, Airy and speckle...
All-digital wavefront sensing for structured light beams
CSIR Research Space (South Africa)
Dudley, Angela L
2014-01-01
Full Text Available We present a new all-digital technique to extract the wavefront of a structured light beam. Our method employs non-homogeneous polarization optics together with dynamic, digital holograms written to a spatial light modulator to measure the phase...
Zonal wavefront sensing using a grating array printed on a polyester film
Energy Technology Data Exchange (ETDEWEB)
Pathak, Biswajit; Boruah, Bosanta R., E-mail: brboruah@iitg.ernet.in [Department of Physics, Indian Institute of Technology Guwahati, Guwahati, Assam 781039 (India); Kumar, Suraj [Department of Applied Sciences, Gauhati University, Guwahati, Assam 781014 (India)
2015-12-15
In this paper, we describe the development of a zonal wavefront sensor that comprises an array of binary diffraction gratings realized on a transparent sheet (i.e., polyester film) followed by a focusing lens and a camera. The sensor works in a manner similar to that of a Shack-Hartmann wavefront sensor. The fabrication of the array of gratings is immune to certain issues associated with the fabrication of the lenslet array which is commonly used in zonal wavefront sensing. Besides the sensing method offers several important advantages such as flexible dynamic range, easy configurability, and option to enhance the sensing frame rate. Here, we have demonstrated the working of the proposed sensor using a proof-of-principle experimental arrangement.
Common-Path Interferometric Wavefront Sensing for Space Telescopes
Wallace, James Kent
2011-01-01
This paper presents an optical configuration for a common-path phase-shifting interferometric wavefront sensor.1 2 This sensor has a host of attractive features which make it well suited for space-based adaptive optics. First, it is strictly reflective and therefore operates broadband, second it is common mode and therefore does not suffer from systematic errors (like vibration) that are typical in other interferometers, third it is a phase-shifting interferometer and therefore benefits from both the sensitivity of interferometric sensors as well as the noise rejection afforded by synchronous detection. Unlike the Shack-Hartman wavefront sensor, it has nearly uniform sensitivity to all pupil modes. Optical configuration, theory and simulations for such a system will be discussed along with predicted performance.
FOCAL PLANE WAVEFRONT SENSING USING RESIDUAL ADAPTIVE OPTICS SPECKLES
Energy Technology Data Exchange (ETDEWEB)
Codona, Johanan L.; Kenworthy, Matthew, E-mail: jlcodona@gmail.com [Steward Observatory, University of Arizona, Tucson, AZ 85721 (United States)
2013-04-20
Optical imperfections, misalignments, aberrations, and even dust can significantly limit sensitivity in high-contrast imaging systems such as coronagraphs. An upstream deformable mirror (DM) in the pupil can be used to correct or compensate for these flaws, either to enhance the Strehl ratio or suppress the residual coronagraphic halo. Measurement of the phase and amplitude of the starlight halo at the science camera is essential for determining the DM shape that compensates for any non-common-path (NCP) wavefront errors. Using DM displacement ripples to create a series of probe and anti-halo speckles in the focal plane has been proposed for space-based coronagraphs and successfully demonstrated in the lab. We present the theory and first on-sky demonstration of a technique to measure the complex halo using the rapidly changing residual atmospheric speckles at the 6.5 m MMT telescope using the Clio mid-IR camera. The AO system's wavefront sensor measurements are used to estimate the residual wavefront, allowing us to approximately compute the rapidly evolving phase and amplitude of speckle halo. When combined with relatively short, synchronized science camera images, the complex speckle estimates can be used to interferometrically analyze the images, leading to an estimate of the static diffraction halo with NCP effects included. In an operational system, this information could be collected continuously and used to iteratively correct quasi-static NCP errors or suppress imperfect coronagraphic halos.
Focal Plane Wavefront Sensing using Residual Adaptive Optics Speckles
Codona, Johanan L
2013-01-01
Optical imperfections, misalignments, aberrations, and even dust can significantly limit sensitivity in high-contrast imaging systems such as coronagraphs. An upstream deformable mirror (DM) in the pupil can be used to correct or compensate for these flaws, either to enhance Strehl ratio or suppress residual coronagraphic halo. Measurement of the phase and amplitude of the starlight halo at the science camera is essential for determining the DM shape that compensates for any non-common-path (NCP) wavefront errors. Using DM displacement ripples to create a series of probe and anti-halo speckles in the focal plane has been proposed for space-based coronagraphs and successfully demonstrated in the lab. We present the theory and first on-sky demonstration of a technique to measure the complex halo using the rapidly-changing residual atmospheric speckles at the 6.5m MMT telescope using the Clio mid-IR camera. The AO system's wavefront sensor (WFS) measurements are used to estimate the residual wavefront, allowing ...
3D imaging and wavefront sensing with a plenoptic objective
Rodríguez-Ramos, J. M.; Lüke, J. P.; López, R.; Marichal-Hernández, J. G.; Montilla, I.; Trujillo-Sevilla, J.; Femenía, B.; Puga, M.; López, M.; Fernández-Valdivia, J. J.; Rosa, F.; Dominguez-Conde, C.; Sanluis, J. C.; Rodríguez-Ramos, L. F.
2011-06-01
Plenoptic cameras have been developed over the last years as a passive method for 3d scanning. Several superresolution algorithms have been proposed in order to increase the resolution decrease associated with lightfield acquisition with a microlenses array. A number of multiview stereo algorithms have also been applied in order to extract depth information from plenoptic frames. Real time systems have been implemented using specialized hardware as Graphical Processing Units (GPUs) and Field Programmable Gates Arrays (FPGAs). In this paper, we will present our own implementations related with the aforementioned aspects but also two new developments consisting of a portable plenoptic objective to transform every conventional 2d camera in a 3D CAFADIS plenoptic camera, and the novel use of a plenoptic camera as a wavefront phase sensor for adaptive optics (OA). The terrestrial atmosphere degrades the telescope images due to the diffraction index changes associated with the turbulence. These changes require a high speed processing that justify the use of GPUs and FPGAs. Na artificial Laser Guide Stars (Na-LGS, 90km high) must be used to obtain the reference wavefront phase and the Optical Transfer Function of the system, but they are affected by defocus because of the finite distance to the telescope. Using the telescope as a plenoptic camera allows us to correct the defocus and to recover the wavefront phase tomographically. These advances significantly increase the versatility of the plenoptic camera, and provides a new contribution to relate the wave optics and computer vision fields, as many authors claim.
Optimization of scanning strategy of digital Shack-Hartmann wavefront sensing.
Guo, Wenjiang; Zhao, Liping; Li, Xiang; Chen, I-Ming
2012-01-01
In the traditional Shack-Hartmann wavefront sensing (SHWS) system, a lenslet array with a bigger configuration is desired to achieve a higher lateral resolution. However, practical implementation limits the configuration and this parameter is contradicted with the measurement range. We have proposed a digital scanning technique by making use of the high flexibility of a spatial light modulator to sample the reflected wavefront [X. Li, L. P. Zhao, Z. P. Fang, and C. S. Tan, "Improve lateral resolution in wavefront sensing with digital scanning technique," in Asia-Pacific Conference of Transducers and Micro-Nano Technology (2006)]. The lenslet array pattern is programmed to laterally scan the whole aperture. In this paper, the methodology to optimize the scanning step for the purpose of form measurement is proposed. The correctness and effectiveness are demonstrated in numerical simulation and experimental investigation.
An iterative wavefront sensing algorithm for high-contrast imaging systems *
Institute of Scientific and Technical Information of China (English)
Jiang-Pei Dou; De-Qing Ren; Yong-Tian Zhu
2011-01-01
Wavefront sensing from multiple focal plane images is a promising technique for high-contrast imaging systems. However, the wavefront error of an optics system can be properly reconstructed only when it is very small. This paper presents an iterative optimization algorithm for the direct measurement of large static wavefront errors from only one focal plane image. We first measure the intensity of the pupil image to get the pupil function of the system and acquire the aberrated image on the focal plane with a phase error that will be measured. Then we induce a dynamic phase on the tested pupil function and calculate the associated intensity of the reconstructed image on the focal plane. The algorithm will then try to minimize the intensity difference between the reconstructed image and the aberrated test image in the focal plane, where the induced phase is a variable of the optimization algorithm.The simulation shows that the wavefront of an optical system can theoretically be reconstructed with high precision, which indicates that such an iterative algorithm may be an effective way to perform wavefront sensing for high-contrast imaging systems.
Snapshot coherence-gated direct wavefront sensing for multi-photon microscopy
Van Werkhoven, T.I.M.; Antonello, J.; Truong, H.H.; Verhaegen, M.; Gerritsen, H.C.; Keller, C.U.
2014-01-01
Deep imaging in turbid media such as biological tissue is challenging due to scattering and optical aberrations. Adaptive optics has the potential to compensate the tissue aberrations. We present a wavefront sensing scheme for multi-photon scanning microscopes using the pulsed, near-infrared light r
Optically sensitive Medipix2 detector for adaptive optics wavefront sensing
Vallerga, John; Tremsina, Anton; Siegmund, Oswald; Mikulec, Bettina; Clark, Allan G; CERN. Geneva
2005-01-01
A new hybrid optical detector is described that has many of the attributes desired for the next generation adaptive optics (AO) wavefront sensors. The detector consists of a proximity focused microchannel plate (MCP) read out by multi-pixel application specific integrated circuit (ASIC) chips developed at CERN ("Medipix2") with individual pixels that amplify, discriminate and count input events. The detector has 256 x 256 pixels, zero readout noise (photon counting), can be read out at 1 kHz frame rates and is abutable on 3 sides. The Medipix2 readout chips can be electronically shuttered down to a temporal window of a few microseconds with an accuracy of 10 ns. When used in a Shack-Hartmann style wavefront sensor, a detector with 4 Medipix chips should be able to centroid approximately 5000 spots using 7 x 7 pixel sub-apertures resulting in very linear, off-null error correction terms. The quantum efficiency depends on the optical photocathode chosen for the bandpass of interest.
Gousset, Silvère; Petit, Cyril; Michau, Vincent; Fusco, Thierry; Robert, Clelia
2015-12-01
Near-infrared wavefront sensing allows for the enhancement of sky coverage with adaptive optics. The recently developed HgCdTe avalanche photodiode arrays are promising due to their very low detector noise, but still present an imperfect cosmetic that may directly impact real-time wavefront measurements for adaptive optics and thus degrade performance in astronomical applications. We propose here a model of a Shack-Hartmann wavefront measurement in the presence of residual fixed pattern noise and defective pixels. To adjust our models, a fine characterization of such an HgCdTe array, the RAPID sensor, is proposed. The impact of the cosmetic defects on the Shack-Hartmann measurement is assessed through numerical simulations. This study provides both a new insight on the applicability of cadmium mercury telluride (CMT) avalanche photodiodes detectors for astronomical applications and criteria to specify the cosmetic qualities of future arrays.
Wavefront sensing with the differential optical transfer function
Hart, Michael; Codona, Johanan L.
2012-10-01
Recently a new technique for estimating the complex field in the pupil of a telescope from image-plane intensity measurements has been introduced by Codona.1, 2 The simplest form of the method uses two images of a point source, one with a small modification introduced in the pupil. The algorithm to recover the pupil field uses a functional derivative of the optical transfer function (OTF), and is simple and non-iterative. The derivative is approximated empirically by the difference between the Fourier transforms of the two PSFs: the differential OTF or dOTF. In keeping with the Hermitian symmetry of the OTF, the dOTF includes two conjugate copies of the pupil field overlapping at the point of modification. By placing the modification near the edge of the pupil, the overlap region can be kept small. It can be eliminated altogether by using a second modification and a third image. The technique can be used in broadband light, at the cost of blurring in the recovered phase that is proportional to the fractional bandwidth. Although the dOTF is unlikely to find application in high frame rate astronomical adaptive optics, it has many potential uses such as optical shop testing, non-common-path wavefront error estimation, segmented telescope phasing and general imaging system diagnostics. In this paper, we review the dOTF concept, theory, and initial experiments to demonstrate the technique.
Testbed Demonstration of Low Order Wavefront Sensing and Control Technology for WFIRST Coronagraph
Shi, Fang; Balasubramanian, K.; Cady, E.; Kern, B.; Lam, R.; Mandic, M.; Patterson, K.; Poberezhskiy, I.; Shields, J.; Seo, J.; Tang, H.; Truong, T.; Wilson, D.
2017-01-01
NASA’s WFIRST-AFTA Coronagraph will be capable of directly imaging and spectrally characterizing giant exoplanets similar to Neptune and Jupiter, and possibly even super-Earths, around nearby stars. To maintain the required coronagraph performance in a realistic space environment, a Low Order Wavefront Sensing and Control (LOWFS/C) subsystem is necessary. The LOWFS/C will use the rejected stellar light to sense and suppress the telescope pointing drift and jitter as well as low order wavefront errors due to the changes in thermal loading of the telescope and the rest of the observatory. The LOWFS/C uses a Zernike phase contrast wavefront sensor with the phase shifting disk combined with the stellar light rejecting occulting mask, a key concept to minimize the non-common path error. Developed as a part of the Dynamic High Contrast Imaging Testbed (DHCIT), the LOWFS/C subsystem also consists of an Optical Telescope Assembly Simulator (OTA-S) to generate the realistic line-of-sight (LoS) drift and jitter as well as low order wavefront error from WFIRST-AFTA telescope’s vibration and thermal drift. The entire LOWFS/C subsystem have been integrated, calibrated, and tested in the Dynamic High Contrast Imaging Testbed. In this presentation we will show the results of LOWFS/C performance during the dynamic coronagraph tests in which we have demonstrated that LOWFS/C is able to maintain the coronagraph contrast with the presence of WFIRST like line-of-sight drift and jitter as well as low order wavefront drifts.
Wavefront Sensing in Space from the PICTURE-B Sounding Rocket
Douglas, Ewan S; Cook, Timothy A; Chakrabarti, Supriya
2016-01-01
A NASA sounding rocket for high contrast imaging with a visible nulling coronagraph, the Planet Imaging Coronagraphic Technology Using a Reconfigurable Experimental Base (PICTURE-B) payload has made two suborbital attempts to observe the warm dust disk inferred around Epsilon Eridani. We present results from the November 2015 launch demonstrating active wavefront sensing in space with a piezoelectric mirror stage and a micromachine deformable mirror along with precision pointing and lightweight optics in space.
Wavefront sensing in space from the PICTURE-B sounding rocket
Douglas, Ewan S.; Mendillo, Christopher B.; Cook, Timothy A.; Chakrabarti, Supriya
2016-07-01
A NASA sounding rocket for high contrast imaging with a visible nulling coronagraph, the Planet Imaging Coronagraphic Technology Using a Reconfigurable Experimental Base (PICTURE-B) payload has made two suborbital attempts to observe the warm dust disk inferred around Epsilon Eridani. We present results from the November 2015 launch demonstrating active wavefront sensing in space with a piezoelectric mirror stage and a micromachine deformable mirror along with precision pointing and lightweight optics in space.
Digital holography and wavefront sensing principles, techniques and applications
Schnars, Ulf; Watson, John; Jüptner, Werner
2015-01-01
This book presents a self-contained treatment of the principles and major applications of digital hologram recording and numerical reconstruction (Digital Holography). This second edition has been significantly revised and enlarged. The authors have extended the chapter on Digital Holographic Microscopy to incorporate new sections on particle sizing, particle image velocimetry and underwater holography. A new chapter now deals comprehensively and extensively with computational wave field sensing. These techniques represent a fascinating alternative to standard interferometry and Digital Holography. They enable wave field sensing without the requirement of a particular reference wave, thus allowing the use of low brilliance light sources and even liquid-crystal displays (LCD) for interferometric applications.
Polarization dOTF: on-sky focal plane wavefront sensing
Brooks, Keira J; Kenworthy, Matthew A; Crawford, Steven M; Codona, Johanan L
2016-01-01
The differential Optical Transfer Function (dOTF) is a focal plane wavefront sensing method that uses a diversity in the pupil plane to generate two different focal plane images. The difference of their Fourier transforms recovers the complex amplitude of the pupil down to the spatial scale of the diversity. We produce two simultaneous PSF images with diversity using a polarizing filter at the edge of the telescope pupil, and a polarization camera to simultaneously record the two images. Here we present the first on-sky demonstration of polarization dOTF at the 1.0m South African Astronomical Observatory telescope in Sutherland, and our attempt to validate it with simultaneous Shack-Hartmann wavefront sensor images.
Visible and Infrared Wavefront Sensing detectors review in Europe - part I
Feautrier, Philippe; Gach, Jean-luc
2013-12-01
The purpose of this review is to give an overview of the state of the art wavefront sensor detectors developments held in Europe for the last decade. A major breakthrough has been achieved with the development by e2v technologies of the CCD220 between 2004 and 2012. Another major breakthrough is currently achieved with the very successful development of fast low noise infrared arrays called RAPID. The astonishing results of this device will be showed for the first time in an international conference at AO4ELT3.The CCD220, a 240x240 pixels 8 outputs EMCCD (CCD with internal multiplication), offers less than 0.2 e readout noise at a frame rate of 1500 Hz with negligible dark current. The OCAM2 camera is the commercial product that drives this advanced device. This system, commercialized by First Light Imaging, is quickly described in this paper. An upgrade of OCAM2 is currently developed to boost its frame rate to 2 kHz, opening the window of XAO wavefront sensing for the ELT using 4 synchronized cameras and pyramid wavefront sensing. This upgrade and the results obtained are described extensively elsewhere in this conference (Gach et al).Since this major success, new detector developments started in Europe. The NGSD CMOS device is fully dedicated to Natural and Laser Guide Star AO for the E-ELT with ESO involvement. The spot elongation from a LGS Shack Hartman wavefront sensor necessitates an increase of the pixel format. The NGSD will be a 880x840 pixels CMOS detector with a readout noise of 3 e (goal 1e) at 700 Hz frame rate. New technologies will be developed for that purpose: advanced CMOS pixel architecture, CMOS back thinned and back illuminated device for very high QE, full digital outputs with signal digital conversion on chip. This innovative device will be used on the European ELT but also interests potentially all giant telescopes.Additional developments also started in 2009 for wavefront sensing in the infrared based on a new technological breakthrough
C-RED one: ultra-high speed wavefront sensing in the infrared made possible
Gach, J.-L.; Feautrier, Philippe; Stadler, Eric; Greffe, Timothee; Clop, Fabien; Lemarchand, Stéphane; Carmignani, Thomas; Boutolleau, David; Baker, Ian
2016-07-01
First Light Imaging's CRED-ONE infrared camera is capable of capturing up to 3500 full frames per second with a subelectron readout noise. This breakthrough has been made possible thanks to the use of an e-APD infrared focal plane array which is a real disruptive technology in imagery. We will show the performances of the camera, its main features and compare them to other high performance wavefront sensing cameras like OCAM2 in the visible and in the infrared. The project leading to this application has received funding from the European Union's Horizon 2020 research and innovation program under grant agreement N° 673944.
Wang, Jinyu; Léger, Jean-François; Binding, Jonas; Boccara, A Claude; Gigan, Sylvain; Bourdieu, Laurent
2012-10-01
Aberrations limit the resolution, signal intensity and achievable imaging depth in microscopy. Coherence-gated wavefront sensing (CGWS) allows the fast measurement of aberrations in scattering samples and therefore the implementation of adaptive corrections. However, CGWS has been demonstrated so far only in weakly scattering samples. We designed a new CGWS scheme based on a Linnik interferometer and a SLED light source, which is able to compensate dispersion automatically and can be implemented on any microscope. In the highly scattering rat brain tissue, where multiply scattered photons falling within the temporal gate of the CGWS can no longer be neglected, we have measured known defocus and spherical aberrations up to a depth of 400 µm.
Banet, Matthias T.; Spencer, Mark F.; Raynor, Robert A.; Marker, Dan K.
2016-09-01
Digital holography in the pupil-plane recording geometry shows promise as a wavefront sensor for use in adaptive-optics systems. Because current wavefront sensors suffer from decreased performance in the presence of turbulence and thermal blooming, there is a need for a more robust wavefront sensor in such distributed-volume atmospheric conditions. Digital holography fulfills this roll by accurately estimating the wrapped phase of the complex optical field after propagation through the atmosphere to the pupil plane of an optical system. This paper examines wave-optics simulations of spherical-wave propagation through both turbulence and thermal blooming; it also quantifies the performance of digital holography as a wavefront sensor by generating field-estimated Strehl ratios as a function of the number of pixels in the detector array, the Rytov number, and the Fried coherence diameter. Altogether the results indicate that digital holography wavefront sensing in the pupil-plane recording geometry is a valid and accurate method for estimating the wrapped phase of the complex optical field in the presence of distributed-volume atmospheric aberrations.
Spencer, Mark F.; Raynor, Robert A.; Banet, Matthias T.; Marker, Dan K.
2017-03-01
This paper develops wave-optics simulations which explore the estimation accuracy of digital-holographic detection for wavefront sensing in the presence of distributed-volume or "deep" turbulence and detection noise. Specifically, the analysis models spherical-wave propagation through varying deep-turbulence conditions along a horizontal propagation path and formulates the field-estimated Strehl ratio as a function of the diffraction-limited sampling quotient and signal-to-noise ratio. Such results will allow the reader to assess the number of pixels, pixel field of view, pixel-well depth, and read-noise standard deviation needed from a focal-plane array when using digital-holographic detection in the off-axis image plane recording geometry for deep-turbulence wavefront sensing.
A Demonstration of Wavefront Sensing and Mirror Phasing from the Image Domain
Pope, Benjamin; Cheetham, Anthony; Martinache, Frantz; Norris, Barnaby; Tuthill, Peter
2014-01-01
In astronomy and microscopy, distortions in the wavefront affect the dynamic range of a high contrast imaging system. These aberrations are either imposed by a turbulent medium such as the atmosphere, by static or thermal aberrations in the optical path, or by imperfectly phased subapertures in a segmented mirror. Active and adaptive optics (AO), consisting of a wavefront sensor and a deformable mirror, are employed to address this problem. Nevertheless, the non-common-path between the wavefront sensor and the science camera leads to persistent quasi-static speckles that are difficult to calibrate and which impose a floor on the image contrast. In this paper we present the first experimental demonstration of a novel wavefront sensor requiring only a minor asymmetric obscuration of the pupil, using the science camera itself to detect high order wavefront errors from the speckle pattern produced. We apply this to correct errors imposed on a deformable microelectromechanical (MEMS) segmented mirror in a closed l...
Finding the Dark Hole with the Lights On: A New Approach to Focal Plane Wavefront Sensing
Frazin, Richard A
2016-01-01
In direct imaging of exoplanets from space, achieving the required dynamic range (i.e., planet-to-star contrast in brightness) currently relies on coronagraphic technology combined with active control of one or more deformable mirrors (DMs) to create a dark region in the image plane, sometimes called a "dark hole." While many algorithms have been proposed for this purpose, all of them employ focal plane wavefront sensing (FPWS) in order to calculate the optimal DM configuration to create the desired dark hole. All current algorithms are limited by their own success in that, as the dark hole is achieved, the FPWS procedure becomes shot-noise limited due to he low intensity in the dark hole. This article proposes a FPWS procedure that allows determination of the optimal DM configuration without relying on information obtained when the DM is near the optimal configuration. This article gives regression procedures for FPWS that do not assume the DM step size is small, which should allow two important improvements...
Distributed Computing Architecture for Image-Based Wavefront Sensing and 2 D FFTs
Smith, Jeffrey S.; Dean, Bruce H.; Haghani, Shadan
2006-01-01
Image-based wavefront sensing (WFS) provides significant advantages over interferometric-based wavefi-ont sensors such as optical design simplicity and stability. However, the image-based approach is computational intensive, and therefore, specialized high-performance computing architectures are required in applications utilizing the image-based approach. The development and testing of these high-performance computing architectures are essential to such missions as James Webb Space Telescope (JWST), Terrestial Planet Finder-Coronagraph (TPF-C and CorSpec), and Spherical Primary Optical Telescope (SPOT). The development of these specialized computing architectures require numerous two-dimensional Fourier Transforms, which necessitate an all-to-all communication when applied on a distributed computational architecture. Several solutions for distributed computing are presented with an emphasis on a 64 Node cluster of DSPs, multiple DSP FPGAs, and an application of low-diameter graph theory. Timing results and performance analysis will be presented. The solutions offered could be applied to other all-to-all communication and scientifically computationally complex problems.
Optical solutions for accommodating ELT LGS wave-front sensing to small format detectors
Gendron, E.
2016-07-01
Sodium laser guide stars (LGS) will be used on extremely large telescopes (ELT) for increasing the sky coverage of adaptive optics systems. The thickness of the sodium layer combined with a perspective effect makes the laser beacon to appear as an elongated plume when observed from a pupil location distant from the laser launch telescope. The wave-front sensing with a Shack-Hartmann on such a peculiar object requires a large number of pixels per sub-aperture in order to cope with the required field of view. As a large number of sub-apertures is required on an ELT, this leads to detector formats exceeding 1500 × 1500 pixels. It is worth noticing however that most of these numerous pixels are useless, as many of them won't receive any light due to the arrangement of the pattern of spots. We present in this article some potential optical solutions for relaxing the requirements of the detector format by a significant amount. This is obtained by re-arranging the pattern of the elongated spots in order to avoid any loss of space between them. Depending on the geometry of the system, a factor of ≍2 on the pixel count can be gained along both directions.
Performance of a Novel PMMA Polymer Imaging Bundle for Field Acquisition and Wavefront Sensing
Richards, S. N.; Leon-Saval, S.; Goodwin, M.; Zheng, J.; Lawrence, J. S.; Bryant, J. J.; Bland-Hawthorn, J.; Norris, B.; Cvetojevic, N.; Argyros, A.
2017-01-01
Imaging bundles provide a convenient way to translate a spatially coherent image, yet conventional imaging bundles made from silica fibre optics typically remain expensive with large losses due to poor filling factors ( 40%). We present the characterisation of a novel polymer imaging bundle made from poly(methyl methacrylate) (PMMA) that is considerably cheaper and a better alternative to silica imaging bundles over short distances ( 1 m; from the middle to the edge of a telescope's focal plane). The large increase in filling factor (92% for the polymer imaging bundle) outweighs the large increase in optical attenuation from using PMMA (1 dB/m) instead of silica (10-3 dB/m). We present and discuss current and possible future multi-object applications of the polymer imaging bundle in the context of astronomical instrumentation including: field acquisition, guiding, wavefront sensing, narrow-band imaging, aperture masking, and speckle imaging. The use of PMMA limits its use in low-light applications (e.g., imaging of galaxies); however, it is possible to fabricate polymer imaging bundles from a range of polymers that are better suited to the desired science.
High-speed imaging and wavefront sensing with an infrared avalanche photodiode array
Baranec, Christoph; Riddle, Reed; Hall, Donald; Jacobson, Shane; Law, Nicholas M; Chun, Mark
2015-01-01
Infrared avalanche photodiode arrays represent a panacea for many branches of astronomy by enabling extremely low-noise, high-speed and even photon-counting measurements at near-infrared wavelengths. We recently demonstrated the use of an early engineering-grade infrared avalanche photodiode array that achieves a correlated double sampling read noise of 0.73 e- in the lab, and a total noise of 2.52 e- on sky, and supports simultaneous high-speed imaging and tip-tilt wavefront sensing with the Robo-AO visible-light laser adaptive optics system at the Palomar Observatory 1.5-m telescope. We report here on the improved image quality achieved simultaneously at visible and infrared wavelengths by using the array as part of an image stabilization control-loop with adaptive-optics sharpened guide stars. We also discuss a newly enabled survey of nearby late M-dwarf multiplicity as well as future uses of this technology in other adaptive optics and high-contrast imaging applications.
Pyramid wavefront sensing with a laser guide star for an ELT
Le Roux, Brice
2010-07-01
The wavefront sensor [WFS] is a key element of an Adaptive Optics [AO] system. It gives access to a direct measurement of the turbulent phase, its curvature or its slope, from which the mirror voltages are computed. The ability of the system to correct efficiently the atmospheric turbulence is strongly dependent on the performance of the WFS in estimating the turbulent phase. The Shack-Hartmann [SH] WFS has been for a long time the standard used in AO systems. In 1996, it has been proposed1 a new generation WFS, the pyramid WFS. It is a focal plane WFS, based on the principle of a Foucault knife-edge. It has been demonstrated that it provides a consistent gain with respect to the Shack-Hartmann.2,5-7 More recently, improvements were proposed to increase the pyramid performance.3, 4 On the framework of the developpement of extremely large telescopes, the interest of a pyramid wave front sensor appears clearly. But its behaviour with laser guide stars [LGS], most probably necessary in any Extremely Large Telescope [ELT], is still relatively unknown. Some WFS dedicated to LGS wave front sensing has already been proposed8,9 but a full study of the pyramid WFS behaviour is still necessary. This work's aim is to bring answers to this topic.
Wavefront sensing for deformable space-based optics exploiting natural and synthetic guide stars
McComas, Brian K.; Friedman, Edward J.
2002-08-01
Natural and synthetic guide stars can serve as beacons for Shack-Hartmann wavefront sensors in space-based applications. In this paper, the authors determine the key equations that govern the optimization of the wavefront sensor employed on a space- based imaging system. There are two major products of this analysis. First, the number of subapertures can be optimized. Second, the number of modes used in the wavefront recovery can be optimized. Finally, the process for optimizing these values is explained. For the examples shown, the optimal number of retrieved modes and the optimal number of subapertures are determined.
Single-Grating Talbot Imaging for Wavefront Sensing and X-Ray Metrology
Energy Technology Data Exchange (ETDEWEB)
Grizolli, Walan; Shi, Xianbo; Kolodziej, Tomasz; Shvyd' ko, Yuri; Assoufid, Lahsen
2017-01-01
Single-grating Talbot imaging relies on high-spatial-resolution detectors to perform accurate measurements of X-ray beam wavefronts. The wavefront can be retrieved with a single image, and a typical measurement and data analysis can be performed in few seconds. These qualities make it an ideal tool for synchrotron beamline diagnostics and in-situ metrology. The wavefront measurement can be used both to obtain a phase contrast image of an object and to characterize an X-ray beam. In this work, we explore the concept in two cases: at-wavelength metrology of 2D parabolic beryllium lenses and a wavefront sensor using a diamond crystal beam splitter.
A demonstration of wavefront sensing and mirror phasing from the image domain
Pope, Benjamin; Cvetojevic, Nick; Cheetham, Anthony; Martinache, Frantz; Norris, Barnaby; Tuthill, Peter
2014-05-01
In astronomy and microscopy, distortions in the wavefront affect the dynamic range of a high-contrast imaging system. These aberrations are either imposed by a turbulent medium such as the atmosphere, by static or thermal aberrations in the optical path, or by imperfectly phased subapertures in a segmented mirror. Active and adaptive optics (AO), consisting of a wavefront sensor and a deformable mirror, are employed to address this problem. Nevertheless, the non-common-path between the wavefront sensor and the science camera leads to persistent quasi-static speckles that are difficult to calibrate and which impose a floor on the image contrast. In this paper, we present the first experimental demonstration of a novel wavefront sensor requiring only a minor asymmetric obscuration of the pupil, using the science camera itself to detect high-order wavefront errors from the speckle pattern produced. We apply this to correct errors imposed on a deformable microelectromechanical segmented mirror in a closed loop, restoring a high-quality point spread function and residual wavefront errors of the order of ˜10 nm using 1600 nm light, from a starting point of ˜300 nm in piston and ˜0.3 mrad in tip-tilt. We recommend this as a method for measuring the non-common-path error in AO-equipped ground based telescopes, as well as an approach to phasing difficult segmented mirrors such as on the James Webb Space Telescope primary and as a future direction for extreme AO.
First tests of wavefront sensing with a constellation of laser guide beacons
Lloyd-Hart, M; Milton, N M; Stalcup, T; Snyder, M; Putnam, N; Angel, J R P
2005-01-01
Adaptive optics to correct current telescopes over wide fields, or future very large telescopes over even narrow fields, will require real-time wavefront measurements made with a constellation of laser beacons. Here we report the first such measurements, made at the 6.5 m MMT with five Rayleigh beacons in a 2 arcmin pentagon. Each beacon is made with a pulsed beam at 532 nm, of 4 W at the exit pupil of the projector. The return is range-gated from 20-29 km and recorded at 53 Hz by a 36-element Shack-Hartmann sensor. Wavefronts derived from the beacons are compared with simultaneous wavefronts obtained for individual natural stars within or near the constellation. Observations were made in seeing averaging 1.0 arcsec with 2/3 of the aberration measured to be from a ground layer of mean height 380 m. Under these conditions, subtraction of the simple instantaneous average of the five beacon wavefronts from the stellar wavefronts yielded a 40% rms reduction in the measured modes of the distortion over a 2 arcmin ...
Experimental Verification of Sparse Aperture Mask for Low Order Wavefront Sensing
Subedi, Hari; Kasdin, N. Jeremy
2017-01-01
To directly image exoplanets, future space-based missions are equipped with coronagraphs which manipulate the diffraction of starlight and create regions of high contrast called dark holes. Theoretically, coronagraphs can be designed to achieve the high level of contrast required to image exoplanets, which are billions of times dimmer than their host stars, however the aberrations caused by optical imperfections and thermal fluctuations cause the degradation of contrast in the dark holes. Focal plane wavefront control (FPWC) algorithms using deformable mirrors (DMs) are used to mitigate the quasi-static aberrations caused by optical imperfections. Although the FPWC methods correct the quasi-static aberrations, they are blind to dynamic errors caused by telescope jitter and thermal fluctuations. At Princeton's High Contrast Imaging Lab we have developed a new technique that integrates a sparse aperture mask with the coronagraph to estimate these low-order dynamic wavefront errors. This poster shows the effectiveness of a SAM Low-Order Wavefront Sensor in estimating and correcting these errors via simulation and experiment and compares the results to other methods, such as the Zernike Wavefront Sensor planned for WFIRST.
Gao, Weihua
orientation of the photoreceptor and ganglion axons that compose the layers, respectively. The reflectance of HFL and RNFL were consistent with scattering from cylindrical structures. Apparent thickness and brightness of HFL varied significantly with pupil entry position. Brightness of RNFL also varied significantly with entry position, but its apparent thickness did not. The overall retinal directionality was found consistent with the optical SCE reported in the literature. The third objective evaluated a second optical method, based on Shack-Hartman wavefront sensing (SHWS), for measuring the optical SCE. Using a modified research-grade SHWS with custom algorithm, I demonstrated that the retinal reflectance can be readily extracted from the SHWS measurement and the spatial distribution of which is consistent with the optical SCE. This new method represents an attractive alternative to the conventional, highly customized instruments traditionally used for measuring the optical SCE and provides a more complete description of the eye's optical performance than currently implemented with SHWS technology.
Singh, Garima; Guyon, Olivier; Baudoz, Pierre; Jovanovic, Nemanja; Martinache, Frantz; Kudo, Tomoyuki; Serabyn, Eugene; Kuhn, Jonas
2015-01-01
The ability to characterize exoplanets by spectroscopy of their atmospheres requires direct imaging techniques to isolate planet signal from the bright stellar glare. One of the limitations with the direct detection of exoplanets, either with ground- or space-based coronagraphs, is pointing errors and other low-order wavefront aberrations. The coronagraphic detection sensitivity at the diffraction limit therefore depends on how well low-order aberrations upstream of the focal plane mask are corrected. To prevent starlight leakage at the inner working angle of a phase mask coronagraph, we have introduced a Lyot-based low-order wavefront sensor (LLOWFS), which senses aberrations using the rejected starlight diffracted at the Lyot plane. In this paper, we present the implementation, testing and results of LLOWFS on the Subaru Coronagraphic Extreme Adaptive Optics system (SCExAO) at the Subaru Telescope. We have controlled thirty-five Zernike modes of a H-band vector vortex coronagraph in the laboratory and ten Z...
Light-efficient, quantum-limited interferometric wavefront estimation by virtual mode sensing.
Lauterbach, Marcel A; Ruckel, Markus; Denk, Winfried
2006-05-01
We describe and analyze an interferometer-based virtual modal wavefront sensor (VMWS) that can be configured to measure, for example, Zernike coefficients directly. This sensor is particularly light efficient because the determination of each modal coefficient benefits from all the available photons. Numerical simulations show that the VMWS outperforms state-of-the-art phase unwrapping at low light levels. Including up to Zernike mode 21, aberrations can be determined with a precision of about 0.17 rad (lambda/37) using low resolution (65 x 65 pixels) images and only about 400 photons total.
Institute of Scientific and Technical Information of China (English)
Heng Mao; Xiao Wang; Dazun Zhao
2007-01-01
@@ Baseline algorithm, as a tool in wavefront sensing (WFS), incorporates the phase-diverse phase retrieval (PDPR) method with hybrid-unwrapping approach to ensure a unique pupil phase estimate with high WFS accuracy even in the case of high dynamic range aberration, as long as the pupil shape is of a convex set.However, for a complicated pupil, such as that in obstructed pupil optics, the said unwrapping approach would fail owing to the fake values at points located in obstructed areas of the pupil. Thus a modified unwrapping approach that can minimize the negative effects of the obstructed areas is proposed. Simulations have shown the validity of this unwrapping approach when it is embedded in Baseline algorithm.
Holzlöhner, R.; Taubenberger, S.; Rakich, A. P.; Noethe, L.; Schipani, P.; Kuijken, K.
2016-08-01
We study a novel focal plane wavefront sensing and active optics control scheme at the VST on Cerro Paranal, an f/5.5 survey telescope with a 1x1 degree field of view and a 2.6m primary mirror. This scheme analyzes the elongation pattern of stellar PSFs across the full science image (256 Mpixels) and compares their second moments with an analytical model based on 5th-order geometrical optics. We consider 11 scalar degrees of freedom in mirror misalignments and deformations (M2 piston, tip/tilt and lateral displacement, detector tip/tilt, plus M1 figure astigmatism and trefoil). Using a numerical optimization method, we extract up to 4000 stars and complete the fitting process in under one minute. We demonstrate successful closed-loop active optics control based on maximum likelihood filtering.
First Experimental Results Using Sparse Aperture Mask for Low Order Wavefront Sensing
Subedi, Hari; Zimmerman, Neil T.; Kasdin, N. Jeremy; Eldorado Riggs, A. J.
2016-01-01
We can determine the existence of life outside of earth by analyzing the spectra of exoplanets. Such direct imaging will provide the capability to thoroughly characterize an exoplanet's atmosphere. Direct imaging of exoplanets, however, has many technical challenges and difficulties: scattering and diffraction of light and the large difference in contrast, which is the ratio of brightness between the bright star and the dimmer planet. A coronagraph is an optical device that manipulates the diffraction of starlight and creates a region of high contrast (dark hole) where the dimmer planets can be seen. While in principle the level of contrast required for direct imaging of exoplanets can be achieved by stellar coronagraphic imaging, the resulting dark hole is highly sensitive to phase aberrations. In order to effectively suppress starlight for exoplanet imaging applications, low-order wavefront aberrations entering a coronagraph such as tip-tilt, defocus and coma must be determined and compensated for. A sparse-aperture mask (SAM) can be integrated in the telescopic imaging system to make precise estimate of low-order wavefront aberrations. In this technique, the starlight rejected by the coronagraph's focal plane stop is collimated to a relay pupil, where the mask forms an interference fringe pattern on a detector and the phase aberrations are inferred from this fringe pattern. At Princeton's High Contrast Imaging Lab (HCIL), we have numerically proved this concept and we are currently working on verifying it experimentally.
In-focus wavefront sensing using non-redundant mask-induced pupil diversity
Greenbaum, Alexandra
2016-01-01
Wavefront estimation using in-focus image data is critical to many applications. This data is invariant to a sign flip with complex conjugation of the complex amplitude in the pupil, making for a non-unique solution. Information from an in-focus image taken through a non-redundant pupil mask (NRM) can break this ambiguity, enabling the true aberration to be determined. We demonstrate this by priming a full pupil Gerchberg-Saxton phase retrieval with NRM fringe phase information. We apply our method to measure simulated aberrations on the segmented James Webb Space Telescope (JWST) mirror using full pupil and NRM data from its Near Infrared Imager and Slitless Spectrograph (NIRISS).
A stochastic atmospheric model for remote sensing applications
Turner, R. E.
1983-01-01
There are many factors which reduce the accuracy of classification of objects in the satellite remote sensing of Earth's surface. One important factor is the variability in the scattering and absorptive properties of the atmospheric components such as particulates and the variable gases. For multispectral remote sensing of the Earth's surface in the visible and infrared parts of the spectrum the atmospheric particulates are a major source of variability in the received signal. It is difficult to design a sensor which will determine the unknown atmospheric components by remote sensing methods, at least to the accuracy needed for multispectral classification. The problem of spatial and temporal variations in the atmospheric quantities which can affect the measured radiances are examined. A method based upon the stochastic nature of the atmospheric components was developed, and, using actual data the statistical parameters needed for inclusion into a radiometric model was generated. Methods are then described for an improved correction of radiances. These algorithms will then result in a more accurate and consistent classification procedure.
High resolution retinal image restoration with wavefront sensing and self-extracted filtering
Yang, Shuyu; Erry, Gavin; Nemeth, Sheila; Mitra, Sunanda; Soliz, Peter
2005-04-01
Diagnosis and treatment of retinal diseases such as diabetic retinopathy commonly rely on a clear view of the retina. The challenge in obtaining high quality retinal image lies in the design of the imaging system that can reduce the strong aberrations of the human eye. Since the amplitudes of human eye aberrations decrease rapidly as the aberration order goes up, it is more cost-effective to correct low order aberrations with adaptive optical devices while process high order aberrations through image processing. A cost effective fundus imaging device that can capture high quality retinal images with 2-5 times higher resolution than conventional retinal images has been designed [1]. This imager improves image quality by attaching complementary adaptive optical components to a conventional fundus camera. However, images obtained with the high resolution camera are still blurred due to some uncorrected aberrations as well as defocusing resulting from non-isoplanatic effect. Therefore, advanced image restoration algorithms have been employed for further improvement in image quality. In this paper, we use wavefront-based and self-extracted blind deconvolution techniques to restore images captured by the high resolution fundus camera. We demonstrate that through such techniques, pathologies that are critical to retinal disease diagnosis but not clear or not observable in the original image can be observed clearly in the restored images. Image quality evaluation is also used to finalize the development of a cost-effective, fast, and automated diagnostic system that can be used clinically.
Coronagraphic wavefront sensing with COFFEE: high spatial-frequency diversity and other news
Mugnier, L. M.; Sauvage, J.-F.; Herscovici-Schiller, O.; Baudoz, P.; Galicher, R.; Le Duigou, J.-M.
2016-07-01
The final performance of current and future instruments dedicated to exoplanet detection and characterization is limited by intensity residuals in the scientific image plane, which originate in uncorrected optical aberrations. In order to reach very high contrasts, these aberrations needs to be compensated for. We have proposed a focalplane wave-font sensor called COFFEE (for COronagraphic Focal-plane wave-Front Estimation for Exoplanet detection), which consists in an extension of conventional phase diversity to a coronagraphic system. In this communication, we study the extension of COFFEE to the joint estimation of the phase and the amplitude in the context of space-based coronagraphic instruments: we optimize the diversity phase in order to minimize the reconstruction error; we also propose and optimize a novel low-amplitude high-frequency diversity that should allow the phase-diverse images to still be used for science. Lastly, we perform a first experimental validation of COFFEE in the very high, space-like contrast conditions of the THD bench and show that COFFEE is able to distinguish between phase and amplitude aberrations.
Theory and application of differential OTF (dOTF) wavefront sensing
Codona, Johanan L.
2012-07-01
A new image-based technique for measuring the complex field in the pupil of a telescope is presented. The simplest form of the method uses two point source images, one with a small modification introduced in the pupil. The processing of the images is very simple and non-iterative. The method is based on a specially-defined complex functional derivative of the OTF. This derivative is approximated empirically by the difference between the Fourier transforms of the two PSFs: the differential OTF or "dOTF." Due to the complex conjugate in the OTF, the dOTF includes two complex images of the complex pupil field overlapping at the point of pupil modification. By placing the modification near the edge of the pupil, the overlap region can be minimized. The overlap region is typically small, but can be eliminated altogether by using a second modification and a third image. The technique can use broadband light, but the result incurs a radial blurring proportional to the fractional bandwidth. This is also easily dealt with using another modification and image. Although the dOTF a poor match for high frame rate astronomical AO applications, it has many potential uses. Optical shop testing, non-common-path wavefront error estimation, alignment and vignetting, telescope segment phasing, general imaging system diagnostics and testing applications are considered. More advanced applications are possible with extensions to the theory, such as extended incoherence background scenes as sources instead of stars, and 3-D tomographic aberration and transmission mapping open up many new applications.
Performance of wavefront-sensorless adaptive optics using modal and zonal correction
Anzuola, Esdras; Segel, Max; Gladysz, Szymon; Stein, Karin
2016-10-01
Unconventional wavefront sensing strategies are being developed to provide alternatives for measuring the wavefront deformation of a laser beam propagating through strong turbulence and/or along a horizontal-path. In this paper we present results from two "wavefront-sensorless" approaches: stochastic parallel gradient descent (SPGD) and its modal version (M-SPGD). We compare the performance of both algorithms through experimental measurements under emulated dynamic atmospheric turbulence by using the coupling efficiency in a single mode fiber as performance metric. We estimate probability density function of coupling efficiency for free-space optical links using adaptive optics (AO) as a function of key parameters such us turbulence strength and AO loop rate. We demonstrate faster convergence rate of the M-SPGD algorithm as compared to the traditional SPGD, although classic SPGD achieves higher correction. Additionally, we constrain the main temporal requirements of an AO system using wavefront-sensorless architectures.
Zhou, Fan; Hong, Xin; Miller, Donald T.; Thibos, Larry N.; Bradley, Arthur
2004-05-01
A corneal aberrometer based on Shack-Hartmann wave-front sensing was developed and validated by using calibrated aspheric surfaces. The aberrometer was found to accurately measure corneal reflective aberrations, from which corneal topography and corneal refractive aberrations were derived. Measurements of reflective aberrations correlated well with theory (R^2=0.964 to 0.994). The sag error root mean square (RMS) was small, ranging from 0.1 to 0.17 Âµm for four of the five calibrated surfaces with the fifth at 0.36 Âµm as a result of residual defocus. Measured refractive aberrations matched with theory and whole-eye aberrometry to within a small fraction of a wavelength. Measurements on three human corneas revealed very large refractive astigmatism (0.65-1.2 Âµm) and appreciable levels of trefoil (0.08-0.47 Âµm), coma (0.14-0.19 Âµm), and spherical aberration (0.18-0.25 Âµm). The mean values of these aberrations were significantly larger than the RMS in repeated measurements.
Lee, Hanshin; Hill, Gary J.; Tuttle, Sarah E.; Noyola, Eva; Peterson, Trent; Vattiat, Brian L.
2014-07-01
Teague introduced a phase retrieval method that uses the image shape moments. More recently, an independent study arrived at a similar technique, which was then applied to in-situ full-field image-quality evaluation of spectroscopic systems. This moment-based wavefront sensing (MWFS) method relies on the geometric relation between the image shape moments and the geometric wavefront modal coefficients. The MWFS method allows a non-iterative determination of the modal coefficients from focus-modulated images at arbitrary spatial resolutions. The determination of image moments is a direct extension of routine centroid and image size calculation, making its implementation easy. Previous studies showed that the MWFS works well in capturing large low-order modes, and is quite suitable for in-situ alignment diagnostics. At the Astronomical Instrumentation conference in 2012, we presented initial results of the application of the moment-based wavefront sensing to a fiber-fed astronomical spectrograph, called VIRUS (a set of replicated 150 identical integral-field unit spectrographs contained in 75 unit pairs). This initial result shows that the MWFS can provide accurate full-field image-quality assessment for efficiently aligning these 150 spectrographs. Since then, we have assembled more than 24 unit pairs using this technique. In this paper, we detail the technical update/progress made so far for the moment-based wavefront sensing method and the statistical estimates of the before/after alignment aberrations, image-quality, and various efficiency indicators of the unit spectrograph alignment process.
Impulsive control of stochastic system under the sense of stochastic asymptotical stability
Institute of Scientific and Technical Information of China (English)
Niu Yu-Jun; Ma Ge
2010-01-01
This paper studies the stochastic asymptotical stability of stochastic impulsive differential equations,and establishes a comparison theory to ensure the trivial solution's stochastic asymptotical stability.From the comparison theory,it can find out whether the stochastic impulsive differential system is stable just by studying the stability of a deterimpulsive control method,and numerical simulations are employed to verify the feasibility of this method.
Vinas, Maria; Dorronsoro, Carlos; Cortes, Daniel; Pascual, Daniel; Marcos, Susana
2015-03-01
Longitudinal Chromatic Aberration (LCA) influences the optical quality of the eye. However, the reported LCA varies across studies, likely associated to differences in the measurement techniques. We present LCA measured in subjects using wavefront sensing, double-pass retinal images, and psychophysical methods with a custom-developed polychromatic Adaptive Optics system in a wide spectral range (450-950 nm), with control of subjects' natural aberrations. LCA measured psychophysically was significantly higher than that from reflectometric techniques (1.51 D vs 1.00 D in the 488-700 nm range). Ours results indicate that the presence of natural aberrations is not the cause for the discrepancies across techniques.
Differential OTF Wavefront Sensing
Codona, Johanan L
2013-01-01
An image-based technique for measuring the complex field in the pupil of an imaging system is presented. Two point source images, one with a small modification introduced in the pupil, are combined using a simple and non-iterative algorithm. The non-interferometric method is based on the change in the optical transfer function (OTF), giving a differential OTF (dOTF). The dOTF includes two images of the complex pupil field, conjugated and reflected about the position of the pupil modification, leaving an overlap that obscures some the the pupil. The overlap can be minimized by introducing the modification near the edge of the pupil. The overlap region can be eliminated altogether by using a second modification and a third point source image. The pupil field is convolved by the change in the pupil field, so smaller modification areas are preferred. The non-monochromatic light, but the result incurs a proportional radial blurring determined by the fractional bandwidth. We include some simple demonstration experi...
MSEE: Stochastic Cognitive Linguistic Behavior Models for Semantic Sensing
2013-09-01
study of human language in terms of neonatal development and evolution in human physiology, sociology, and psychology [1][2]. It offers a different...simple, and universally understood. They are the fundamental gestalts for reasoning. In semantic sensing domain, things would be the most common objects...related places. The cognitive linguistics notion of path organizes places into the structure of an event. A path is a precognitive gestalt that
Stochastic models of cover class dynamics. [remote sensing of vegetation
Barringer, T. H.; Robinson, V. B.
1981-01-01
Investigations related to satellite remote sensing of vegetation have been concerned with questions of signature identification and extension, cover inventory accuracy, and change detection and monitoring. Attention is given to models of ecological succession, present directions in successional modeling and analysis, nondynamic spatial models, issues in the analysis of spatial data, and aspects of spatial modeling. Issues in time-series analysis are considered along with dynamic spatial models, and problems of model specification and identification.
Wavefront Measurement in Ophthalmology
Molebny, Vasyl
Wavefront sensing or aberration measurement in the eye is a key problem in refractive surgery and vision correction with laser. The accuracy of these measurements is critical for the outcome of the surgery. Practically all clinical methods use laser as a source of light. To better understand the background, we analyze the pre-laser techniques developed over centuries. They allowed new discoveries of the nature of the optical system of the eye, and many served as prototypes for laser-based wavefront sensing technologies. Hartmann's test was strengthened by Platt's lenslet matrix and the CCD two-dimensional photodetector acquired a new life as a Hartmann-Shack sensor in Heidelberg. Tscherning's aberroscope, invented in France, was transformed into a laser device known as a Dresden aberrometer, having seen its reincarnation in Germany with Seiler's help. The clinical ray tracing technique was brought to life by Molebny in Ukraine, and skiascopy was created by Fujieda in Japan. With the maturation of these technologies, new demands now arise for their wider implementation in optometry and vision correction with customized contact and intraocular lenses.
Digital pyramid wavefront sensor with tunable modulation.
Akondi, Vyas; Castillo, Sara; Vohnsen, Brian
2013-07-29
The pyramid wavefront sensor is known for its high sensitivity and dynamic range that can be tuned by mechanically altering its modulation amplitude. Here, a novel modulating digital scheme employing a reflecting phase only spatial light modulator is demonstrated. The use of the modulator allows an easy reconfigurable pyramid with digital control of the apex angle and modulation geometry without the need of any mechanically moving parts. Aberrations introduced by a 140-actuator deformable mirror were simultaneously sensed with the help of a commercial Hartmann-Shack wavefront sensor. The wavefronts reconstructed using the digital pyramid wavefront sensor matched very closely with those sensed by the Hartmann-Shack. It is noted that a tunable modulation is necessary to operate the wavefront sensor in the linear regime and to accurately sense aberrations. Through simulations, it is shown that the wavefront sensor can be extended to astronomical applications as well. This novel digital pyramid wavefront sensor has the potential to become an attractive option in both open and closed loop adaptive optics systems.
Li, Edward; Shafiee, Mohammad Javad; Haider, Masoom A; Wong, Alexander
2015-01-01
Magnetic Resonance Imaging (MRI) is a crucial medical imaging technology for the screening and diagnosis of frequently occurring cancers. However image quality may suffer by long acquisition times for MRIs due to patient motion, as well as result in great patient discomfort. Reducing MRI acquisition time can reduce patient discomfort and as a result reduces motion artifacts from the acquisition process. Compressive sensing strategies, when applied to MRI, have been demonstrated to be effective at decreasing acquisition times significantly by sparsely sampling the \\emph{k}-space during the acquisition process. However, such a strategy requires advanced reconstruction algorithms to produce high quality and reliable images from compressive sensing MRI. This paper proposes a new reconstruction approach based on cross-domain stochastically fully connected conditional random fields (CD-SFCRF) for compressive sensing MRI. The CD-SFCRF introduces constraints in both \\emph{k}-space and spatial domains within a stochas...
Institute of Scientific and Technical Information of China (English)
张天天; 易仕和; 朱杨柱; 何霖
2015-01-01
Background oriented schlieren based wavefront sensing (BOS-WS) is a new experimental technique for measuring the two-dimensional distribution of optical wavefronts and the optical path differences (OPDs) induced by the flow-field density variations. Background oriented schlieren (BOS) is traditionally used to test the flow-field density distribution, which restricts the obtaining of useful information since the obtained density information is integrated over the optical path. The OPD is very important for predicting the optical distortion when light travels through the flow field and it is tested by BOS-WS. In order to obtain the optical distortion generated by aero-optic effect, and restore the original image from the distortion known information so as to explore a new kind of supersonic imaging guidance method, theory analysis, numerical simulation and experimental methods are used based on BOS-WS. Through theoretical analysis, the wavefront measurement method based on BOS is verified and the calculation methods of using wavefront information known to predict distortion displacement field and using known displacement field to reconstruct wavefront are explored. By numerical simulation, the error sizes and the result rationalities of one stepped integral algorithm and Southwell method on the wavefront reconstruction are compared, and through the error analysis it is proved that the Southwell method is more accurate and reasonable. By a wavefront aberration experiment carried out in the flow field above the candle flame and a lens perturbation experiment, the methods of using OPD known to reconstruct distorted displacement field and correcting image distortion by the field are creatively explored. The verification experiments show the effectiveness of the correction method.%背景纹影波前传感(background oriented schlieren based wavefront sensing, BOS-WS)是利用背景纹影技术测量光学波前二维分布的新型实验手段,可定量测量光线通过
High-speed SPGD wavefront controller for an adaptive optics system without wavefront sensor
Wang, Caixia; Li, Xinyang; Li, Mei; Ye, Jongwei; Chen, Bo
2010-10-01
A non-conventional adaptive optics system based on direct system performance metric optimization is illustrated. The system does not require wave-front sensor which is difficult to work under the poor condition such as beam cleanup for the anomalous light beam. The system comprises a high speed wavefront controller based on Stochastic Parallel Gradient Descent (SPGD) Algorithm, a deformable mirror, a tip/tilt mirror and a far-field system performance metric sensor. The architecture of the wave-front controller is based on a combination of Field Programmable Gate Array (FPGA) and floating-point Digital Signal Processor (DSP). The Zernike coefficient information is applied to improve the iteration speed. The experimental results show that the beam cleanup system based on SPGD keep a high iteration speed. The controller can compensate the wavefront aberration and tilt excursion effectively.
Coded Shack-Hartmann Wavefront Sensor
Wang, Congli
2016-12-01
Wavefront sensing is an old yet fundamental problem in adaptive optics. Traditional wavefront sensors are limited to time-consuming measurements, complicated and expensive setup, or low theoretically achievable resolution. In this thesis, we introduce an optically encoded and computationally decodable novel approach to the wavefront sensing problem: the Coded Shack-Hartmann. Our proposed Coded Shack-Hartmann wavefront sensor is inexpensive, easy to fabricate and calibrate, highly sensitive, accurate, and with high resolution. Most importantly, using simple optical flow tracking combined with phase smoothness prior, with the help of modern optimization technique, the computational part is split, efficient, and parallelized, hence real time performance has been achieved on Graphics Processing Unit (GPU), with high accuracy as well. This is validated by experimental results. We also show how optical flow intensity consistency term can be derived, using rigor scalar diffraction theory with proper approximation. This is the true physical law behind our model. Based on this insight, Coded Shack-Hartmann can be interpreted as an illumination post-modulated wavefront sensor. This offers a new theoretical approach for wavefront sensor design.
Wavefront Control for Extreme Adaptive Optics
Energy Technology Data Exchange (ETDEWEB)
Poyneer, L A
2003-07-16
Current plans for Extreme Adaptive Optics systems place challenging requirements on wave-front control. This paper focuses on control system dynamics, wave-front sensing and wave-front correction device characteristics. It may be necessary to run an ExAO system after a slower, low-order AO system. Running two independent systems can result in very good temporal performance, provided specific design constraints are followed. The spatially-filtered wave-front sensor, which prevents aliasing and improves PSF sensitivity, is summarized. Different models of continuous and segmented deformable mirrors are studied. In a noise-free case, a piston-tip-tilt segmented MEMS device can achieve nearly equivalent performance to a continuous-sheet DM in compensating for a static phase aberration with use of spatial filtering.
Rousset, G.; Gratadour, D.; Gendron, E.; Buey, T.; Myers, R.; Morris, T.; Basden, A.; Talbot, G.; Bonaccini Calia, D.; Marchetti, E.; Pfrommer, T.
2014-08-01
Wavefront (WF) sensing using Sodium (Na) Laser Guide Stars (LGS) is a key concern for the design of a number of first generation Extremely Large Telescope (ELT) Adaptive Optics (AO) modules. One of the main challenges is the mitigation of the effects induced by extreme LGS spot elongation on the WF measurements. Before the final design studies of the E-ELT instruments, a Na LGS WF sensing on-sky experiment at the E-ELT scale is mandatory to achieve the full validation of the proposed mitigation strategies and their performance. This experiment will provide unique spatial and temporal WF measurements on a true Na LGS, perturbed by the atmospheric turbulence and mesospheric variability. The fine comparative analysis of such data with synchronously acquired WF measurements on at least one natural guide star (NGS) will be fundamental to test a number of algorithms, configurations for spot sampling and truncation and WF reconstruction schemes including multi-LGS configurations. A global error budget for the whole experiment will be derived with time to feed into the numerical simulation and the design of subsequent E-ELT LGS-AO modules. The data produced will be made available to the E-ELT community. We propose to use CANARY, the Multi-Object AO demonstrator installed at the 4.2m WHT which is a modular AO platform, equipped with several NGS WF Sensor (WFS) and Rayleigh multi-LGS unit and WFS. The transportable 20W Sodium laser unit (WLGSU), developed at ESO, will be positioned at a varying distance from the WHT to provide off-axis launching (up to 40m), simulating the whole range of LGS spot elongations obtained on the E-ELT. In such a case, the WHT pupil will represent an off-axis sub-pupil of the main E-ELT pupil. In addition, this experiment will include a Na layer profiler and the capability for open and closed loop operations. The experiment is scheduled before the end of 2016.
Wave-front analysis of personal eye protection.
Eppig, Timo; Zoric, Katja; Speck, Alexis; Zelzer, Benedikt; Götzelmann, Jens; Nagengast, Dieter; Langenbucher, Achim
2012-07-30
Shack-Hartmann wave-front sensing has been successfully applied to many fields of optical testing including the human eye itself. We propose wave-front measurement for testing protective eye wear for production control and investigation of aberrations. Refractive power data is derived from the wave-front data and compared to a subjective measurement technique based on a focimeter. Additional image quality classification was performed with a multivariate model using objective parameters to resample a subjectively determined visual quality. Wave-front measurement advances optical testing of protective eye wear and may be used for objective quality control.
Directory of Open Access Journals (Sweden)
Mohammed Alawad
2015-03-01
Full Text Available This paper considers the problem of how to efficiently measure a large and complex information field with optimally few observations. Specifically, we investigate how to stochastically estimate modular criticality values in a large-scale digital circuit with a very limited number of measurements in order to minimize the total measurement efforts and time. We prove that, through sparsity-promoting transform domain regularization and by strategically integrating compressive sensing with Bayesian learning, more than 98% of the overall measurement accuracy can be achieved with fewer than 10% of measurements as required in a conventional approach that uses exhaustive measurements. Furthermore, we illustrate that the obtained criticality results can be utilized to selectively fortify large-scale digital circuits for operation with narrow voltage headrooms and in the presence of soft-errors rising at near threshold voltage levels, without excessive hardware overheads. Our numerical simulation results have shown that, by optimally allocating only 10% circuit redundancy, for some large-scale benchmark circuits, we can achieve more than a three-times reduction in its overall error probability, whereas if randomly distributing such 10% hardware resource, less than 2% improvements in the target circuit’s overall robustness will be observed. Finally, we conjecture that our proposed approach can be readily applied to estimate other essential properties of digital circuits that are critical to designing and analyzing them, such as the observability measure in reliability analysis and the path delay estimation in stochastic timing analysis. The only key requirement of our proposed methodology is that these global information fields exhibit a certain degree of smoothness, which is universally true for almost any physical phenomenon.
Kopsaftopoulos, Fotios; Nardari, Raphael; Li, Yu-Hung; Wang, Pengchuan; Chang, Fu-Kuo
2016-04-01
In this work, the system design, integration, and wind tunnel experimental evaluation are presented for a bioinspired self-sensing intelligent composite unmanned aerial vehicle (UAV) wing. A total of 148 micro-sensors, including piezoelectric, strain, and temperature sensors, in the form of stretchable sensor networks are embedded in the layup of a composite wing in order to enable its self-sensing capabilities. Novel stochastic system identification techniques based on time series models and statistical parameter estimation are employed in order to accurately interpret the sensing data and extract real-time information on the coupled air flow-structural dynamics. Special emphasis is given to the wind tunnel experimental assessment under various flight conditions defined by multiple airspeeds and angles of attack. A novel modeling approach based on the recently introduced Vector-dependent Functionally Pooled (VFP) model structure is employed for the stochastic identification of the "global" coupled airflow-structural dynamics of the wing and their correlation with dynamic utter and stall. The obtained results demonstrate the successful system-level integration and effectiveness of the stochastic identification approach, thus opening new perspectives for the state sensing and awareness capabilities of the next generation of "fly-by-fee" UAVs.
Curvature sensor for ocular wavefront measurement.
Díaz-Doutón, Fernando; Pujol, Jaume; Arjona, Montserrat; Luque, Sergio O
2006-08-01
We describe a new wavefront sensor for ocular aberration determination, based on the curvature sensing principle, which adapts the classical system used in astronomy for the living eye's measurements. The actual experimental setup is presented and designed following a process guided by computer simulations to adjust the design parameters for optimal performance. We present results for artificial and real young eyes, compared with the Hartmann-Shack estimations. Both methods show a similar performance for these cases. This system will allow for the measurement of higher order aberrations than the currently used wavefront sensors in situations in which they are supposed to be significant, such as postsurgery eyes.
Integrated Wavefront Corrector Project
National Aeronautics and Space Administration — One of the critical issues for NASA missions requiring high contrast astrophysical imaging such as Terrestrial Planet Finder (TPF) is wavefront control. Without use...
Burse, Mahesh; Chattopadhyay, Sabyasachi; Ramaprakash, A. N.; Sinha, Sakya; Prabhudesai, Swapnil; Punnadi, Sujit; Chordia, Pravin; Kohok, Abhay
2016-07-01
As a part of a design study for the On-Instrument Low Order Wave-front Sensor (OIWFS) for the TMT Infra-Red Imaging Spectrograph (IRIS), we recently evaluated the noise performance of a detector control system consisting of IUCAA SIDECAR DRIVE ELECRONICS CONTROLLER (ISDEC), SIDECAR ASIC and HAWAII-2RG (H2RG) MUX. To understand and improve the performance of this system to serve as a near infrared wavefront sensor, we implemented new read out modes like multiple regions of interest with differential multi-accumulate readout schemes for the HAWAII-2RG (H2RG) detector. In this system, the firmware running in SIDECAR ASIC programs the detector for ROI readout, reads the detector, processes the detector output and writes the digitized data into its internal memory. ISDEC reads the digitized data from ASIC, performs the differential multi-accumulate operations and then sends the processed data to a PC over a USB interface. A special loopback board was designed and used to measure and reduce the noise from SIDECAR ASIC DC biases2. We were able to reduce the mean r.m.s read noise of this system down to 1-2 e. for any arbitrary window frame of 4x4 size at frame rates below about 200 Hz.
The Asymmetric Pupil Fourier Wavefront Sensor
Martinache, Frantz
2013-01-01
This paper introduces a novel wavefront sensing approach that relies on the Fourier analysis of a single conventional direct image. In the high Strehl ratio regime, the relation between the phase measured in the Fourier plane and the wavefront errors in the pupil can be linearized, as was shown in a previous work that introduced the notion of generalized closure-phase, or kernel-phase. The technique, to be usable as presented requires two conditions to be met: (1) the wavefront errors must be kept small (of the order of one radian or less) and (2) the pupil must include some asymmetry, that can be introduced with a mask, for the problem to become solvable. Simulations show that this asymmetric pupil Fourier wavefront sensing or APF-WFS technique can improve the Strehl ratio from 50 to over 90 % in just a few iterations, with excellent photon noise sensitivity properties, suggesting that on-sky close loop APF-WFS is possible with an extreme adaptive optics system.
Advanced Wavefront Control Techniques
Energy Technology Data Exchange (ETDEWEB)
Olivier, S S; Brase, J M; Avicola, K; Thompson, C A; Kartz, M W; Winters, S; Hartley, R; Wihelmsen, J; Dowla, F V; Carrano, C J; Bauman, B J; Pennington, D M; Lande, D; Sawvel, R M; Silva, D A; Cooke, J B; Brown, C G
2001-02-21
Programs at LLNL that involve large laser systems--ranging from the National Ignition Facility to new tactical laser weapons--depend on the maintenance of laser beam quality through precise control of the optical wavefront. This can be accomplished using adaptive optics, which compensate for time-varying aberrations that are often caused by heating in a high-power laser system. Over the past two decades, LLNL has developed a broad capability in adaptive optics technology for both laser beam control and high-resolution imaging. This adaptive optics capability has been based on thin deformable glass mirrors with individual ceramic actuators bonded to the back. In the case of high-power lasers, these adaptive optics systems have successfully improved beam quality. However, as we continue to extend our applications requirements, the existing technology base for wavefront control cannot satisfy them. To address this issue, this project studied improved modeling tools to increase our detailed understanding of the performance of these systems, and evaluated novel approaches to low-order wavefront control that offer the possibility of reduced cost and complexity. We also investigated improved beam control technology for high-resolution wavefront control. Many high-power laser systems suffer from high-spatial-frequency aberrations that require control of hundreds or thousands of phase points to provide adequate correction. However, the cost and size of current deformable mirrors can become prohibitive for applications requiring more than a few tens of phase control points. New phase control technologies are becoming available which offer control of many phase points with small low-cost devices. The goal of this project was to expand our wavefront control capabilities with improved modeling tools, new devices that reduce system cost and complexity, and extensions to high spatial and temporal frequencies using new adaptive optics technologies. In FY 99, the second year of
Wavefront coding with adaptive optics
Agbana, Temitope E.; Soloviev, Oleg; Bezzubik, Vitalii; Patlan, Vsevolod; Verhaegen, Michel; Vdovin, Gleb
2015-03-01
We have implemented an extended depth of field optical system by wavefront coding with a micromachined membrane deformable mirror. This approach provides a versatile extension to standard wavefront coding based on fixed phase mask. First experimental results validate the feasibility of the use of adaptive optics for variable depth wavefront coding in imaging optical systems.
Focal plane wave-front sensin8 algorithm for high-contrast imaging
Institute of Scientific and Technical Information of China (English)
DOU JiangPei; REN DeQing; ZHU YongTian; ZHANG Xi
2009-01-01
High-contrast imaging provided by a coronagraph is critical for the direction imaging of the Earth-like planet orbiting its bright parent star. A major limitation for such direct imaging is the speckle noise that is induced from the wave-front error of an optical system. We derive an algorithm for the wave-front measurement directly from 3 focal plane images. The 3 images are achieved through a deformable mirror to provide specific phases for the optics system. We introduce an extra amplitude modulation on one deformable mirror configuration to create an uncorrelated wave-front, which is a critical procedure for wave-front sensing. The simulation shows that the reconstructed wave-front is consistent with the original wave-front theoretically, which indicates that such an algorithm is a promising technique for the wave-front measurement for the high-contrast imaging.
Asymptotic stability of monostable wavefronts in discrete-time integral recursions
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The aim of this work is to study the traveling wavefronts in a discrete-time integral recursion with a Gauss kernel in R2.We first establish the existence of traveling wavefronts as well as their precise asymptotic behavior.Then,by employing the comparison principle and upper and lower solutions technique,we prove the asymptotic stability and uniqueness of such monostable wavefronts in the sense of phase shift and circumnutation.We also obtain some similar results in R.
DEFF Research Database (Denmark)
Knudsen, Thomas Skov
1997-01-01
For stochastic differential equations (SDEs) of the form dX(t) = b(X)(t)) dt + sigma(X(t))dW(t) where b and sigma are Lipschitz continuous, it is shown that if we consider a fixed sigma is an element of C-5, bounded and with bounded derivatives, the random field of solutions is pathwise locally...
Deconvolution from Wavefront Sensing Using Optimal Wavefront Estimators
1996-12-01
874-1641. 2. Arfken , George. Mathematical Methods for Pyhsicists (Third Edition). San Diego: Academic Press, Inc., 1985. 3. Bate, Roger R., et al...expression takes the form i(x, y) = -JJ o(, 71)h(x - 6, y - (2) 12 Fortunately, Fourier analysis methods can greatly simplify the mathematics . The...1 1.1 The Problem: Imaging Through Atmospheric Turbulence . 1 1.2 Mitigation Methods . .. .. ... ... ... ... ... ... 2 1.3 Deconvolution
Making Sense of Stochastic Variation and Causality in a Virtual Environment
Prodromou, Theodosia; Pratt, Dave
2013-01-01
This paper presents a case study of students (age 14-15) as they attempt to make sense of distribution, adopting a range of causal meanings for the variation observed in the animated computer display and in the graphs generated by a "BasketBall" simulation. The student activity is analysed through dimensions of complex causality. The…
Bahrdt, J
2005-01-01
The design of beamlines for VUV and x-ray FEL facilities requires a detailed knowledge of the coherent radiation source. Time dependent simulations with FEL codes like GENESIS provide the electric field distribution at the end of the FEL which represents the complete information. Ray tracing codes used to transform the light from the source to the sample are generally based on geometrical optics and do not include directly the coherent properties of the FEL radiation. On the other hand Fourier optic techniques are usually applied to the propagation across normal incidence optics. We present an algorithm based on physical optics which permits the propagation of wavefronts across grazing incidence optics including interference effects, diffraction, polarization variation and pulse lengthening. Some examples are given for the proposed BESSY soft x-ray FEL.
Phase-Controlled Magnetic Mirror for Wavefront Correction
Hagopian, John; Wollack, Edward
2011-01-01
Typically, light interacts with matter via the electric field and interaction with weakly bound electrons. In a magnetic mirror, a patterned nanowire is fabricated over a metallic layer with a dielectric layer in between. Oscillation of the electrons in the nanowires in response to the magnetic field of incident photons causes a re-emission of photons and operation as a "magnetic mirror." By controlling the index of refraction in the dielectric layer using a local applied voltage, the phase of the emitted radiation can be controlled. This allows electrical modification of the reflected wavefront, resulting in a deformable mirror that can be used for wavefront control. Certain applications require wavefront quality in the few-nanometer regime, which is a major challenge for optical fabrication and alignment of mirrors or lenses. The use of a deformable magnetic mirror allows for a device with no moving parts that can modify the phase of incident light over many spatial scales, potentially with higher resolution than current approaches. Current deformable mirrors modify the incident wavefront by using nano-actuation of a substrate to physically bend the mirror to a desired shape. The purpose of the innovation is to modify the incident wavefront for the purpose of correction of fabrication and alignment-induced wavefront errors at the system level. The advanced degree of precision required for some applications such as gravity wave detection (LISA - Laser Interferometer Space Antenna) or planet finding (FKSI - Fourier-Kelvin Stellar Interferometer) requires wavefront control at the limits of the current state of the art. All the steps required to fabricate a magnetic mirror have been demonstrated. The modification is to apply a bias voltage to the dielectric layer so as to change the index of refraction and modify the phase of the reflected radiation. Light is reflected off the device and collected by a phase-sensing interferometer. The interferometer determines the
Directory of Open Access Journals (Sweden)
Frances S. Ligler
2008-06-01
Full Text Available We present a simplified, highly reproducible process to fabricate arrays of tapered silicon micro-funnels and micro-channels using a single lithographic step with a silicon oxide (SiO2 hard mask on at a wafer scale. Two approaches were used for the fabrication. The first one involves a single wet anisotropic etch step in concentrated potassium hydroxide (KOH and the second one is a combined approach comprising Deep Reactive Ion Etch (DRIE followed by wet anisotropic etching. The etching is performed through a 500 mm thick silicon wafer, and the resulting structures are characterized by sharp tapered ends with a sub-micron cross-sectional area at the tip. We discuss the influence of various parameters involved in the fabrication such as the size and thickness variability of the substrate, dry and wet anisotropic etching conditions, the etchant composition, temperature, diffusion and micro-masking effects, the quality of the hard mask in the uniformity and reproducibility of the structures, and the importance of a complete removal of debris and precipitates. The presence of apertures at the tip of the structures is corroborated through current voltage measurements and by the translocation of DNA through the apertures. The relevance of the results obtained in this report is discussed in terms of the potential use of these structures for stochastic sensing.
The NGS Pyramid wavefront sensor for ERIS
Riccardi, A.; Antichi, J.; Quirós-Pacheco, F.; Esposito, S.; Carbonaro, L.; Agapito, G.; Biliotti, V.; Briguglio, R.; Di Rico, G.; Dolci, M.; Ferruzzi, D.; Pinna, E.; Puglisi, A.; Xompero, M.; Marchetti, E.; Fedrigo, E.; Le Louarn, M.; Conzelmann, R.; Delabre, B.; Amico, P.; Hubin, N.
2014-07-01
ERIS is the new Single Conjugate Adaptive Optics (AO) instrument for VLT in construction at ESO with the collaboration of Max-Planck Institut fuer Extraterrestrische Physik, ETH-Institute for Astronomy and INAF - Osservatorio Astrofisico di Arcetri. The ERIS AO system relies on a 40×40 sub-aperture Pyramid Wavefront Sensor (PWFS) for two operating modes: a pure Natural Guide Star high-order sensing for high Strehl and contrast correction and a low-order visible sensing in support of the Laser Guide Star AO mode. In this paper we present in detail the preliminary design of the ERIS PWFS that is developed under the responsibility of INAF-Osservatorio Astrofisico di Arcetri in collaboration with ESO.
Limited by sensing - A minimal stochastic model of the lag-phase during diauxic growth.
Chu, Dominique
2017-02-07
Many microbes when grown on a mixture of two carbon sources utilise first and exclusively the preferred sugar, before switching to the less preferred carbon source. This results in two distinct exponential growth phases, often interrupted by a lag-phase of reduced growth termed the lag-phase. While the lag-phase appears to be an evolved feature, it is not clear what drives its evolution, as it comes with a substantial up-front fitness penalty due to lost growth. In this article a minimal mathematical model based on a master-equation approach is proposed. This model can explain many empirically observed phenomena. It suggests that the lag-phase can be understood as a manifestation of the trade-off between switching speed and switching efficiency. Moreover, the model predicts heterogeneity of the population during the lag-phase. Finally, it is shown that the switch from one carbon source to another one is a sensing problem and the lag-phase is a manifestation of known fundamental limitations of biological sensors.
A space-time stochastic model of rainfall for satellite remote-sensing studies
Bell, Thomas L.
1987-01-01
A model of the spatial and temporal distribution of rainfall is described that produces random spatial rainfall patterns with these characteristics: (1) the model is defined on a grid with each grid point representing the average rain rate over the surrounding grid box, (2) rain occurs at any one grid point, on average, a specified percentage of the time and has a lognormal probability distribution, (3) spatial correlation of the rainfall can be arbitrarily prescribed, and (4) time stepping is carried out so that large-scale features persist longer than small-scale features. Rain is generated in the model from the portion of a correlated Gaussian random field that exceeds a threshold. The portion of the field above the threshold is rescaled to have a lognormal probability distribution. Sample output of the model designed to mimic radar observations of rainfall during the Global Atmospheric Research Program Atlantic Tropical Experiment (GATE), is shown. The model is intended for use in evaluating sampling strategies for satellite remote-sensing of rainfall and for development of algorithms for converting radiant intensity received by an instrument from its field of view into rainfall amount.
Wavefront Curvature Sensing from Image Projections
2006-09-01
sort the polynomials and two other indices, (n;m), to identify radial order and azimuthal order. Two common ordering methods are provided by Malacara ...18] and Noll [7]. Each ordering scheme has its respective bene�ts. For instance, Malacara �s ordering o¤ers a simple relationship between the primary...1961. 17. I. S. Gradshteyn and I. M. Ryzhik. Table of Integrals, Series, and Products (6th Edi- tion). Academic Press, 2000. 18. D. Malacara
The DeMi CubeSat: Wavefront Control with a MEMS Deformable Mirror in Space
Douglas, Ewan S.; Bendek, Eduardo; Marinan, Anne; Belikov, Ruslan; Merck, John; Cahoy, Kerri Lynn
2017-01-01
High-contrast imaging instruments on future space telescopes will require precise wavefront correction to detect small exoplanets near their host stars. High-actuator count microelectromechanical system (MEMS) deformable mirrors provide a compact form of wavefront control. The 6U DeMi CubeSat will demonstrate wavefront control with a MEMS deformable mirror over a yearlong mission. The payload includes both an internal laser source and a small telescope, with both focal plane and pupil plane sensing, for deformable mirror characterization. We detail the DeMi payload design, and describe future astrophysics enabled by high-actuator count deformable mirrors and small satellites.
Spatial Light Modulator for wavefront correction
Vyas, Akondi; Banyal, Ravinder Kumar; Prasad, B Raghavendra
2009-01-01
We present a liquid crystal method of correcting the phase of an aberrated wavefront using a spatial light modulator. A simple and efficient lab model has been demonstrated for wavefront correction. The crux of a wavefront correcting system in an adaptive optics system lies in the speed and the image quality that can be achieved. The speeds and the accuracy of wavefront representation using Zernike polynomials have been presented using a very fast method of computation.
Zhu, Zhaoyi; Mu, Quanquan; Li, Dayu; Yang, Chengliang; Cao, Zhaoliang; Hu, Lifa; Xuan, Li
2016-10-17
The centroid-based Shack-Hartmann wavefront sensor (SHWFS) treats the sampled wavefronts in the sub-apertures as planes, and the slopes of the sub-wavefronts are used to reconstruct the whole pupil wavefront. The problem is that the centroid method may fail to sense the high-order modes for strong turbulences, decreasing the precision of the whole pupil wavefront reconstruction. To solve this problem, we propose a sub-wavefront estimation method for SHWFS based on the focal plane sensing technique, by which more Zernike modes than the two slopes can be sensed in each sub-aperture. In this paper, the effects on the sub-wavefront estimation method of the related parameters, such as the spot size, the phase offset with its set amplitude and the pixels number in each sub-aperture, are analyzed and these parameters are optimized to achieve high efficiency. After the optimization, open-loop measurement is realized. For the sub-wavefront sensing, we achieve a large linearity range of 3.0 rad RMS for Zernike modes Z2 and Z3, and 2.0 rad RMS for Zernike modes Z4 to Z6 when the pixel number does not exceed 8 × 8 in each sub-aperture. The whole pupil wavefront reconstruction with the modified SHWFS is realized to analyze the improvements brought by the optimized sub-wavefront estimation method. Sixty-five Zernike modes can be reconstructed with a modified SHWFS containing only 7 × 7 sub-apertures, which could reconstruct only 35 modes by the centroid method, and the mean RMS errors of the residual phases are less than 0.2 rad2, which is lower than the 0.35 rad2 by the centroid method.
Wavefront reconstruction by modal decomposition
CSIR Research Space (South Africa)
Schulze, C
2012-08-01
Full Text Available We propose a new method to determine the wavefront of a laser beam based on modal decomposition by computer-generated holograms. The hologram is encoded with a transmission function suitable for measuring the amplitudes and phases of the modes...
Closed-loop focal plane wavefront control with the SCExAO instrument
Martinache, Frantz; Jovanovic, Nemanja; Guyon, Olivier
2016-09-01
Aims: This article describes the implementation of a focal plane based wavefront control loop on the high-contrast imaging instrument SCExAO (Subaru Coronagraphic Extreme Adaptive Optics). The sensor relies on the Fourier analysis of conventional focal-plane images acquired after an asymmetric mask is introduced in the pupil of the instrument. Methods: This absolute sensor is used here in a closed-loop to compensate for the non-common path errors that normally affects any imaging system relying on an upstream adaptive optics system.This specific implementation was used to control low-order modes corresponding to eight zernike modes (from focus to spherical). Results: This loop was successfully run on-sky at the Subaru Telescope and is used to offset the SCExAO deformable mirror shape used as a zero-point by the high-order wavefront sensor. The paper details the range of errors this wavefront-sensing approach can operate within and explores the impact of saturation of the data and how it can be bypassed, at a cost in performance. Conclusions: Beyond this application, because of its low hardware impact, the asymmetric pupil Fourier wavefront sensor (APF-WFS) can easily be ported in a wide variety of wavefront sensing contexts, for ground- as well space-borne telescopes, and for telescope pupils that can be continuous, segmented or even sparse. The technique is powerful because it measures the wavefront where it really matters, at the level of the science detector.
Directory of Open Access Journals (Sweden)
Chen Bor-Sen
2012-10-01
Full Text Available Abstract Background Collective rhythms of gene regulatory networks have been a subject of considerable interest for biologists and theoreticians, in particular the synchronization of dynamic cells mediated by intercellular communication. Synchronization of a population of synthetic genetic oscillators is an important design in practical applications, because such a population distributed over different host cells needs to exploit molecular phenomena simultaneously in order to emerge a biological phenomenon. However, this synchronization may be corrupted by intrinsic kinetic parameter fluctuations and extrinsic environmental molecular noise. Therefore, robust synchronization is an important design topic in nonlinear stochastic coupled synthetic genetic oscillators with intrinsic kinetic parameter fluctuations and extrinsic molecular noise. Results Initially, the condition for robust synchronization of synthetic genetic oscillators was derived based on Hamilton Jacobi inequality (HJI. We found that if the synchronization robustness can confer enough intrinsic robustness to tolerate intrinsic parameter fluctuation and extrinsic robustness to filter the environmental noise, then robust synchronization of coupled synthetic genetic oscillators is guaranteed. If the synchronization robustness of a population of nonlinear stochastic coupled synthetic genetic oscillators distributed over different host cells could not be maintained, then robust synchronization could be enhanced by external control input through quorum sensing molecules. In order to simplify the analysis and design of robust synchronization of nonlinear stochastic synthetic genetic oscillators, the fuzzy interpolation method was employed to interpolate several local linear stochastic coupled systems to approximate the nonlinear stochastic coupled system so that the HJI-based synchronization design problem could be replaced by a simple linear matrix inequality (LMI-based design problem
Analysis of wavefront reconstruction in 8 meter ring solar telescope
Dai, Yichun; Jin, Zhenyu
2016-07-01
Chinese Giant Solar Telescope (CGST) is the next generation infrared and optical solar telescope of China, which is proposed and pushed by the solar astronomy community of China and listed into the National Plans of Major Science and Technology Infrastructures. CGST is currently proposed to be an 8 meter Ring Solar Telescope (RST) with width of 1 meter, the hollow and symmetric structure of such an annular aperture facilitates the thermal control and high precision magnetic field measurement for a solar telescope. Adaptive optics (AO) is an indispensable tool of RST to obtain diffraction limited observations. How to realize AO involved wavefront sensing and correcting, and the degree of compensating in a narrow annular aperture is the primary problem of AO implementation of RST. Wavefront reconstruction involved problems of RST are first investigated and discussed in this paper using end to end simulation based on Shack-Hartmann wavefront sensing (SHWFS). The simulation results show that performance of zonal reconstruction with measurement noise no more than 0.05 arc sec can meets the requirement of RST for diffraction-limited imaging at wavelength of 1μm, which satisfies most science cases of RST in near infrared waveband.
Modal liquid crystal wavefront corrector.
Kotova, S; Kvashnin, M; Rakhmatulin, M; Zayakin, O; Guralnik, I; Klimov, N; Clark, P; Love, Gordon; Naumov, A; Saunter, C; Loktev, M; Vdovin, G; Toporkova, L
2002-11-04
Results are presented of the properties of a liquid crystal wavefront corrector for adaptive optics. The device is controlled using modal addressing in which case the device behaves more like a continuous facesheet deformable mirror than a segmented one. Furthermore, the width and shape of the influence functions are electrically controllable. We describe the construction of the device, the optical properties, and we show experimental results of low order aberration generation.
Telescope interferometers: an alternative to classical wavefront sensors
Henault, Francois
2008-01-01
Several types of Wavefront Sensors (WFS) are nowadays available in the field of Adaptive Optics (AO). Generally speaking, their basic principle consists in measuring slopes or curvatures of Wavefront Errors (WFE) transmitted by a telescope, subsequently reconstructing WFEs digitally. Such process, however, does not seem to be well suited for evaluating co-phasing or piston errors of future large segmented telescopes in quasi real-time. This communication presents an original, recently proposed technique for direct WFE sensing. The principle of the device, which is named "Telescope-Interferometer" (TI), is based on the addition of a reference optical arm into the telescope pupil plane. Then incident WFEs are deduced from Point Spread Function (PSF) measurements at the telescope focal plane. Herein are described two different types of TIs, and their performance are discussed in terms of intrinsic measurement accuracy and spatial resolution. Various error sources are studied by means of numerical simulations, am...
Stochastic dynamic equations on general time scales
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Martin Bohner
2013-02-01
Full Text Available In this article, we construct stochastic integral and stochastic differential equations on general time scales. We call these equations stochastic dynamic equations. We provide the existence and uniqueness theorem for solutions of stochastic dynamic equations. The crucial tool of our construction is a result about a connection between the time scales Lebesgue integral and the Lebesgue integral in the common sense.
Aronstein, David L.; Smith, J. Scott; Zielinski, Thomas P.; Telfer, Randal; Tournois, Severine C.; Moore, Dustin B.; Fienup, James R.
2016-01-01
The science instruments (SIs) comprising the James Webb Space Telescope (JWST) Integrated Science Instrument Module (ISIM) were tested in three cryogenic-vacuum test campaigns in the NASA Goddard Space Flight Center (GSFC)'s Space Environment Simulator (SES) test chamber. In this paper, we describe the results of optical wavefront-error performance characterization of the SIs. The wavefront error is determined using image-based wavefront sensing, and the primary data used by this process are focus sweeps, a series of images recorded by the instrument under test in its as-used configuration, in which the focal plane is systematically changed from one image to the next. High-precision determination of the wavefront error also requires several sources of secondary data, including 1) spectrum, apodization, and wavefront-error characterization of the optical ground-support equipment (OGSE) illumination module, called the OTE Simulator (OSIM), 2) F-number and pupil-distortion measurements made using a pseudo-nonredundant mask (PNRM), and 3) pupil geometry predictions as a function of SI and field point, which are complicated because of a tricontagon-shaped outer perimeter and small holes that appear in the exit pupil due to the way that different light sources are injected into the optical path by the OGSE. One set of wavefront-error tests, for the coronagraphic channel of the Near-Infrared Camera (NIRCam) Longwave instruments, was performed using data from transverse translation diversity sweeps instead of focus sweeps, in which a sub-aperture is translated and/or rotated across the exit pupil of the system. Several optical-performance requirements that were verified during this ISIM-level testing are levied on the uncertainties of various wavefront-error-related quantities rather than on the wavefront errors themselves. This paper also describes the methodology, based on Monte Carlo simulations of the wavefront-sensing analysis of focus-sweep data, used to establish
Broadband, Common-path, Interferometric Wavefront Sensor
Wallace, James Kent (Inventor)
2015-01-01
Hybrid sensors comprising Shack-Hartmann Wavefront Sensor (S-HWFS) and Zernike Wavefront Sensor (Z-WFS) capabilities are presented. The hybrid sensor includes a Z-WFS optically arranged in-line with a S-HWFS such that the combined wavefront sensor operates across a wide dynamic range and noise conditions. The Z-WFS may include the ability to introduce a dynamic phase shift in both transmissive and reflective modes.
Negating effects from sodium profile variations for TMT: the MOR truth wavefront sensor of NFIRAOS
Andersen, David R.; Conan, Rodolphe; Ellerbroek, Brent; Herriot, Glen; Véran, Jean-Pierre
2008-07-01
The Moderate Order Radial (MOR) Truth Wavefront Sensor (TWFS) of NFIRAOS, the facility AO system for TMT, is a visible light order 12x12 subaperture Shack-Hartmann WFS. Its role is to sense radial wavefront errors arising from variations in the Sodium layer profile that are not sensed by the on-instrument near infrared tip-tilt focus wavefront sensor at a sampling frequency on the order of one Herz. It works in concert with the High Order Low bandwidth (HOL) TWFS, which will use a 120x120 subaperture Shack-Hartmann WFS that senses slow variations in telescope flexure and the rotation of the pupil. Top-level requirements for NFIRAOS leave little margin for degradation in sky coverage or additional implementation wavefront errors introduced by the operation of the MOR TWFS. In this paper, we explore MOR TWFS design trade studies on the number of subapertures, sampling rate, the width of the MOR TWFS visible bandpass, and the split in light between the MOR and HOL TWFS, and present a design for a system which meets the top level requirements by not degrading the high sky coverage of NFIRAOS (50% sky coverage at the Galactic poles) and rejecting the radial modes with a residual wavefront error of 10nm.
X-ray grating interferometer for in situ and at-wavelength wavefront metrology.
Kayser, Yves; David, Christian; Flechsig, Uwe; Krempasky, Juraj; Schlott, Volker; Abela, Rafael
2017-01-01
A wavefront metrology setup based on the X-ray grating interferometry technique for spatially resolved, quantitative, in situ and at-wavelength measurements of the wavefront at synchrotron radiation and hard X-ray free-electron laser beamlines is reported. Indeed, the ever-increasing demands on the optical components to preserve the wavefront shape and the coherence of the delivered X-ray beam call for more and more sensitive diagnostic instruments. Thanks to its angular sensitivity, X-ray grating interferometry has been established in recent years as an adequate wavefront-sensing technique for quantitatively assessing the quality of the X-ray wavefront under working conditions and hence for the in situ investigation of X-ray optical elements. In order to characterize the optical elements at any given beamline by measuring the aberrations introduced in the wavefront, a transportable X-ray grating interferometry setup was realised at the Swiss Light Source (SLS). The instrument, which is expected to be a valuable tool for investigating the quality of the X-ray beam delivered at an endstation, will be described hereafter in terms of the hardware setup and the related data analysis procedure. Several exemplary experiments performed at the X05DA Optics beamline of the SLS will be presented.
Ma, Xingkun; Huang, Lei; Bian, Qi; Gong, Mali
2014-09-10
The wavefront correction ability of a deformable mirror with a multireflection waveguide was investigated and compared via simulations. By dividing a conventional actuator array into a multireflection waveguide that consisted of single-actuator units, an arbitrary actuator pattern could be achieved. A stochastic parallel perturbation algorithm was proposed to find the optimal actuator pattern for a particular aberration. Compared with conventional an actuator array, the multireflection waveguide showed significant advantages in correction of higher order aberrations.
CMOS-based Integrated Wavefront Sensor
De Lima Monteiro, D.W.
2002-01-01
This thesis addresses the design, implementation and performance of an integrated Hartmann-Shack wavefront sensor suitable for real-time operation and compatible with a standard technology. A wavefront sensor can be used for the detection of distortions in the profile of a light beam or of an optica
Kraenkel, R. A.; da Silva, D. J. Pamplona
2010-01-01
We consider the dynamics of a biological population described by the Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) equation in the case where the spatial domain consists of alternating favorable and adverse patches whose sizes are distributed randomly. For the one-dimensional case we define a stochastic analogue of the classical critical patch size. We address the issue of persistence of a population and we show that the minimum fraction of the length of favorable segments to the total length is always smaller in the stochastic case than in a periodic arrangement. In this sense, spatial stochasticity favors viability of a population.
Parasuraman, Ramviyas; Molinari, Luca; Kershaw, Keith; Di Castro, Mario; Masi, Alessandro; Ferre, Manuel
2014-01-01
The reliability of wireless communication in a network of mobile wireless robot nodes depends on the received radio signal strength (RSS). When the robot nodes are deployed in hostile environments with ionizing radiations (such as in some scientific facilities), there is a possibility that some electronic components may fail randomly (due to radiation effects), which causes problems in wireless connectivity. The objective of this paper is to maximize robot mission capabilities by maximizing the wireless network capacity and to reduce the risk of communication failure. Thus, in this paper, we consider a multi-node wireless tethering structure called the “server-relay-client” framework that uses (multiple) relay nodes in between a server and a client node. We propose a robust stochastic optimization (RSO) algorithm using a multi-sensor-based RSS sampling method at the relay nodes to efficiently improve and balance the RSS between the source and client nodes to improve the network capacity and to provide red...
Individual eye model based on wavefront aberration
Guo, Huanqing; Wang, Zhaoqi; Zhao, Qiuling; Quan, Wei; Wang, Yan
2005-03-01
Based on the widely used Gullstrand-Le Grand eye model, the individual human eye model has been established here, which has individual corneal data, anterior chamber depth and the eyeball depth. Furthermore, the foremost thing is that the wavefront aberration calculated from the individual eye model is equal to the eye's wavefront aberration measured with the Hartmann-shack wavefront sensor. There are four main steps to build the model. Firstly, the corneal topography instrument was used to measure the corneal surfaces and depth. And in order to input cornea into the optical model, high-order aspheric surface-Zernike Fringe Sag surface was chosen to fit the corneal surfaces. Secondly, the Hartmann-shack wavefront sensor, which can offer the Zernike polynomials to describe the wavefront aberration, was built to measure the wavefront aberration of the eye. Thirdly, the eye's axial lengths among every part were measured with A-ultrasonic technology. Then the data were input into the optical design software-ZEMAX and the crystalline lens's shapes were optimized with the aberration as the merit function. The individual eye model, which has the same wavefront aberrations with the real eye, is established.
Quirós-Pacheco, Fernando; Agapito, Guido; Riccardi, Armando; Esposito, Simone; Le Louarn, Miska; Marchetti, Enrico
2012-07-01
This paper presents the performance analysis based on numerical simulations of the Pyramid Wavefront sensor Module (PWM) to be included in ERIS, the new Adaptive Optics (AO) instrument for the Adaptive Optics Facility (AOF). We have analyzed the performance of the PWM working either in a low-order or in a high-order wavefront sensing mode of operation. We show that the PWM in the high-order sensing mode can provide SR > 90% in K band using bright guide stars under median seeing conditions (0.85 arcsec seeing and 15 m/s of wind speed). In the low-order sensing mode, the PWM can sense and correct Tip-Tilt (and if requested also Focus mode) with the precision required to assist the LGS observations to get an SR > 60% and > 20% in K band, using up to a ~16.5 and ~19.5 R-magnitude guide star, respectively.
Parasuraman, Ramviyas; Fabry, Thomas; Molinari, Luca; Kershaw, Keith; Di Castro, Mario; Masi, Alessandro; Ferre, Manuel
2014-12-12
The reliability of wireless communication in a network of mobile wireless robot nodes depends on the received radio signal strength (RSS). When the robot nodes are deployed in hostile environments with ionizing radiations (such as in some scientific facilities), there is a possibility that some electronic components may fail randomly (due to radiation effects), which causes problems in wireless connectivity. The objective of this paper is to maximize robot mission capabilities by maximizing the wireless network capacity and to reduce the risk of communication failure. Thus, in this paper, we consider a multi-node wireless tethering structure called the "server-relay-client" framework that uses (multiple) relay nodes in between a server and a client node. We propose a robust stochastic optimization (RSO) algorithm using a multi-sensor-based RSS sampling method at the relay nodes to efficiently improve and balance the RSS between the source and client nodes to improve the network capacity and to provide redundant networking abilities. We use pre-processing techniques, such as exponential moving averaging and spatial averaging filters on the RSS data for smoothing. We apply a receiver spatial diversity concept and employ a position controller on the relay node using a stochastic gradient ascent method for self-positioning the relay node to achieve the RSS balancing task. The effectiveness of the proposed solution is validated by extensive simulations and field experiments in CERN facilities. For the field trials, we used a youBot mobile robot platform as the relay node, and two stand-alone Raspberry Pi computers as the client and server nodes. The algorithm has been proven to be robust to noise in the radio signals and to work effectively even under non-line-of-sight conditions.
Directory of Open Access Journals (Sweden)
Ramviyas Parasuraman
2014-12-01
Full Text Available The reliability of wireless communication in a network of mobile wireless robot nodes depends on the received radio signal strength (RSS. When the robot nodes are deployed in hostile environments with ionizing radiations (such as in some scientific facilities, there is a possibility that some electronic components may fail randomly (due to radiation effects, which causes problems in wireless connectivity. The objective of this paper is to maximize robot mission capabilities by maximizing the wireless network capacity and to reduce the risk of communication failure. Thus, in this paper, we consider a multi-node wireless tethering structure called the “server-relay-client” framework that uses (multiple relay nodes in between a server and a client node. We propose a robust stochastic optimization (RSO algorithm using a multi-sensor-based RSS sampling method at the relay nodes to efficiently improve and balance the RSS between the source and client nodes to improve the network capacity and to provide redundant networking abilities. We use pre-processing techniques, such as exponential moving averaging and spatial averaging filters on the RSS data for smoothing. We apply a receiver spatial diversity concept and employ a position controller on the relay node using a stochastic gradient ascent method for self-positioning the relay node to achieve the RSS balancing task. The effectiveness of the proposed solution is validated by extensive simulations and field experiments in CERN facilities. For the field trials, we used a youBot mobile robot platform as the relay node, and two stand-alone Raspberry Pi computers as the client and server nodes. The algorithm has been proven to be robust to noise in the radio signals and to work effectively even under non-line-of-sight conditions.
Directory of Open Access Journals (Sweden)
Michele Meroni
2013-01-01
Full Text Available Multitemporal optical remote sensing constitutes a useful, cost efficient method for crop status monitoring over large areas. Modelers interested in yield monitoring can rely on past and recent observations of crop reflectance to estimate aboveground biomass and infer the likely yield. Therefore, in a framework constrained by information availability, remote sensing data to yield conversion parameters are to be estimated. Statistical models are suitable for this purpose, given their ability to deal with statistical errors. This paper explores the performance in yield estimation of various remote sensing indicators based on varying degrees of bio-physical insight, in interaction with statistical methods (linear regressions that rely on different hypotheses. Performances in estimating the temporal and spatial variability of yield, and implications of data scarcity in both dimensions are investigated. Jackknifed results (leave one year out are presented for the case of wheat yield regional estimation in Tunisia using the SPOT-VEGETATION instrument. Best performances, up to 0.8 of R2, are achieved using the most physiologically sound remote sensing indicator, in conjunction with statistical specifications allowing for parsimonious spatial adjustment of the parameters.
Stochastic longshore current dynamics
Restrepo, Juan M.; Venkataramani, Shankar
2016-12-01
We develop a stochastic parametrization, based on a 'simple' deterministic model for the dynamics of steady longshore currents, that produces ensembles that are statistically consistent with field observations of these currents. Unlike deterministic models, stochastic parameterization incorporates randomness and hence can only match the observations in a statistical sense. Unlike statistical emulators, in which the model is tuned to the statistical structure of the observation, stochastic parametrization are not directly tuned to match the statistics of the observations. Rather, stochastic parameterization combines deterministic, i.e physics based models with stochastic models for the "missing physics" to create hybrid models, that are stochastic, but yet can be used for making predictions, especially in the context of data assimilation. We introduce a novel measure of the utility of stochastic models of complex processes, that we call consistency of sensitivity. A model with poor consistency of sensitivity requires a great deal of tuning of parameters and has a very narrow range of realistic parameters leading to outcomes consistent with a reasonable spectrum of physical outcomes. We apply this metric to our stochastic parametrization and show that, the loss of certainty inherent in model due to its stochastic nature is offset by the model's resulting consistency of sensitivity. In particular, the stochastic model still retains the forward sensitivity of the deterministic model and hence respects important structural/physical constraints, yet has a broader range of parameters capable of producing outcomes consistent with the field data used in evaluating the model. This leads to an expanded range of model applicability. We show, in the context of data assimilation, the stochastic parametrization of longshore currents achieves good results in capturing the statistics of observation that were not used in tuning the model.
Wavefront Control and Image Restoration with Less Computing
Lyon, Richard G.
2010-01-01
PseudoDiversity is a method of recovering the wavefront in a sparse- or segmented- aperture optical system typified by an interferometer or a telescope equipped with an adaptive primary mirror consisting of controllably slightly moveable segments. (PseudoDiversity should not be confused with a radio-antenna-arraying method called pseudodiversity.) As in the cases of other wavefront- recovery methods, the streams of wavefront data generated by means of PseudoDiversity are used as feedback signals for controlling electromechanical actuators of the various segments so as to correct wavefront errors and thereby, for example, obtain a clearer, steadier image of a distant object in the presence of atmospheric turbulence. There are numerous potential applications in astronomy, remote sensing from aircraft and spacecraft, targeting missiles, sighting military targets, and medical imaging (including microscopy) through such intervening media as cells or water. In comparison with prior wavefront-recovery methods used in adaptive optics, PseudoDiversity involves considerably simpler equipment and procedures and less computation. For PseudoDiversity, there is no need to install separate metrological equipment or to use any optomechanical components beyond those that are already parts of the optical system to which the method is applied. In Pseudo- Diversity, the actuators of a subset of the segments or subapertures are driven to make the segments dither in the piston, tilt, and tip degrees of freedom. Each aperture is dithered at a unique frequency at an amplitude of a half wavelength of light. During the dithering, images on the focal plane are detected and digitized at a rate of at least four samples per dither period. In the processing of the image samples, the use of different dither frequencies makes it possible to determine the separate effects of the various dithered segments or apertures. The digitized image-detector outputs are processed in the spatial
Lai, Puxiang; Tay, Jian Wei; Wang, Lihong V
2014-01-01
Non-invasively focusing light into strongly scattering media, such as biological tissue, is highly desirable but challenging. Recently, wavefront shaping technologies guided by ultrasonic encoding or photoacoustic sensing have been developed to address this limitation. So far, these methods provide only acoustic diffraction-limited optical focusing. Here, we introduce nonlinear photoacoustic wavefront shaping (PAWS), which achieves optical diffraction-limited (i.e. single-speckle-grain) focusing in scattering media. We develop an efficient dual-pulse excitation approach to generate strong nonlinear photoacoustic (PA) signals based on the Grueneisen memory effect. These nonlinear PA signals are used as feedback to guide iterative wavefront optimization. By maximizing the amplitude of the nonlinear PA signal, light is effectively focused to a single optical speckle grain. Experimental results demonstrate a clear optical focus on the scale of 5-7 micrometers, which is ~10 times smaller than the acoustic focus in...
Wilby, Michael J; Snik, Frans; Korkiakoski, Visa; Pietrow, Alexander G M
2016-01-01
The raw coronagraphic performance of current high-contrast imaging instruments is limited by the presence of a quasi-static speckle (QSS) background, resulting from instrumental non-common path errors (NCPEs). Rapid development of efficient speckle subtraction techniques in data reduction has enabled final contrasts of up to 10-6 to be obtained, however it remains preferable to eliminate the underlying NCPEs at the source. In this work we introduce the coronagraphic Modal Wavefront Sensor (cMWS), a new wavefront sensor suitable for real-time NCPE correction. This pupil-plane optic combines the apodizing phase plate coronagraph with a holographic modal wavefront sensor, to provide simultaneous coronagraphic imaging and focal-plane wavefront sensing using the science point spread function. We first characterise the baseline performance of the cMWS via idealised closed-loop simulations, showing that the sensor successfully recovers diffraction-limited coronagraph performance over an effective dynamic range of +/...
Advanced Imaging Optics Utilizing Wavefront Coding.
Energy Technology Data Exchange (ETDEWEB)
Scrymgeour, David [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Boye, Robert [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Adelsberger, Kathleen [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-06-01
Image processing offers a potential to simplify an optical system by shifting some of the imaging burden from lenses to the more cost effective electronics. Wavefront coding using a cubic phase plate combined with image processing can extend the system's depth of focus, reducing many of the focus-related aberrations as well as material related chromatic aberrations. However, the optimal design process and physical limitations of wavefront coding systems with respect to first-order optical parameters and noise are not well documented. We examined image quality of simulated and experimental wavefront coded images before and after reconstruction in the presence of noise. Challenges in the implementation of cubic phase in an optical system are discussed. In particular, we found that limitations must be placed on system noise, aperture, field of view and bandwidth to develop a robust wavefront coded system.
Landrock, Clinton K.
Falls are the leading cause of all external injuries. Outcomes of falls include the leading cause of traumatic brain injury and bone fractures, and high direct medical costs in the billions of dollars. This work focused on developing three areas of enabling component technology to be used in postural control monitoring tools targeting the mitigation of falls. The first was an analysis tool based on stochastic fractal analysis to reliably measure levels of motor control. The second focus was on thin film wearable pressure sensors capable of relaying data for the first tool. The third was new thin film advanced optics for improving phototherapy devices targeting postural control disorders. Two populations, athletes and elderly, were studied against control groups. The results of these studies clearly show that monitoring postural stability in at-risk groups can be achieved reliably, and an integrated wearable system can be envisioned for both monitoring and treatment purposes. Keywords: electro-active polymer, ionic polymer-metal composite, postural control, motor control, fall prevention, sports medicine, fractal analysis, physiological signals, wearable sensors, phototherapy, photobiomodulation, nano-optics.
An Optical Wavefront Sensor Based on a Double Layer Microlens Array
Directory of Open Access Journals (Sweden)
Hsiang-Chun Wei
2011-10-01
Full Text Available In order to determine light aberrations, Shack-Hartmann optical wavefront sensors make use of microlens arrays (MLA to divide the incident light into small parts and focus them onto image planes. In this paper, we present the design and fabrication of long focal length MLA with various shapes and arrangements based on a double layer structure for optical wavefront sensing applications. A longer focal length MLA could provide high sensitivity in determining the average slope across each microlens under a given wavefront, and spatial resolution of a wavefront sensor is increased by numbers of microlenses across a detector. In order to extend focal length, we used polydimethysiloxane (PDMS above MLA on a glass substrate. Because of small refractive index difference between PDMS and MLA interface (UV-resin, the incident light is less refracted and focused in further distance. Other specific focal lengths could also be realized by modifying the refractive index difference without changing the MLA size. Thus, the wavefront sensor could be improved with better sensitivity and higher spatial resolution.
Wavefronts and Light Cones for Kerr Spacetimes
Frutos-Alfaro, Francisco; Mueller, Thomas; Adis, Daria
2014-01-01
We investigate the light propagation by means of simulations of wavefronts and light cones for Kerr spacetimes. Simulations of this kind give us a new insight to better understand the light propagation in presence of massive rotating black holes. A relevant result is that wavefronts are back scattered with winding around the black hole. To generate these visualizations, an interactive computer program with a graphical user interface, called JWFront, was written in Java.
Stochastic volatility and stochastic leverage
DEFF Research Database (Denmark)
Veraart, Almut; Veraart, Luitgard A. M.
This paper proposes the new concept of stochastic leverage in stochastic volatility models. Stochastic leverage refers to a stochastic process which replaces the classical constant correlation parameter between the asset return and the stochastic volatility process. We provide a systematic...... treatment of stochastic leverage and propose to model the stochastic leverage effect explicitly, e.g. by means of a linear transformation of a Jacobi process. Such models are both analytically tractable and allow for a direct economic interpretation. In particular, we propose two new stochastic volatility...... models which allow for a stochastic leverage effect: the generalised Heston model and the generalised Barndorff-Nielsen & Shephard model. We investigate the impact of a stochastic leverage effect in the risk neutral world by focusing on implied volatilities generated by option prices derived from our new...
Correlations between corneal and total wavefront aberrations
Mrochen, Michael; Jankov, Mirko; Bueeler, Michael; Seiler, Theo
2002-06-01
Purpose: Corneal topography data expressed as corneal aberrations are frequently used to report corneal laser surgery results. However, the optical image quality at the retina depends on all optical elements of the eye such as the human lens. Thus, the aim of this study was to investigate the correlations between the corneal and total wavefront aberrations and to discuss the importance of corneal aberrations for representing corneal laser surgery results. Methods: Thirty three eyes of 22 myopic subjects were measured with a corneal topography system and a Tschernig-type wavefront analyzer after the pupils were dilated to at least 6 mm in diameter. All measurements were centered with respect to the line of sight. Corneal and total wavefront aberrations were calculated up to the 6th Zernike order in the same reference plane. Results: Statistically significant correlations (p corneal and total wavefront aberrations were found for the astigmatism (C3,C5) and all 3rd Zernike order coefficients such as coma (C7,C8). No statistically significant correlations were found for all 4th to 6th order Zernike coefficients except for the 5th order horizontal coma C18 (p equals 0.003). On average, all Zernike coefficients for the corneal aberrations were found to be larger compared to Zernike coefficients for the total wavefront aberrations. Conclusions: Corneal aberrations are only of limited use for representing the optical quality of the human eye after corneal laser surgery. This is due to the lack of correlation between corneal and total wavefront aberrations in most of the higher order aberrations. Besides this, the data present in this study yield towards an aberration balancing between corneal aberrations and the optical elements within the eye that reduces the aberration from the cornea by a certain degree. Consequently, ideal customized ablations have to take both, corneal and total wavefront aberrations, into consideration.
Fast modulation and dithering on a pyramid wavefront sensor bench
van Kooten, Maaike; Bradley, Colin; Veran, Jean-Pierre; Herriot, Glen; Lardiere, Olivier
2016-07-01
A pyramid wavefront sensor (PWFS) bench has been setup at NRC-Herzberg (Victoria, Canada) to investigate, first, the feasibility of a double roof prism PWFS, and second, test the proposed pyramid wavefront sensing methodology to be used in NFIRAOS for the Thirty Meter Telescope. Traditional PWFS require shallow angles and strict apex tolerances, making them difficult to manufacture. Roof prisms, on the other hand, are common optical components and can easily be made to the desired specifications. Understanding the differences between a double roof prism PWFS and traditional PWFS will allow for the double roof prism PWFS to become more widely used as an alternative to the standard pyramid, especially in a laboratory setting. In this work, the response of the double roof prism PWFS as the amount of modulation is changed, is compared to an ideal PWFS modelled using the adaptive optics toolbox, OOMAO in MATLAB. The object oriented toolbox uses physical optics to model complete AO systems. Fast modulation and dithering using a PI mirror has been implemented using a micro-controller to drive the mirror and trigger the camera. The various trade offs of this scheme, in a controlled laboratory environment, are studied and reported.
Stochastic Shadowing and Stochastic Stability
Todorov, Dmitry
2014-01-01
The notion of stochastic shadowing property is introduced. Relations to stochastic stability and standard shadowing are studied. Using tent map as an example it is proved that, in contrast to what happens for standard shadowing, there are significantly non-uniformly hyperbolic systems that satisfy stochastic shadowing property.
Aronstein, David L.; Smith, J. S.; Zielinski, Thomas P.; Telfer, Randal; Tournois, Severine C.; Moore, Dustin B.; Fienup, James R.
2016-07-01
The science instruments (SIs) comprising the James Webb Space Telescope (JWST) Integrated Science Instrument Module (ISIM) were tested in three cryogenic-vacuum test campaigns in the NASA Goddard Space Flight Center (GSFC)'s Space Environment Simulator (SES) test chamber. In this paper, we describe the results of optical wavefront-error performance characterization of the SIs. The wavefront error is determined using image-based wavefront sensing, and the primary data used by this process are focus sweeps, a series of images recorded by the instrument under test in its as-used configuration, in which the focal plane is systematically changed from one image to the next. High-precision determination of the wavefront error also requires several sources of secondary data, including 1) spectrum, apodization, and wavefront-error characterization of the optical ground-support equipment (OGSE) illumination module, called the OTE Simulator (OSIM), 2) f/# and pupil-distortion measurements made using a pseudo-nonredundant mask (PNRM), and 3) pupil-geometry predictions for each SI field point tested, which are complicated because of a tricontagon-shaped outer perimeter and small holes that appear in the exit pupil due to the way that different light sources are injected into the optical path by the OGSE. One set of wavefront-error tests, for the coronagraphic channel of the Near-Infrared Camera (NIRCam) Longwave instruments, was performed using data from transverse-translation diversity (TTD) sweeps instead of focus sweeps, in which a subaperture is translated and/or rotated across the exit pupil of the system from one image to the next. Several optical-performance requirements that were verified during this ISIM Element-level testing are levied on the uncertainties of various wavefront-error-related quantities rather than on the wavefront errors themselves. This paper also gives an overview of the methodology, based on Monte Carlo simulations of the wavefront-sensing analysis
The MCAO systems within LINC-NIRVANA: control aspects beyond wavefront correction
Bertram, T.; Arcidiacono, C.; Berwein, J.; Bizenberger, P.; Briegel, F.; Diolaiti, E.; Farinato, J.; Gässler, W.; Herbst, T. M.; Hofferbert, R.; Kittmann, F.; Kürster, M.; Ragazzoni, R.; Schreiber, L.; Trowitzsch, J.; Viotto, V.
2010-07-01
LINC-NIRVANA is the near-infrared homothetic imaging camera for the Large Binocular Telescope. Once operational, it will provide an unprecedented combination of angular resolution, sensitivity and field of view. Its layer-oriented MCAO systems (one for each arm of the interferometer) are conjugated to the ground layer and an additional layer in the upper atmosphere. In this contribution MCAO wavefront control is discussed in the context of the overall control scheme for LINC-NIRVANA. Special attention is paid to a set of auxiliary control tasks which are mandatory for MCAO operation: The Fields of View of each wavefront sensor in the instrument have to be derotated independent from each other and independently from the science field. Any wavefront information obtained by the sensors has to be matched to the time invariant modes of the deformable mirrors in the system. The tip/tilt control scheme is outlined, in which atmospheric, but also instrumental tip/tilt corrections are sensed with the high layer wavefront sensor and corrected by the adaptive secondary mirror of the LBT. Slow image motion effects on the science detector have to be considered, which are caused by flexure in the non-common path between AO and the science camera, atmospheric differential refraction, and alignment tolerances of the derotators. Last but not least: The sensor optics (pyramids) have to be accurately positioned at the images of natural reference stars.
Liquid crystal wavefront corrector on silicon
Loktev, M.; Vdovin, G.; Nanver, L.
2005-01-01
A reflective-type liquid crystal (LC) wavefront corrector with modal addressing is described. The corrector’s backplane has an array of pixel electrodes interconnected by a network of discrete resistors. The resistive network serves to form the local voltage profile that controls the phase distribut
Improved wavefront reconstruction algorithm from slope measurements
Phuc, Phan Huy; Manh, Nguyen The; Rhee, Hyug-Gyo; Ghim, Young-Sik; Yang, Ho-Soon; Lee, Yun-Woo
2017-03-01
In this paper, we propose a wavefront reconstruction algorithm from slope measurements based on a zonal method. In this algorithm, the slope measurement sampling geometry used is the Southwell geometry, in which the phase values and the slope data are measured at the same nodes. The proposed algorithm estimates the phase value at a node point using the slope measurements of eight points around the node, as doing so is believed to result in better accuracy with regard to the wavefront. For optimization of the processing time, a successive over-relaxation method is applied to iteration loops. We use a trial-and-error method to determine the best relaxation factor for each type of wavefront in order to optimize the iteration time and, thus, the processing time of the algorithm. Specifically, for a circularly symmetric wavefront, the convergence rate of the algorithm can be improved by using the result of a Fourier Transform as an initial value for the iteration. Various simulations are presented to demonstrate the improvements realized when using the proposed algorithm. Several experimental measurements of deflectometry are also processed by using the proposed algorithm.
A modified phase diversity wavefront sensor with a diffraction grating
Institute of Scientific and Technical Information of China (English)
Luo Qun; Huang Lin-Hai; Gu Nai-Ting; Rao Chang-Hui
2012-01-01
The phase diversity wavefront sensor is one of the tools used to estimate wavefront aberration,and it is often used as a wavefront sensor in adaptive optics systems.However,the performance of the traditional phase diversity wavefront sensor is limited by the accuracy and dynamic ranges of the intensity distribution at the focus and defocus positions of the CCD camera.In this paper,a modified phase diversity wavefront sensor based on a diffraction grating is proposed to improve the ability to measure the wavefront aberration with larger amplitude and higher spatial frequency.The basic principle and the optics construction of the proposed method are also described in detail.The noise propagation property of the proposed method is also analysed by using the numerical simulation method,and comparison between the diffraction grating phase diversity wavefront sensor and the traditional phase diversity wavefront sensor is also made.The simulation results show that the diffraction grating phase diversity wavefront sensor can obviously improve the ability to measure the wavefront aberration,especially the wavefront aberration with larger amplitude and higher spatial frequency.
Optical wavefront distortion due to supersonic flow fields
Institute of Scientific and Technical Information of China (English)
CHEN ZhiQiang; FU Song
2009-01-01
The optical wavefront distortion caused by a supersonic flow field around a half model of blunt nose cone was studied in a wind tunnel. A Shack-Hartmann wavefront sensor was used to measure the dis-totted optical wavefront. Interesting optical parameters including the peak variation (PV), root of mean square (RMS) and Strehl ratio were obtained under different test conditions during the experiment. During the establishing process of the flow field in the wind tunnel test section, the wavefront shape was unstable. However after the flow field reached the steady flow state, the wavefront shape kept sta-ble, and the relative error of wavefront aberration was found small. The Shack-Hartmann wavefront sensor developed was proved to be credible in measuring quantitatively the optical phase change of light traveling through the flow field around model window.
Vyas, Akondi; Prasad, B Raghavendra
2010-01-01
We present the details of predicting atmospheric turbulence by mining Zernike moment data obtained from simulations as well as experiments. Temporally correlated optical wave-fronts were simulated such that they followed Kolmogorov phase statistics. The wave-fronts reconstructed either by modal or zonal methods can be represented in terms of Zernike moments. The servo lag error in adaptive optics is minimized by predicting Zernike moments in the near future by using the data from the immediate past. It is shown statistically that the prediction accuracy depends on the number of past phase screens used for prediction and servo lag time scales. The algorithm is optimized in terms of these parameters for real time and efficient operation of the adaptive optics system. On an average, we report more than 3% improvement in the wave-front compensation after prediction. This analysis helps in optimizing the design parameters for sensing and correction in closed loop adaptive optics systems.
Wang, Jinyu; Leger, Jean-Francois; Binding, Jonas; Boccara, Claude; Gigan, Sylvain; Bourdieu, Laurent
2012-03-01
Wavefront distortions due to refractive index mismatch and tissue inhomogeneity may limit the resolution, contrast, signal strength and achievable imaging depth of microscope. Traditional Shack-Hartmann wavefront sensors can't be used in strongly scattering biological samples since there is no selection of the ballistic photons originating from the reference point in the sample amongst all the backscattered photons. In contrast, coherence-gated wavefront sensing (CGWS) allows the fast measurement of aberrations in scattering samples and therefore should permit adaptive corrections. We have implemented a new CGWS scheme based on a Linnik interferometer with Super Luminescent Emission Diode as low temporal coherence light source. Compared to the previously described CGWS system based on a femtosecond laser, its main advantages are the automatic compensation of dispersion between the two arms and its easy implementation on any microscope. The configuration of virtual Shack-Hartmann wavefront sensor for wavefront reconstruction was optimized, and the measurement precision was analyzed when multiple scattering was not negligible. In fresh rat brain slices, we successfully measured up to about 400 μm depth a known defocus aberration, obtained by axially displacing the coherence gate with respect to the actual focus in the sample.
Experimental study of an optimised Pyramid wave-front sensor for Extremely Large Telescopes
Bond, Charlotte Z.; El Hadi, Kacem; Sauvage, Jean-François; Correia, Carlos; Fauvarque, Olivier; Rabaud, Didier; Lamb, Masen; Neichel, Benoit; Fusco, Thierry
2016-07-01
Over the last few years the Laboratoire d'Astrophysique de Marseille (LAM) has been heavily involved in R&D for adaptive optics systems dedicated to future large telescopes, particularly in preparation for the European Extremely Large Telescope (E-ELT). Within this framework an investigation into a Pyramid wave-front sensor is underway. The Pyramid sensor is at the cutting edge of high order, high precision wave-front sensing for ground based telescopes. Investigations have demonstrated the ability to achieve a greater sensitivity than the standard Shack-Hartmann wave-front sensor whilst the implementation of a Pyramid sensor on the Large Binocular Telescope (LBT) has provided compelling operational results.1, 2 The Pyramid now forms part of the baseline for several next generation Extremely Large Telescopes (ELTs). As such its behaviour under realistic operating conditions must be further understood in order to optimise performance. At LAM a detailed investigation into the performance of the Pyramid aims to fully characterise the behaviour of this wave-front sensor in terms of linearity, sensitivity and operation. We have implemented a Pyramid sensor using a high speed OCAM2 camera (with close to 0 readout noise and a frame rate of 1.5kHz) in order to study the performance of the Pyramid within a full closed loop adaptive optics system. This investigation involves tests on all fronts, from theoretical models and numerical simulations to experimental tests under controlled laboratory conditions, with an aim to fully understand the Pyramid sensor in both modulated and non-modulated configurations. We include results demonstrating the linearity of the Pyramid signals, compare measured interaction matrices with those derived in simulation and evaluate the performance in closed loop operation. The final goal is to provide an on sky comparison between the Pyramid and a Shack-Hartmann wave-front sensor, at Observatoire de la Côte d'Azur (ONERA-ODISSEE bench). Here we
Development of a hard x-ray wavefront sensor for the EuXFEL
Berujon, Sebastien; Ziegler, Eric; Cojocaru, Ruxandra; Martin, Thierry
2017-05-01
We present developments on a hard X-ray wavefront sensing instrument for characterizing and monitoring the beam of the European X-ray Free Electron Lasers (EuXFEL). The pulsed nature of the intense X-ray beam delivered by this new class of facility gives rise to strong challenges for the optics and their diagnostic. In the frame of the EUCALL project Work Package 7, we are developing a sensor able to observe the beam in the X-ray energy range [8-40] keV without altering it. The sensor is based on the speckle tracking principle and employs two semi-transparent optics optimized such that their X-ray absorption is reduced. Furthermore, this instrument requires a scattering object with small random features placed in the beam and two cameras to record images of the beam at two different propagation distances. The analysis of the speckle pattern and its distortion from one image to the other allows absolute or differential wavefront recovery from pulse to pulse. Herein, we introduce the stakes and challenges of wavefront sensing at an XFEL source and explain the strategies adopted to fulfil the high requirements set by such a source.
Cryogenic wavefront correction using membrane deformable mirrors.
Dyson, H; Sharples, R; Dipper, N; Vdovin, G
2001-01-01
Micro-machined membrane deformable mirrors (MMDMs) are being evaluated for their suitability as wavefront correctors at cryogenic temperatures. Presented here are experimental results for the change in the initial mirror figure of 37-channel MMDMs from OKO Technologies upon cooling to T=78K. The changes in the influence functions are also explored. Of the sample of 3 mirrors tested, one was found to have sufficiently small initial static aberrations to be useful as a wavefront corrector at this temperature. The influence functions at T=78K were found to be similar in shape to both those at room temperature and theoretical predictions of the MMDMs surface shape. The magnitude of the surface deflection at T=78K was reduced by around 20% compared with room temperature values.
Propofol effects on atrial fibrillation wavefront delays.
Cervigón, Raquel; Moreno, Javier; Millet, José; Pérez-Villacastín, Julián; Castells, Francisco
2010-08-01
Since the cardiac activity during atrial fibrillation (AF) may be influenced by autonomic modulations, in this study, a novel method to quantify the effects of the most common anesthetic agent (propofol) in AF ablation procedures is introduced. This study has two main objectives: first, to assess whether the sedation earlier to radio frequency ablation affects the arrhythmia itself, and second, to provide new information that contributes to a better understanding of the influence of the autonomic nervous system on AF. The methodology presented is based on the measurement of synchronization and delay indexes between two atrial activations at adjacent intracavitary electrodes. These parameters aim to estimate whether two activations at different sites may be caused by the same propagating wavefront, or otherwise, are the consequence of independent wavefronts. The results showed that the mentioned indexes have a different behavior at both atria: the right atrium becomes more synchronized with propofol administration, whereas the synchronization index decreases at the left atrium.
Microgenetic optimization algorithm for optimal wavefront shaping
Anderson, Benjamin R; Gunawidjaja, Ray; Eilers, Hergen
2015-01-01
One of the main limitations of utilizing optimal wavefront shaping in imaging and authentication applications is the slow speed of the optimization algorithms currently being used. To address this problem we develop a micro-genetic optimization algorithm ($\\mu$GA) for optimal wavefront shaping. We test the abilities of the $\\mu$GA and make comparisons to previous algorithms (iterative and simple-genetic) by using each algorithm to optimize transmission through an opaque medium. From our experiments we find that the $\\mu$GA is faster than both the iterative and simple-genetic algorithms and that both genetic algorithms are more resistant to noise and sample decoherence than the iterative algorithm.
Wavefront reconstruction using computer-generated holograms
Schulze, Christian; Flamm, Daniel; Schmidt, Oliver A.; Duparré, Michael
2012-02-01
We propose a new method to determine the wavefront of a laser beam, based on modal decomposition using computer-generated holograms (CGHs). Thereby the beam under test illuminates the CGH with a specific, inscribed transmission function that enables the measurement of modal amplitudes and phases by evaluating the first diffraction order of the hologram. Since we use an angular multiplexing technique, our method is innately capable of real-time measurements of amplitude and phase, yielding the complete information about the optical field. A measurement of the Stokes parameters, respectively of the polarization state, provides the possibility to calculate the Poynting vector. Two wavefront reconstruction possibilities are outlined: reconstruction from the phase for scalar beams and reconstruction from the Poynting vector for inhomogeneously polarized beams. To quantify single aberrations, the reconstructed wavefront is decomposed into Zernike polynomials. Our technique is applied to beams emerging from different kinds of multimode optical fibers, such as step-index, photonic crystal and multicore fibers, whereas in this work results are exemplarily shown for a step-index fiber and compared to a Shack-Hartmann measurement that serves as a reference.
Fiber coupler end face wavefront surface metrology
Compertore, David C.; Ignatovich, Filipp V.; Marcus, Michael A.
2015-09-01
Despite significant technological advances in the field of fiber optic communications, one area remains surprisingly `low-tech': fiber termination. In many instances it involves manual labor and subjective visual inspection. At the same time, high quality fiber connections are one of the most critical parameters in constructing an efficient communication link. The shape and finish of the fiber end faces determines the efficiency of a connection comprised of coupled fiber end faces. The importance of fiber end face quality becomes even more critical for fiber connection arrays and for in the field applications. In this article we propose and demonstrate a quantitative inspection method for the fiber connectors using reflected wavefront technology. The manufactured and polished fiber tip is illuminated by a collimated light from a microscope objective. The reflected light is collected by the objective and is directed to a Shack-Hartmann wavefront sensor. A set of lenses is used to create the image of the fiber tip on the surface of the sensor. The wavefront is analyzed by the sensor, and the measured parameters are used to obtain surface properties of the fiber tip, and estimate connection loss. For example, defocus components in the reflected light indicate the presence of bow in the fiber end face. This inspection method provides a contact-free approach for quantitative inspection of fiber end faces and for estimating the connection loss, and can potentially be integrated into a feedback system for automated inspection and polishing of fiber tips and fiber tip arrays.
McKean, Henry P
2005-01-01
This little book is a brilliant introduction to an important boundary field between the theory of probability and differential equations. -E. B. Dynkin, Mathematical Reviews This well-written book has been used for many years to learn about stochastic integrals. The book starts with the presentation of Brownian motion, then deals with stochastic integrals and differentials, including the famous Itô lemma. The rest of the book is devoted to various topics of stochastic integral equations, including those on smooth manifolds. Originally published in 1969, this classic book is ideal for supplemen
Parzen, Emanuel
2015-01-01
Well-written and accessible, this classic introduction to stochastic processes and related mathematics is appropriate for advanced undergraduate students of mathematics with a knowledge of calculus and continuous probability theory. The treatment offers examples of the wide variety of empirical phenomena for which stochastic processes provide mathematical models, and it develops the methods of probability model-building.Chapter 1 presents precise definitions of the notions of a random variable and a stochastic process and introduces the Wiener and Poisson processes. Subsequent chapters examine
Schneider, Johannes J
2007-01-01
This book addresses stochastic optimization procedures in a broad manner. The first part offers an overview of relevant optimization philosophies; the second deals with benchmark problems in depth, by applying a selection of optimization procedures. Written primarily with scientists and students from the physical and engineering sciences in mind, this book addresses a larger community of all who wish to learn about stochastic optimization techniques and how to use them.
Fractional Smoothness of Some Stochastic Integrals
Institute of Scientific and Technical Information of China (English)
Peng XIE; Xi Cheng ZHANG
2007-01-01
We study the fractional smoothness in the sense of Malliavin calculus of stochastic integralsof the form ∫10 φ(Xs)d Xs,where Xs is a semimartingale and φ belongs to some fractional Sobolev spaceover R.
Auto gain control of EMCCD in Shack-Hartmann wavefront sensor for adaptive optics
Zhu, Zhaoyi; Li, Dayu; Hu, Lifa; Mu, QuanQuan; Cao, Zhaoliang; Wang, Yukun; Wang, Shaoxin; Xuan, Li
2016-12-01
Electron multiplying charge-coupled-device (EMCCD) applied in Shack-Hartmann wavefront sensor (S-H WFS) makes the wavefront sensing more efficient for adaptive optics (AO). However when the brightness of the observed target changes in large ranges in a few minutes, a fixed electron multiplying (EM) gain may not be optimum. Thus an auto-gain-control (AGC) method based on the spots image of the S-H WFS is proposed. The designed control value is the average value of the maximum signals of all the light spots in a frame. It has been demonstrated in the experiments that the control value is sensitive to the change of the target brightness, and is stable in the presence of detecting noises and turbulence influence. The goal value for control is predetermined based on the linear relation of the signal with the EM gain and the number of photons collected in sub-apertures. The conditions of the self-protection of the EMCCD are also considered for the goal value. Simulations and experiments indicate that the proposed control method is efficient, and keeps the sensing in a high SNR which reaches the upper SNR limit when sensing with EMCCD. The self-protection of the EMCCD is avoided during the whole sensing process.
Measuring optical transmission matrices by wavefront shaping
Yoon, Jonghee; Park, Jongchan; Park, YongKeun
2015-01-01
We introduce a simple but practical method to measure the optical transmission matrix (TM) of complex media. The optical TM of a complex medium is obtained by modulating the wavefront of a beam impinging on the complex medium and imaging the transmitted full-field speckle intensity patterns. Using the retrieved TM, we demonstrate the generation and linear combination of multiple foci on demand through the complex medium. This method will be used as a versatile tool for coherence control of waves through turbid media.
Closed-loop focal plane wavefront control with the SCExAO instrument
Martinache, Frantz; Guyon, Olivier
2016-01-01
This article describes the implementation of a focal plane based wavefront control loop on the high-contrast imaging instrument SCExAO (Subaru Coronagraphic Extreme Adaptive Optics). The sensor relies on the Fourier analysis of conventional focal-plane images acquired after an asymmetric mask is introduced in the pupil of the instrument. This absolute sensor is used here in a closed-loop to compensate the non-common path errors that normally affects any imaging system relying on an upstream adaptive optics system.This specific implementation was used to control low order modes corresponding to eight zernike modes (from focus to spherical). This loop was successfully run on-sky at the Subaru Telescope and is used to offset the SCExAO deformable mirror shape used as a zero-point by the high-order wavefront sensor. The paper precises the range of errors this wavefront sensing approach can operate within and explores the impact of saturation of the data and how it can be bypassed, at a cost in performance. Beyond...
Integration and bench testing for the GRAVITY Coudé IR adaptive optics (CIAO) wavefront sensor
Deen, C.; Yang, P.; Huber, A.; Suarez-Valles, M.; Hippler, S.; Brandner, W.; Gendron, E.; Clénet, Y.; Kendrew, S.; Glauser, A.; Klein, R.; Laun, W.; Lenzen, R.; Neumann, U.; Panduro, J.; Ramos, J.; Rohloff, R.-R.; Salzinger, A.; Zimmerman, N.; Henning, T.; Perraut, K.; Perrin, G.; Straubmeier, C.; Amorim, A.; Eisenhauer, F.
2014-08-01
GRAVITY, a second generation instrument for the Very Large Telescope Interferometer (VLTI), will provide an astrometric precision of order 10 micro-arcseconds, an imaging resolution of 4 milli-arcseconds, and low/medium resolution spectro-interferometry. These improvements to the VLTI represent a major upgrade to its current infrared interferometric capabilities, allowing detailed study of obscured environments (e.g. the Galactic Center, young dusty planet-forming disks, dense stellar cores, AGN, etc...). Crucial to the final performance of GRAVITY, the Coudé IR Adaptive Optics (CIAO) system will correct for the effects of the atmosphere at each of the VLT Unit Telescopes. CIAO consists of four new infrared Shack-Hartmann wavefront sensors (WFS) and associated real-time computers/software which will provide infrared wavefront sensing from 1.45-2.45 microns, allowing AO corrections even in regions where optically bright reference sources are scarce. We present here the latest progress on the GRAVITY wavefront sensors. We describe the adaptation and testing of a light-weight version of the ESO Standard Platform for Adaptive optics Real Time Applications (SPARTA-Light) software architecture to the needs of GRAVITY. We also describe the latest integration and test milestones for construction of the initial wave front sensor.
Optimization-based wavefront sensorless adaptive optics for multiphoton microscopy
Antonello, J.; Werkhoven, T. van; Verhaegen, M.; Truong, H.H.; Keller, C.U.; Gerritsen, H.C.
2014-01-01
Optical aberrations have detrimental effects in multiphoton microscopy. These effects can be curtailed by implementing model-based wavefront sensorless adaptive optics, which only requires the addition of a wavefront shaping device, such as a deformable mirror (DM) to an existing microscope. The abe
The National Ignition Facility (NIF) wavefront control system
Energy Technology Data Exchange (ETDEWEB)
Van Atta, L; Bliss, E; Bruns, D; Feldman, M; Grey, A; Henesian, M; J; Koch, J; LaFiandra, C; Lawson; Sacks, R; Salmon, T; Toeppen, J; Winters, S; Woods, B; Zacharias, R
1998-08-17
A wavefront control system will be employed on NIF to correct beam aberrations that otherwise would limit the minimum target focal spot size. For most applications, NIF requires a focal spot that is a few times the diffraction limit. Sources of aberrations that must be corrected include prompt pump-induced distortions in the laser slabs, thermal distortions in the laser slabs from previous shots, manufacturing figure errors in the optics, beam off-axis effects, gas density variations, and gravity, mounting, and coating- induced optic distortions. The NIF Wavefront Control System consists of five subsystems: 1) a deformable mirror, 2) a wavefront sensor, 3) a computer controller, 4) a wavefront reference system, and 5) a system of fast actuators to allow the wavefront control system to operate to within one second of the laser shot. The system includes the capability for in situ calibrations and operates in closed loop prior to the shot. Shot wavefront data is recorded. This paper describes the function, realization, and performance of each wavefront control subsystem. Subsystem performance will be characterized by computer models and by test results. The focal spot improvement in the NIF laser system effected by the wavefront control system will be characterized through computer models.
Geometry of fast magnetosonic rays, wavefronts and shock waves
Núñez, Manuel
2016-11-01
Fast magnetosonic waves in a two-dimensional plasma are studied in the geometrical optics approximation. The geometry of rays and wavefronts influences decisively the formation and ulterior evolution of shock waves. It is shown that the curvature of the curve where rays start and the angle between rays and wavefronts are the main parameters governing a wide variety of possible outcomes.
Improving active space telescope wavefront control using predictive thermal modeling
Gersh-Range, Jessica; Perrin, Marshall D.
2015-01-01
Active control algorithms for space telescopes are less mature than those for large ground telescopes due to differences in the wavefront control problems. Active wavefront control for space telescopes at L2, such as the James Webb Space Telescope (JWST), requires weighing control costs against the benefits of correcting wavefront perturbations that are a predictable byproduct of the observing schedule, which is known and determined in advance. To improve the control algorithms for these telescopes, we have developed a model that calculates the temperature and wavefront evolution during a hypothetical mission, assuming the dominant wavefront perturbations are due to changes in the spacecraft attitude with respect to the sun. Using this model, we show that the wavefront can be controlled passively by introducing scheduling constraints that limit the allowable attitudes for an observation based on the observation duration and the mean telescope temperature. We also describe the implementation of a predictive controller designed to prevent the wavefront error (WFE) from exceeding a desired threshold. This controller outperforms simpler algorithms even with substantial model error, achieving a lower WFE without requiring significantly more corrections. Consequently, predictive wavefront control based on known spacecraft attitude plans is a promising approach for JWST and other future active space observatories.
Chang, Mou-Hsiung
2015-01-01
The classical probability theory initiated by Kolmogorov and its quantum counterpart, pioneered by von Neumann, were created at about the same time in the 1930s, but development of the quantum theory has trailed far behind. Although highly appealing, the quantum theory has a steep learning curve, requiring tools from both probability and analysis and a facility for combining the two viewpoints. This book is a systematic, self-contained account of the core of quantum probability and quantum stochastic processes for graduate students and researchers. The only assumed background is knowledge of the basic theory of Hilbert spaces, bounded linear operators, and classical Markov processes. From there, the book introduces additional tools from analysis, and then builds the quantum probability framework needed to support applications to quantum control and quantum information and communication. These include quantum noise, quantum stochastic calculus, stochastic quantum differential equations, quantum Markov semigrou...
Stochastic partial differential equations
Chow, Pao-Liu
2014-01-01
Preliminaries Introduction Some Examples Brownian Motions and Martingales Stochastic Integrals Stochastic Differential Equations of Itô Type Lévy Processes and Stochastic IntegralsStochastic Differential Equations of Lévy Type Comments Scalar Equations of First Order Introduction Generalized Itô's Formula Linear Stochastic Equations Quasilinear Equations General Remarks Stochastic Parabolic Equations Introduction Preliminaries Solution of Stochastic Heat EquationLinear Equations with Additive Noise Some Regularity Properties Stochastic Reaction-Diffusion Equations Parabolic Equations with Grad
Stochastic Constraint Programming
Walsh, Toby
2009-01-01
To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables (which follow a probability distribution). They combine together the best features of traditional constraint satisfaction, stochastic integer programming, and stochastic satisfiability. We give a semantics for stochastic constraint programs, and propose a number...
Wilby, M. J.; Keller, C. U.; Snik, F.; Korkiakoski, V.; Pietrow, A. G. M.
2017-01-01
The raw coronagraphic performance of current high-contrast imaging instruments is limited by the presence of a quasi-static speckle (QSS) background, resulting from instrumental Non-Common Path Errors (NCPEs). Rapid development of efficient speckle subtraction techniques in data reduction has enabled final contrasts of up to 10-6 to be obtained, however it remains preferable to eliminate the underlying NCPEs at the source. In this work we introduce the coronagraphic Modal Wavefront Sensor (cMWS), a new wavefront sensor suitable for real-time NCPE correction. This combines the Apodizing Phase Plate (APP) coronagraph with a holographic modal wavefront sensor to provide simultaneous coronagraphic imaging and focal-plane wavefront sensing with the science point-spread function. We first characterise the baseline performance of the cMWS via idealised closed-loop simulations, showing that the sensor is able to successfully recover diffraction-limited coronagraph performance over an effective dynamic range of ±2.5 radians root-mean-square (rms) wavefront error within 2-10 iterations, with performance independent of the specific choice of mode basis. We then present the results of initial on-sky testing at the William Herschel Telescope, which demonstrate that the sensor is capable of NCPE sensing under realistic seeing conditions via the recovery of known static aberrations to an accuracy of 10 nm (0.1 radians) rms error in the presence of a dominant atmospheric speckle foreground. We also find that the sensor is capable of real-time measurement of broadband atmospheric wavefront variance (50% bandwidth, 158 nm rms wavefront error) at a cadence of 50 Hz over an uncorrected telescope sub-aperture. When combined with a suitable closed-loop adaptive optics system, the cMWS holds the potential to deliver an improvement of up to two orders of magnitude over the uncorrected QSS floor. Such a sensor would be eminently suitable for the direct imaging and spectroscopy of
Energy Technology Data Exchange (ETDEWEB)
Bisognano, J.; Leemann, C.
1982-03-01
Stochastic cooling is the damping of betatron oscillations and momentum spread of a particle beam by a feedback system. In its simplest form, a pickup electrode detects the transverse positions or momenta of particles in a storage ring, and the signal produced is amplified and applied downstream to a kicker. The time delay of the cable and electronics is designed to match the transit time of particles along the arc of the storage ring between the pickup and kicker so that an individual particle receives the amplified version of the signal it produced at the pick-up. If there were only a single particle in the ring, it is obvious that betatron oscillations and momentum offset could be damped. However, in addition to its own signal, a particle receives signals from other beam particles. In the limit of an infinite number of particles, no damping could be achieved; we have Liouville's theorem with constant density of the phase space fluid. For a finite, albeit large number of particles, there remains a residue of the single particle damping which is of practical use in accumulating low phase space density beams of particles such as antiprotons. It was the realization of this fact that led to the invention of stochastic cooling by S. van der Meer in 1968. Since its conception, stochastic cooling has been the subject of much theoretical and experimental work. The earliest experiments were performed at the ISR in 1974, with the subsequent ICE studies firmly establishing the stochastic cooling technique. This work directly led to the design and construction of the Antiproton Accumulator at CERN and the beginnings of p anti p colliding beam physics at the SPS. Experiments in stochastic cooling have been performed at Fermilab in collaboration with LBL, and a design is currently under development for a anti p accumulator for the Tevatron.
Stochastic geometry for image analysis
Descombes, Xavier
2013-01-01
This book develops the stochastic geometry framework for image analysis purpose. Two main frameworks are described: marked point process and random closed sets models. We derive the main issues for defining an appropriate model. The algorithms for sampling and optimizing the models as well as for estimating parameters are reviewed. Numerous applications, covering remote sensing images, biological and medical imaging, are detailed. This book provides all the necessary tools for developing an image analysis application based on modern stochastic modeling.
Probability, Statistics, and Stochastic Processes
Olofsson, Peter
2011-01-01
A mathematical and intuitive approach to probability, statistics, and stochastic processes This textbook provides a unique, balanced approach to probability, statistics, and stochastic processes. Readers gain a solid foundation in all three fields that serves as a stepping stone to more advanced investigations into each area. This text combines a rigorous, calculus-based development of theory with a more intuitive approach that appeals to readers' sense of reason and logic, an approach developed through the author's many years of classroom experience. The text begins with three chapters that d
Eichhorn, Ralf; Aurell, Erik
2014-04-01
'Stochastic thermodynamics as a conceptual framework combines the stochastic energetics approach introduced a decade ago by Sekimoto [1] with the idea that entropy can consistently be assigned to a single fluctuating trajectory [2]'. This quote, taken from Udo Seifert's [3] 2008 review, nicely summarizes the basic ideas behind stochastic thermodynamics: for small systems, driven by external forces and in contact with a heat bath at a well-defined temperature, stochastic energetics [4] defines the exchanged work and heat along a single fluctuating trajectory and connects them to changes in the internal (system) energy by an energy balance analogous to the first law of thermodynamics. Additionally, providing a consistent definition of trajectory-wise entropy production gives rise to second-law-like relations and forms the basis for a 'stochastic thermodynamics' along individual fluctuating trajectories. In order to construct meaningful concepts of work, heat and entropy production for single trajectories, their definitions are based on the stochastic equations of motion modeling the physical system of interest. Because of this, they are valid even for systems that are prevented from equilibrating with the thermal environment by external driving forces (or other sources of non-equilibrium). In that way, the central notions of equilibrium thermodynamics, such as heat, work and entropy, are consistently extended to the non-equilibrium realm. In the (non-equilibrium) ensemble, the trajectory-wise quantities acquire distributions. General statements derived within stochastic thermodynamics typically refer to properties of these distributions, and are valid in the non-equilibrium regime even beyond the linear response. The extension of statistical mechanics and of exact thermodynamic statements to the non-equilibrium realm has been discussed from the early days of statistical mechanics more than 100 years ago. This debate culminated in the development of linear response
Crisan, Dan
2011-01-01
"Stochastic Analysis" aims to provide mathematical tools to describe and model high dimensional random systems. Such tools arise in the study of Stochastic Differential Equations and Stochastic Partial Differential Equations, Infinite Dimensional Stochastic Geometry, Random Media and Interacting Particle Systems, Super-processes, Stochastic Filtering, Mathematical Finance, etc. Stochastic Analysis has emerged as a core area of late 20th century Mathematics and is currently undergoing a rapid scientific development. The special volume "Stochastic Analysis 2010" provides a sa
Wavefront shaping for opaque cylindrical lenses
Di Battista, Diego; Ancora, Daniele; Lemonaki, Krystalia; Liapis, Evangelos; Tzortzakis, Stelios; Zacharakis, Giannis
2016-01-01
Wavefront shaping has revolutionized the concepts of optical imaging and focusing. Contrary to what was believed, strong scattering in the optical paths can be exploited in favor of light focusing through turbid media and ultimately improve optical imaging and light manipulation capabilities. The use of light shapers and appropriately engineered scattering structures, i.e. opaque lenses enables the production of nano-scale confined foci and of extended fields of view. Exploiting this concept we fabricate configurable scattering structures by direct femtosecond laser writing. The properly shaped light trespassing the customized structure, a photonic lattice of parallel rods, forms a light-sheet at user defined positions. We demonstrate that our technique enables light-sheets with sub-micron resolution and extended depth of focus, a significant advantage when compared to the existing free space systems. Moreover, our approach permits to focus light of different wavelengths onto the same defined position without...
Manipulation of wavefront using helical metamaterials.
Yang, Zhenyu; Wang, Zhaokun; Tao, Huan; Zhao, Ming
2016-08-01
Helical metamaterials, a kind of 3-dimensional structure, has relatively strong coupling effect among the helical nano-wires. Therefore, it is expected to be a good candidate for generating phase shift and controlling wavefront with high efficiency. In this paper, using the finite-difference time-domain (FDTD) method, we studied the phase shift properties in the helical metamaterials. It is found that the phase shift occurs for both transmitted and reflected light waves. And the maximum of reflection coefficients can reach over 60%. In addition, the phase shift (φ) is dispersionless in the range of 600 nm to 860 nm, that is, it is only dominated by the initial angle (θ) of the helix. The relationship between them is φ = ± 2θ. Using Jones calculus we give a further explanation for these properties. Finally, by arranging the helixes in an array with a constant phase gradient, the phenomenon of anomalous refraction was also observed in a broad wavelength range.
Hamilton's Optics: The Power of Wavefronts
Indian Academy of Sciences (India)
2016-06-01
Building on work by Fermat and Huygens, Hamiltontransformed the study of geometrical opticsin his very first paper, presented when still inhis teens. His ‘characteristic function’ was ananalytical way to describe wavefronts, and in hishands a powerful tool to look at families of raysrather than isolated ones. His prediction of internaland external conical refraction in somecrystals and its spectacular verification in a fewmonths established his reputation among his contemporaries.This formulation of optics uncoveredmany general properties, not easy to seein the conventional method of tracing individualrays. The deepest outcome of his early opticalwork was a parallel view of the mechanics ofparticles, which played a fundamental role in thebirth of quantum mechanics and continues to bethe standard framework for classical mechanicsup to the present time.
Wavefront Propagation and Fuzzy Based Autonomous Navigation
Directory of Open Access Journals (Sweden)
Adel Al-Jumaily
2005-06-01
Full Text Available Path planning and obstacle avoidance are the two major issues in any navigation system. Wavefront propagation algorithm, as a good path planner, can be used to determine an optimal path. Obstacle avoidance can be achieved using possibility theory. Combining these two functions enable a robot to autonomously navigate to its destination. This paper presents the approach and results in implementing an autonomous navigation system for an indoor mobile robot. The system developed is based on a laser sensor used to retrieve data to update a two dimensional world model of therobot environment. Waypoints in the path are incorporated into the obstacle avoidance. Features such as ageing of objects and smooth motion planning are implemented to enhance efficiency and also to cater for dynamic environments.
Propagation of aberrated wavefronts using a ray transfer matrix.
Raasch, Thomas W
2014-05-01
A ray transfer matrix is used to calculate the propagation of aberrated wavefronts across a homogeneous refractive index. The wavefront is represented by local surface normals, i.e., by a ray bundle, and the propagation is accomplished by transferring those rays across the space. Wavefront shape is generated from the slopes and positions of the collection of rays. Calculation methods are developed for the paraxial case, for higher-order expansions, and for the exact tangent case. A numerical example is used to compare results between an analytical method and the methods developed here.
Initial Performance of the Keck AO Wavefront Controller System
Energy Technology Data Exchange (ETDEWEB)
Johansson, E M; Acton, D S; An, J R; Avicola, K; Beeman, B V; Brase, J M; Carrano, C J; Gathright, J; Gavel, D T; Hurd, R L; Lai, O; Lupton, W; Macintosh, B A; Max, C E; Olivier, S S; Shelton, J C; Stomski, P J; Tsubota, K; Waltjen, K E; Watson, J A; Wizinowich, P L
2001-03-01
The wavefront controller for the Keck Observatory AO system consists of two separate real-time control loops: a tip-tilt control loop to remove tilt from the incoming wavefront, and a deformable mirror control loop to remove higher-order aberrations. In this paper, we describe these control loops and analyze their performance using diagnostic data acquired during the integration and testing of the AO system on the telescope. Disturbance rejection curves for the controllers are calculated from the experimental data and compared to theory. The residual wavefront errors due to control loop bandwidth are also calculated from the data, and possible improvements to the controller performance are discussed.
Telescope Multi-Field Wavefront Control with a Kalman Filter
Lou, John Z.; Redding, David; Sigrist, Norbert; Basinger, Scott
2008-01-01
An effective multi-field wavefront control (WFC) approach is demonstrated for an actuated, segmented space telescope using wavefront measurements at the exit pupil, and the optical and computational implications of this approach are discussed. The integration of a Kalman Filter as an optical state estimator into the wavefront control process to further improve the robustness of the optical alignment of the telescope will also be discussed. Through a comparison of WFC performances between on-orbit and ground-test optical system configurations, the connection (and a possible disconnection) between WFC and optical system alignment under these circumstances are analyzed. Our MACOS-based computer simulation results will be presented and discussed.
Development of a pyramidal wavefront sensor test-bench at INO
Turbide, Simon; Wang, Min; Gauvin, Jonny; Martin, Olivier; Savard, Maxime; Bourqui, Pascal; Veran, Jean-Pierre; Deschenes, William; Anctil, Genevieve; Chateauneuf, François
2013-12-01
The key technical element of the adaptive optics in astronomy is the wavefront sensing (WFS). One of the advantages of the pyramid wavefront sensor (P-WFS) over the widely used Shack-Hartmann wavefront sensor seems to be the increased sensitivity in closed-loop applications. A high-sensitivity and large dynamic-range WFS, such as P-WFS technology, still needs to be further investigated for proper justification in future Extremely Large Telescopes application. At INO, we have recently carried out the optical design, testing and performance evaluation of a P-WFS bench setup. The optical design of the bench setup mainly consists of the super-LED fiber source, source collimator, spatial light modulator (SLM), relay lenses, tip-tilt mirror, Fourier-transforming lens, and a four-faceted glass pyramid with a large vertex angle as well as pupil re-imaged optics. The phase-only SLM has been introduced in the bench setup to generate atmospheric turbulence with a maximum phase shift of more than 2π at each pixel (256 grey levels). Like a modified Foucault knife-edge test, the refractive pyramid element is used to produce four images of the entrance pupil on a CCD camera. The Fourier-transforming lens, which is used before the pyramid prism, is designed for telecentric output to allow dynamic modulation (rotation of the beam around the pyramid-prism center) from a tip-tilt mirror. Furthermore, a P-WFS diffraction-based model has been developed. This model includes most of the system limitations such as the SLM discrete voltage steps and the CCD pixel pitch. The pyramid effects (edges and tip) are considered as well. The modal wavefront reconstruction algorithm relies on the construction of an interaction matrix (one for each modulation's amplitude). Each column of the interaction matrix represents the combination of the four pupil images for a given wavefront aberration. The nice agreement between the data and the model suggest that the limitation of the system is not the P
Holographic Wavefront Correction for ShADOE LIDAR Receivers Project
National Aeronautics and Space Administration — Current shared aperture diffractive optical elements (ShADOE) have intrinsic residual wavefront errors on the order of 50 waves which limits the angular resolution...
Manipulating acoustic wavefront by inhomogeneous impedance and steerable extraordinary reflection.
Zhao, Jiajun; Li, Baowen; Chen, Zhining; Qiu, Cheng-Wei
2013-01-01
We unveil the connection between the acoustic impedance along a flat surface and the reflected acoustic wavefront, in order to empower a wide wariety of novel applications in acoustic community. Our designed flat surface can generate double reflections: the ordinary reflection and the extraordinary one whose wavefront is manipulated by the proposed impedance-governed generalized Snell's law of reflection (IGSL). IGSL is based on Green's function and integral equation, instead of Fermat's principle for optical wavefront manipulation. Remarkably, via the adjustment of the designed specific acoustic impedance, extraordinary reflection can be steered for unprecedented acoustic wavefront while that ordinary reflection can be surprisingly switched on or off. The realization of the complex discontinuity of the impedance surface has been proposed using Helmholtz resonators.
A Method for Wavefront Curvature Ranging of Speech Sources ...
African Journals Online (AJOL)
A Method for Wavefront Curvature Ranging of Speech Sources. ... A new approach for estimating the location of a speech source in a reverberant environment is presented. The approach ... EMAIL FREE FULL TEXT EMAIL FREE FULL TEXT
Gaussian weighting of ocular wave-front measurements.
Schwiegerling, Jim
2004-11-01
The measurement of ocular wave-front error gives insight into the optical performance of the eye and possibly a means for assessing visual performance. The visual system responds not only to the quality of the optical image formed on the retina but also to the processing that occurs in the retina and the brain. To develop a metric of visual performance based on wave-front error measurements, these latter processes must somehow be incorporated. In representing the wave-front error in terms of Zernike polynomials, it appears that terms with lower angular frequency have a greater deleterious effect on visual performance than higher-angular-frequency terms. A technique for weighting the pupil function of the eye with a Gaussian filter is demonstrated. It is further demonstrated that the variance of the Gaussian-weighted wave-front error is well correlated with visual performance.
Holographic Wavefront Correction for SHADOE LIDAR Receivers Project
National Aeronautics and Space Administration — Current shared aperture diffractive optical elements (SHADOE) have intrinsic residual wavefront errors on the order of 20 waves which limits the angular resolution...
Pyramid wavefront sensors for astronomy and for the human eye
Bergomi, Maria
2013-01-01
WaveFront Sensors (WFSs) may be defined as the heart of an adaptive optics system since they analyze the radiation coming from reference sources and allow to quantify the distortion of a wavefront. Among the varieties of existing WFSs, my PhD research thesis focuses especially on innovative optical systems taking advantage of the peculiarities of the Pyramid WFS. In my PhD project I have designed, implemented, characterized or studied three different applications characterized by the f...
Advanced wavefront measurement and analysis of laser system modeling
Energy Technology Data Exchange (ETDEWEB)
Wolfe, C.R.; Auerback, J.M. [Lawrence Livermore National Lab., CA (United States)
1994-11-15
High spatial resolution measurements of the reflected or transmitted wavefronts of large aperture optical components used in high peak power laser systems is now possible. These measurements are produced by phase shifting interferometry. The wavefront data is in the form of 3-D phase maps that reconstruct the wavefront shape. The emphasis of this work is on the characterization of wavefront features in the mid-spatial wavelength range (from 0.1 to 10.0 mm) and has been accomplished for the first time. Wavefront structure from optical components with spatial wavelengths in this range are of concern because their effects in high peak power laser systems. At high peak power, this phase modulation can convert to large magnitude intensity modulation by non-linear processes. This can lead to optical damage. We have developed software to input the measured phase map data into beam propagation codes in order to model this conversion process. We are analyzing this data to: (1) Characterize the wavefront structure produced by current optical components, (2) Refine our understanding of laser system performance, (3) Develop a database from which future optical component specifications can be derived.
The Wavefront Control System for the National Ignition Facility
Energy Technology Data Exchange (ETDEWEB)
Van Atta, L; Perez, M; Zacharias, R; Rivera, W
2001-10-15
The National Ignition Facility (NIF) requires that pulses from each of the 192 laser beams be positioned on target with an accuracy of 50 {micro}m rms. Beam quality must be sufficient to focus a total of 1.8 MJ of 0.351-{micro}m light into a 600-{micro}m-diameter volume. An optimally flat beam wavefront can achieve this pointing and focusing accuracy. The control system corrects wavefront aberrations by performing closed-loop compensation during laser alignment to correct for gas density variations. Static compensation of flashlamp-induced thermal distortion is established just prior to the laser shot. The control system compensates each laser beam at 10 Hz by measuring the wavefront with a 77-lenslet Hartmann sensor and applying corrections with a 39-actuator deformable mirror. The distributed architecture utilizes SPARC AXi computers running Solaris to perform real-time image processing of sensor data and PowerPC-based computers running VxWorks to compute mirror commands. A single pair of SPARC and PowerPC processors accomplishes wavefront control for a group of eight beams. The software design uses proven adaptive optic control algorithms that are implemented in a multi-tasking environment to economically control the beam wavefronts in parallel. Prototype tests have achieved a closed-loop residual error of 0.03 waves rms. aberrations, the spot size requirement and goal could not be met without a wavefront control system.
Directory of Open Access Journals (Sweden)
Romanu Ekaterini
2006-01-01
Full Text Available This article shows the similarities between Claude Debussy’s and Iannis Xenakis’ philosophy of music and work, in particular the formers Jeux and the latter’s Metastasis and the stochastic works succeeding it, which seem to proceed parallel (with no personal contact to what is perceived as the evolution of 20th century Western music. Those two composers observed the dominant (German tradition as outsiders, and negated some of its elements considered as constant or natural by "traditional" innovators (i.e. serialists: the linearity of musical texture, its form and rhythm.
Stochastic Physics, Complex Systems and Biology
Qian, Hong
2012-01-01
In complex systems, the interplay between nonlinear and stochastic dynamics gives rise to an evolution process in Darwinian sense with punctuated equilibrium, random "mutations" and "adaptations". The emergent discrete states in such a system, i.e., attractors, have natural robustness against both internal and external perturbations. Epigenetic states of a biological cell, a mesoscopic nonlinear stochastic open biochemical system, could be understood through such a framework.
Energy Technology Data Exchange (ETDEWEB)
Zhang, Qichun; Zhou, Jinglin; Wang, Hong; Chai, Tianyou
2016-08-31
In this paper, stochastic coupling attenuation is investigated for a class of multi-variable bilinear stochastic systems and a novel output feedback m-block backstepping controller with linear estimator is designed, where gradient descent optimization is used to tune the design parameters of the controller. It has been shown that the trajectories of the closed-loop stochastic systems are bounded in probability sense and the stochastic coupling of the system outputs can be effectively attenuated by the proposed control algorithm. Moreover, the stability of the stochastic systems is analyzed and the effectiveness of the proposed method has been demonstrated using a simulated example.
Extension of the modal wave-front reconstruction algorithm to non-uniform illumination.
Ma, Xiaoyu; Mu, Jie; Rao, ChangHui; Yang, Jinsheng; Rao, XueJun; Tian, Yu
2014-06-30
Attempts are made to eliminate the effects of non-uniform illumination on the precision of wave-front measurement. To achieve this, the relationship between the wave-front slope at a single sub-aperture and the distributions of the phase and light intensity of the wave-front were first analyzed to obtain the relevant theoretical formulae. Then, based on the principle of modal wave-front reconstruction, the influence of the light intensity distribution on the wave-front slope is introduced into the calculation of the reconstruction matrix. Experiments were conducted to prove that the corrected modal wave-front reconstruction algorithm improved the accuracy of wave-front reconstruction. Moreover, the correction is conducive to high-precision wave-front measurement using a Hartmann wave-front sensor in the presence of non-uniform illumination.
Wavefront sensors for adaptive optical systems
Lukin, V. P.; Botygina, N. N.; Emaleev, O. N.; Konyaev, P. A.
2010-10-01
A high precision Shack-Hartmann wavefront (WF) sensor has been developed on the basis of a low-aperture off-axis diffraction lens array. The device is capable of measuring WF slopes at array sub-apertures of size 640x640 μm with an error not exceeding 4.80 arcsec (0.15 pixel), which corresponds to the standard deviation equal to 0.017λ at the reconstructed WF with wavelength λ . Also the modification of this sensor for adaptive system of solar telescope using extended scenes as tracking objects, such as sunspot, pores, solar granulation and limb, is presented. The software package developed for the proposed WF sensors includes three algorithms of local WF slopes estimation (modified centroids, normalized cross-correlation and fast Fourier-demodulation), as well as three methods of WF reconstruction (modal Zernike polynomials expansion, deformable mirror response functions expansion and phase unwrapping), that can be selected during operation with accordance to the application.
Photon counting arrays for AO wavefront sensors
Vallerga, J; McPhate, J; Mikulec, Bettina; Clark, Allan G; Siegmund, O; CERN. Geneva
2005-01-01
Future wavefront sensors for AO on large telescopes will require a large number of pixels and must operate at high frame rates. Unfortunately for CCDs, there is a readout noise penalty for operating faster, and this noise can add up rather quickly when considering the number of pixels required for the extended shape of a sodium laser guide star observed with a large telescope. Imaging photon counting detectors have zero readout noise and many pixels, but have suffered in the past with low QE at the longer wavelengths (>500 nm). Recent developments in GaAs photocathode technology, CMOS ASIC readouts and FPGA processing electronics have resulted in noiseless WFS detector designs that are competitive with silicon array detectors, though at ~40% the QE of CCDs. We review noiseless array detectors and compare their centroiding performance with CCDs using the best available characteristics of each. We show that for sub-aperture binning of 6x6 and greater that noiseless detectors have a smaller centroid error at flu...
Stochastic Processes in Gravitropism
Directory of Open Access Journals (Sweden)
Yasmine eMeroz
2014-11-01
Full Text Available In this short review we focus on the role of noise in gravitropism of plants - the reorientation of plants according to the direction of gravity. We briefly introduce the conventional picture of static gravisensing in cells specialized in sensing. This model hinges on the sedimentation of statoliths (high in density and mass relative to other organelles to the lowest part of the sensing cell. We then present experimental observations that cannot currently be understood within this framework. Lastly we introduce some current alternative models and directions that attempt to incorporate and interpret these experimental observations, including: (i {it dynamic sensing}, where gravisensing is suggested to be enhanced by stochastic events due to thermal and mechanical noise. These events both effectively lower the threshold of response, and lead to small-distance sedimentation, allowing amplification and integration of the signal. (ii The role of the cytoskeleton in signal-to-noise modulation and (iii in signal transduction. In closing, we discuss directions that seem to either not have been explored, or that are still poorly understood.
Wilby, M. J.; Keller, C. U.; Haffert, S.; Korkiakoski, V.; Snik, F.; Pietrow, A. G. M.
2016-07-01
Non-Common Path Errors (NCPEs) are the dominant factor limiting the performance of current astronomical high-contrast imaging instruments. If uncorrected, the resulting quasi-static speckle noise floor limits coronagraph performance to a raw contrast of typically 10-4, a value which does not improve with increasing integration time. The coronagraphic Modal Wavefront Sensor (cMWS) is a hybrid phase optic which uses holographic PSF copies to supply focal-plane wavefront sensing information directly from the science camera, whilst maintaining a bias-free coronagraphic PSF. This concept has already been successfully implemented on-sky at the William Herschel Telescope (WHT), La Palma, demonstrating both real-time wavefront sensing capability and successful extraction of slowly varying wavefront errors under a dominant and rapidly changing atmospheric speckle foreground. In this work we present an overview of the development of the cMWS and recent first light results obtained using the Leiden EXoplanet Instrument (LEXI), a high-contrast imager and high-dispersion spectrograph pathfinder instrument for the WHT.
Dunn, Jennifer; Andersen, David; Chapin, Edward; Reshetov, Vlad; Wierzbicki, Ramunas; Herriot, Glen; Chalmer, Dean; Isbrucker, Victor; Larkin, James E.; Moore, Anna M.; Suzuki, Ryuji
2016-08-01
The InfraRed Imaging Spectrograph (IRIS) will be the first light adaptive optics instrument on the Thirty Meter Telescope (TMT). IRIS is being built by a collaboration between Caltech, the University of California, NAOJ and NRC Herzberg. In this paper we present novel aspects of the Support Structure, Rotator and On-Instrument Wavefront Sensor systems being developed at NRC Herzberg. IRIS is suspended from the bottom port of the Narrow Field Infrared Adaptive Optics System (NFIRAOS), and provides its own image de-rotation to compensate for sidereal rotation of the focal plane. This arrangement is a challenge because NFIRAOS is designed to host two other science instruments, which imposes strict mass requirements on IRIS. As the mechanical design of all elements has progressed, we have been tasked with keeping the instrument mass under seven tonnes. This requirement has resulted in a mass reduction of 30 percent for the support structure and rotator compared to the most recent IRIS designs. To accomplish this goal, while still being able to withstand earthquakes, we developed a new design with composite materials. As IRIS is a client instrument of NFIRAOS, it benefits from NFIRAOS's superior AO correction. IRIS plays an important role in providing this correction by sensing low-order aberrations with three On-Instrument Wavefront Sensors (OIWFS). The OIWFS consists of three independently positioned natural guide star wavefront sensor probe arms that patrol a 2-arcminute field of view. We expect tip-tilt measurements from faint stars within the IRIS imager focal plane will further stabilize the delivered image quality. We describe how the use of On-Detector Guide Windows (ODGWs) in the IRIS imaging detector can be incorporated into the AO correction. In this paper, we present our strategies for acquiring and tracking sources with this complex AO system, and for mitigating and measuring the various potential sources of image blur and misalignment due to properties of
Recursive Concurrent Stochastic Games
Etessami, Kousha
2008-01-01
We study Recursive Concurrent Stochastic Games (RCSGs), extending our recent analysis of recursive simple stochastic games [16,17] to a concurrent setting where the two players choose moves simultaneously and independently at each state. For multi-exit games, our earlier work already showed undecidability for basic questions like termination, thus we focus on the important case of single-exit RCSGs (1-RCSGs). We first characterize the value of a 1-RCSG termination game as the least fixed point solution of a system of nonlinear minimax functional equations, and use it to show PSPACE decidability for the quantitative termination problem. We then give a strategy improvement technique, which we use to show that player 1 (maximizer) has \\epsilon-optimal randomized Stackless & Memoryless (r-SM) strategies for all \\epsilon > 0, while player 2 (minimizer) has optimal r-SM strategies. Thus, such games are r-SM-determined. These results mirror and generalize in a strong sense the randomized memoryless determinacy r...
Lanchier, Nicolas
2017-01-01
Three coherent parts form the material covered in this text, portions of which have not been widely covered in traditional textbooks. In this coverage the reader is quickly introduced to several different topics enriched with 175 exercises which focus on real-world problems. Exercises range from the classics of probability theory to more exotic research-oriented problems based on numerical simulations. Intended for graduate students in mathematics and applied sciences, the text provides the tools and training needed to write and use programs for research purposes. The first part of the text begins with a brief review of measure theory and revisits the main concepts of probability theory, from random variables to the standard limit theorems. The second part covers traditional material on stochastic processes, including martingales, discrete-time Markov chains, Poisson processes, and continuous-time Markov chains. The theory developed is illustrated by a variety of examples surrounding applications such as the ...
Energy Technology Data Exchange (ETDEWEB)
Blaskiewicz, M.
2011-01-01
Stochastic Cooling was invented by Simon van der Meer and was demonstrated at the CERN ISR and ICE (Initial Cooling Experiment). Operational systems were developed at Fermilab and CERN. A complete theory of cooling of unbunched beams was developed, and was applied at CERN and Fermilab. Several new and existing rings employ coasting beam cooling. Bunched beam cooling was demonstrated in ICE and has been observed in several rings designed for coasting beam cooling. High energy bunched beams have proven more difficult. Signal suppression was achieved in the Tevatron, though operational cooling was not pursued at Fermilab. Longitudinal cooling was achieved in the RHIC collider. More recently a vertical cooling system in RHIC cooled both transverse dimensions via betatron coupling.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
In this paper, the stochastic flow of mappings generated by a Feller convolution semigroup on a compact metric space is studied. This kind of flow is the generalization of superprocesses of stochastic flows and stochastic diffeomorphism induced by the strong solutions of stochastic differential equations.
Genesis of return stroke current evolution at the wavefront
Kumar, Udaya; Raysaha, Rosy Balaram
2013-07-01
The channel dynamics at the wavefront is complex and is primarily responsible for the evolution of return stroke current. The enhancement of channel conductance at the wavefront is necessary for the evolution of current and hence, return stroke. In this regard several questions arise like: (i) what causes the enhancement of conductance, (ii) as the channel core temperature and electrical conductance are closely related, does one support the other and (iii) is the increase in core temperature on the nascent section of the channel the result of free burning arc of the wavefront just below. The present work investigates on these issues with appropriate transient thermal analysis and a macroscopic physical model for the lightning return stroke. Results clearly indicate that the contribution from the thermal field of the wavefront region to the adjacent nascent channel section is negligible as compared to the field enhancement brought in by the same. In other words, the whole process of return stroke evolution is dependent on the local heat generation at the nascent section caused by the enhancement of electric field due to the arrival of the wavefront.
Wavefront measurement of plastic lenses for mobile-phone applications
Huang, Li-Ting; Cheng, Yuan-Chieh; Wang, Chung-Yen; Wang, Pei-Jen
2016-08-01
In camera lenses for mobile-phone applications, all lens elements have been designed with aspheric surfaces because of the requirements in minimal total track length of the lenses. Due to the diffraction-limited optics design with precision assembly procedures, element inspection and lens performance measurement have become cumbersome in the production of mobile-phone cameras. Recently, wavefront measurements based on Shack-Hartmann sensors have been successfully implemented on injection-molded plastic lens with aspheric surfaces. However, the applications of wavefront measurement on small-sized plastic lenses have yet to be studied both theoretically and experimentally. In this paper, both an in-house-built and a commercial wavefront measurement system configured on two optics structures have been investigated with measurement of wavefront aberrations on two lens elements from a mobile-phone camera. First, the wet-cell method has been employed for verifications of aberrations due to residual birefringence in an injection-molded lens. Then, two lens elements of a mobile-phone camera with large positive and negative power have been measured with aberrations expressed in Zernike polynomial to illustrate the effectiveness in wavefront measurement for troubleshooting defects in optical performance.
Stochastic Averaging and Stochastic Extremum Seeking
Liu, Shu-Jun
2012-01-01
Stochastic Averaging and Stochastic Extremum Seeking develops methods of mathematical analysis inspired by the interest in reverse engineering and analysis of bacterial convergence by chemotaxis and to apply similar stochastic optimization techniques in other environments. The first half of the text presents significant advances in stochastic averaging theory, necessitated by the fact that existing theorems are restricted to systems with linear growth, globally exponentially stable average models, vanishing stochastic perturbations, and prevent analysis over infinite time horizon. The second half of the text introduces stochastic extremum seeking algorithms for model-free optimization of systems in real time using stochastic perturbations for estimation of their gradients. Both gradient- and Newton-based algorithms are presented, offering the user the choice between the simplicity of implementation (gradient) and the ability to achieve a known, arbitrary convergence rate (Newton). The design of algorithms...
Gavel, Don
1989-09-01
Laser light propagating through atmosphere will become distorted as a result of the changing index of refraction along the light path. Wavefront distortions can be actively compensated using adaptive optic systems, which sense the wavefront aberations and compensate by changing the shape of a reflecting surface. Corrections must be done rapidly in order to keep up with the variations in the atmosphere. Numerically, the calculation of the correcting surface is a least-squares fit problem. However, since a typical adaptive optic system has a large number of actuators and sensors, the ordinary solution methods, such as Gaussian elimination, are infeasible for real time application. Instead, advantage must be taken of the structure and sparseness of the equations in order to speed up the calculation. The algorithm proposed requires only O(nq) calculation steps and uses only O(n) memory storage, where n is the total number of actuators and q is the influence width of a single actuator. The derivation of the proposed algorithm, proofs of convergence, and results of several test runs are presented. The algorithm was incorporated into Y division's ORACLE simulation code where it is used to calculate the phase conjugate surfaces necessary to precompensate a high powered laser beam for atmospheric propagation.
Sobczyk, K
1985-01-01
This is a concise, unified exposition of the existing methods of analysis of linear stochastic waves with particular reference to the most recent results. Both scalar and vector waves are considered. Principal attention is concentrated on wave propagation in stochastic media and wave scattering at stochastic surfaces. However, discussion extends also to various mathematical aspects of stochastic wave equations and problems of modelling stochastic media.
Stochastic homothetically revealed preference for tight stochastic demand functions
Jan Heufer
2009-01-01
This paper strengthens the framework of stochastic revealed preferences introduced by Bandyopadhyay et al. (1999, 2004) for stochastic homothetically revealed preferences for tight stochastic demand functions.
A stochastic differential equation with a sticky point
Bass, Richard F.
2012-01-01
We consider a degenerate stochastic differential equation that has a sticky point in the Markov process sense. We prove that weak existence and weak uniqueness hold, but that pathwise uniqueness does not hold nor does a strong solution exist.
Miniaturized Shack-Hartmann Wavefront-Sensors for Starbugs
Goodwin, Michael; Richards, Samuel; Zheng, Jessica; Lawrence, Jon; Leon-Saval, Sergio; Argyros, Alexander
2014-01-01
The ability to position multiple miniaturized wavefront sensors precisely over large focal surfaces are advantageous to multi-object adaptive optics. The Australian Astronomical Observatory (AAO) has prototyped a compact and lightweight Shack-Hartmann wavefront-sensor that fits into a standard Starbug parallel fibre positioning robot. Each device makes use of a polymer coherent fibre imaging bundle to relay an image produced by a microlens array placed at the telescope focal plane to a re-imaging camera mounted elsewhere. The advantages of the polymer fibre bundle are its high-fill factor, high-throughput, low weight, and relatively low cost. Multiple devices can also be multiplexed to a single low-noise camera for cost efficiencies per wavefront sensor. The use of fibre bundles also opens the possibility of applications such as telescope field acquisition, guiding, and seeing monitors to be positioned by Starbugs. We present the design aspects, simulations and laboratory test results.
Polarization-resolved microscopy through scattering media via wavefront shaping
de Aguiar, Hilton B; Brasselet, Sophie
2015-01-01
Wavefront shaping has revolutionized imaging deep in scattering media, being able to spatially and temporally refocus light through or inside the medium. However, wavefront shaping is not compatible yet with polarization-resolved microscopy given the need of polarizing optics to refocus light with a controlled polarization state. Here, we show that wavefront shaping is not only able to restore a focus, but it can also recover the injected polarization state without using any polarizing optics at the detection. This counter-intuitive effect occurs up to several transport mean free path thick samples, which exhibit a speckle with a completely scrambled state. Remarkably, an arbitrary rotation of the input polarization does not degrade the quality of the focus. This unsupervised re-polarization - out of the originally scrambled polarization state - paves the way for polarization-resolved structural microscopy at unprecedented depths. We exploit this phenomenon and demonstrate second harmonic generation (SHG) str...
Traveling wavefront solutions to nonlinear reaction-diffusion-convection equations
Indekeu, Joseph O.; Smets, Ruben
2017-08-01
Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.
Hartmann wavefront sensors and their application at FLASH.
Keitel, Barbara; Plönjes, Elke; Kreis, Svea; Kuhlmann, Marion; Tiedtke, Kai; Mey, Tobias; Schäfer, Bernd; Mann, Klaus
2016-01-01
Different types of Hartmann wavefront sensors are presented which are usable for a variety of applications in the soft X-ray spectral region at FLASH, the free-electron laser (FEL) in Hamburg. As a typical application, online measurements of photon beam parameters during mirror alignment are reported on. A compact Hartmann sensor, operating in the wavelength range from 4 to 38 nm, was used to determine the wavefront quality as well as aberrations of individual FEL pulses during the alignment procedure. Beam characterization and alignment of the focusing optics of the FLASH beamline BL3 were performed with λ(13.5 nm)/116 accuracy for wavefront r.m.s. (w(rms)) repeatability, resulting in a reduction of w(rms) by 33% during alignment.
Wavefront manipulation with a dipolar metasurface under coherent control
Kang, Ming; Wang, Hui-Tian; Zhu, Weiren
2017-07-01
Full phase manipulation with equal amplitude is critical for optical wavefront engineering in various systems. Here we theoretically explore a general approach for optical wavefront manipulation using dipolar metasurfaces under the coherent control. From the microscopic perspective, we theoretically show that the dispersion of a dipolar metasurface under the coherent control can provide the phase manipulation within a full range of [0, 2π] and retain an equal amplitude simultaneously. As an example, such a dipolar metasurface can be constructed by compensatory H-shaped unit resonators to avoid polarization conversion. Specifically, we confirm the feasibility of designed metasurfaces for achieving the beam bending and the vortex-phase beam by the full-wave simulation. The proposed approach enriches the well-established wavefront engineering for extending the functionality of metasurface under the coherent control.
Acoustic Wavefront Manipulation: Impedance Inhomogeneity and Extraordinary Reflection
Zhao, Jiajun; Chen, Zhining; Li, Baowen
2013-01-01
Optical wavefront can be manipulated by interfering elementary beams with phase inhomogeneity. Therefore a surface allowing huge, abrupt and position-variant phase change would enable all possibilities of wavefront engineering. However, one may not have the luxury of efficient abrupt-phase-changing materials in acoustics. This motivates us to establish a counterpart mechanism for acoustics, in order to empower the wide spectrum of novel acoustic applications. Remarkably, the proposed impedance-governed generalized Snell's law (IGSL) of reflection is distinguished from that in optics. Via the manipulation of inhomogeneous acoustic impedance, extraordinary reflection can be tailored for unprecedented wavefront manipulation while ordinary reflection can be surprisingly switched on or off. Our results may power the acoustic-wave manipulation and engineering. We demonstrate novel acoustic applications by planar surfaces designed with IGSL.
Imaging spheres with general incident wavefronts using a dipole decomposition
Izen, Steven H.; Ovryn, Ben
1998-06-01
Although scattering for spheres with plane wave illumination was solved precisely by Mie in 1909, often it is of interest to image spheres with non-planar illumination. An extension of Mie theory which incorporates non-planar illumination requires knowledge of the coefficients for a spherical harmonic expansion of the incident wavefront about the center of the sphere. These coefficients have been determined for a few special cases, such as Gaussian beams, which have a relatively simple model. Using a vectorized Huygen's principle, a general vector wavefront can be represented as a superposition of dipole sources. We have computed the spherical wave function expansion coefficients of an arbitrarily placed dipole and hence the scattering from a sphere illuminated by a general wavefront can be computed. As a special case, Mie's solution of plane wave scattering was recovered. POtential applications include scattering with partially coherent illumination. Experimental results from the scattering from polystyrene spheres using Koehler illumination show agreement with numerical tests.
Spatio-temporal wavefront shaping in a microwave cavity
del Hougne, Philipp; Fink, Mathias; Lerosey, Geoffroy
2016-01-01
Controlling waves in complex media has become a major topic of interest, notably through the concepts of time reversal and wavefront shaping. Recently, it was shown that spatial light modulators can counter-intuitively focus waves both in space and time through multiple scattering media when illuminated with optical pulses. In this letter we transpose the concept to a microwave cavity using flat arrays of electronically tunable resonators. We prove that maximizing the Green's function between two antennas at a chosen time yields diffraction limited spatio-temporal focusing. Then, changing the photons' dwell time inside the cavity, we modify the relative distribution of the spatial and temporal degrees of freedom (DoF), and we demonstrate that it has no impact on the field enhancement: wavefront shaping makes use of all available DoF, irrespective of their spatial or temporal nature. Our results prove that wavefront shaping using simple electronically reconfigurable arrays of reflectors is a viable approach to...
N'Diaye, Mamadou; Mazoyer, Johan; Choquet, Élodie; Pueyo, Laurent; Perrin, Marshall D.; Egron, Sylvain; Leboulleux, Lucie; Levecq, Olivier; Carlotti, Alexis; Long, Chris A.; Lajoie, Rachel; Soummer, Rémi
2015-09-01
HiCAT is a high-contrast imaging testbed designed to provide complete solutions in wavefront sensing, control and starlight suppression with complex aperture telescopes. The pupil geometry of such observatories includes primary mirror segmentation, central obstruction, and spider vanes, which make the direct imaging of habitable worlds very challenging. The testbed alignment was completed in the summer of 2014, exceeding specifications with a total wavefront error of 12nm rms over a 18mm pupil. The installation of two deformable mirrors for wavefront control is to be completed in the winter of 2015. In this communication, we report on the first testbed results using a classical Lyot coronagraph. We also present the coronagraph design for HiCAT geometry, based on our recent development of Apodized Pupil Lyot Coronagraph (APLC) with shaped-pupil type optimizations. These new APLC-type solutions using two-dimensional shaped-pupil apodizer render the system quasi-insensitive to jitter and low-order aberrations, while improving the performance in terms of inner working angle, bandpass and contrast over a classical APLC.
Stochastic flux freezing and magnetic dynamo.
Eyink, Gregory L
2011-05-01
Magnetic flux conservation in turbulent plasmas at high magnetic Reynolds numbers is argued neither to hold in the conventional sense nor to be entirely broken, but instead to be valid in a statistical sense associated to the "spontaneous stochasticity" of Lagrangian particle trajectories. The latter phenomenon is due to the explosive separation of particles undergoing turbulent Richardson diffusion, which leads to a breakdown of Laplacian determinism for classical dynamics. Empirical evidence is presented for spontaneous stochasticity, including numerical results. A Lagrangian path-integral approach is then exploited to establish stochastic flux freezing for resistive hydromagnetic equations and to argue, based on the properties of Richardson diffusion, that flux conservation must remain stochastic at infinite magnetic Reynolds number. An important application of these results is the kinematic, fluctuation dynamo in nonhelical, incompressible turbulence at magnetic Prandtl number (Pr(m)) equal to unity. Numerical results on the Lagrangian dynamo mechanisms by a stochastic particle method demonstrate a strong similarity between the Pr(m)=1 and 0 dynamos. Stochasticity of field-line motion is an essential ingredient of both. Finally, some consequences for nonlinear magnetohydrodynamic turbulence, dynamo, and reconnection are briefly considered.
Asphericity analysis using corneal wavefront and topographic meridional fits
Arba-Mosquera, Samuel; Merayo-Lloves, Jesús; de Ortueta, Diego
2010-03-01
The calculation of corneal asphericity as a 3-D fit renders more accurate results when it is based on the corneal wavefront aberrations rather than on the corneal topography of the principal meridians. A more accurate prediction could be obtained for hyperopic treatments compared to myopic treatments. We evaluate a method to calculate corneal asphericity and asphericity changes after refractive surgery. Sixty eyes of 15 consecutive myopic patients and 15 consecutive hyperopic patients (n=30 each) are retrospectively evaluated. Preoperative and 3-month-postoperative topographic and corneal wavefront analyses are performed using corneal topography. Ablations are performed using a laser with an aberration-free profile. Topographic changes in asphericity and corneal aberrations are evaluated for a 6-mm corneal diameter. The induction of corneal spherical aberrations and asphericity changes correlates with the achieved defocus correction. Preoperatively as well as postoperatively, asphericity calculated from the topography meridians correlates with asphericity calculated from the corneal wavefront in myopic and hyperopic treatments. A stronger correlation between postoperative asphericity and the ideally expected/predicted asphericity is obtained based on aberration-free assumptions calculated from corneal wavefront values rather than from the meridians. In hyperopic treatments, a better correlation can be obtained compared to the correlation in myopic treatments. Corneal asphericity calculated from corneal wavefront aberrations represents a 3-D fit of the corneal surface; asphericity calculated from the main topographic meridians represents a 2-D fit of the principal corneal meridians. Postoperative corneal asphericity can be calculated from corneal wavefront aberrations with higher fidelity than from corneal topography of the principal meridians. Hyperopic treatments show a greater accuracy than myopic treatments.
Broadband manipulation of acoustic wavefronts by pentamode metasurface
Energy Technology Data Exchange (ETDEWEB)
Tian, Ye; Wei, Qi, E-mail: weiqi@nju.edu.cn; Cheng, Ying [Key Laboratory of Modern Acoustics, Department of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093 (China); Xu, Zheng [School of Physics Science and Engineering, Tongji University, Shanghai 200092 (China); Liu, Xiaojun, E-mail: liuxiaojun@nju.edu.cn [Key Laboratory of Modern Acoustics, Department of Physics, Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093 (China); State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190 (China)
2015-11-30
An acoustic metasurface with a sub-wavelength thickness can manipulate acoustic wavefronts freely by the introduction of abrupt phase variation. However, the existence of a narrow bandwidth and a low transmittance limits further applications. Here, we present a broadband and highly transparent acoustic metasurface based on a frequency-independent generalized acoustic Snell's law and pentamode metamaterials. The proposal employs a gradient velocity to redirect refracted waves and pentamode metamaterials to improve impedance matching between the metasurface and the background medium. Excellent wavefront manipulation based on the metasurface is further demonstrated by anomalous refraction, generation of non-diffracting Bessel beam, and sub-wavelength flat focusing.
Min Gong; Yi Liu; Bi Yang
2013-01-01
Effective methods of evaluating postoperative visual quality include wavefront aberration and contrast sensitivity test. This article provides a review of the concepts and clinical applications as well as their interactions of wavefront aberration and contrast sensitivity test.This article also provides a comprehensive assessment of the effectiveness of wavefront aberration and contrast sensitivity test as evaluation tools of postoperative visual quality.
Towards sub-optimal stochastic control of partially observable stochastic systems
Ruzicka, G. J.
1980-01-01
The paper deals with a class of multidimensional stochastic control problems with noisy data and bounded controls encountered in aerospace design. The emphasis is on suboptimal design, the optimality being taken in quadratic mean sense. To that effect the problem is viewed as a stochastic version of the Lurie problem known from nonlinear control theory. The main result is a separation theorem (involving a nonlinear Kalman-like filter) suitable for Lurie-type approximations. The theorem allows for discontinuous characteristics. As a byproduct the existence of strong solutions to a class of non-Lipschitzian stochastic differential equations in n dimensions is proved.
Crass, Jonathan; Femenia, Bruno; King, David L; Mackay, Craig D; Rebolo-López, Rafael; Labadie, Lucas; Garrido, Antonio Pérez; Balcells, Marc; Sánchez, Anastasio Díaz; Fuensalida, Jesús Jimenez; Lopez, Roberto L; Oscoz, Alejandro; Prieto, Jorge A Pérez; Rodríguez-Ramos, Luis F; Villó, Isidro
2012-01-01
The Adaptive Optics Lucky Imager (AOLI) is a new instrument under development to demonstrate near diffraction limited imaging in the visible on large ground-based telescopes. We present the adaptive optics system being designed for the instrument comprising a large stroke deformable mirror, fixed component non-linear curvature wavefront sensor and photon-counting EMCCD detectors. We describe the optical design of the wavefront sensor where two photoncounting CCDs provide a total of four reference images. Simulations of the optical characteristics of the system are discussed, with their relevance to low and high order AO systems. The development and optimisation of high-speed wavefront reconstruction algorithms are presented. Finally we discuss the results of simulations to demonstrate the sensitivity of the system.
Adaptation in stochastic environments
Clark, Colib
1993-01-01
The classical theory of natural selection, as developed by Fisher, Haldane, and 'Wright, and their followers, is in a sense a statistical theory. By and large the classical theory assumes that the underlying environment in which evolution transpires is both constant and stable - the theory is in this sense deterministic. In reality, on the other hand, nature is almost always changing and unstable. We do not yet possess a complete theory of natural selection in stochastic environ ments. Perhaps it has been thought that such a theory is unimportant, or that it would be too difficult. Our own view is that the time is now ripe for the development of a probabilistic theory of natural selection. The present volume is an attempt to provide an elementary introduction to this probabilistic theory. Each author was asked to con tribute a simple, basic introduction to his or her specialty, including lively discussions and speculation. We hope that the book contributes further to the understanding of the roles of "Cha...
Conjugate adaptive optics in widefield microscopy with an extended-source wavefront sensor
Li, Jiang; Paudel, Hari; Barankov, Roman; Bifano, Thomas; Mertz, Jerome
2015-01-01
Adaptive optics is a strategy to compensate for sample-induced aberrations in microscopy applications. Generally, it requires the presence of "guide stars" in the sample to serve as localized reference targets. We describe an implementation of conjugate adaptive optics that is amenable to widefield (i.e. non-scanning) microscopy, and can provide aberration corrections over potentially large fields of view without the use of guide stars. A unique feature of our implementation is that it is based on wavefront sensing with a single-shot partitioned-aperture sensor that provides large dynamic range compatible with extended samples. Combined information provided by this sensor and the imaging camera enable robust image de-blurring based on a rapid estimation of sample and aberrations obtained by closed-loop feedback. We present the theoretical principle of our technique and proof of concept experimental demonstrations.
Receding-horizon adaptive contyrol of aero-optical wavefronts
Tesch, J.; Gibson, S.; Verhaegen, M.
2013-01-01
A new method for adaptive prediction and correction of wavefront errors in adaptive optics (AO) is introduced. The new method is based on receding-horizon control design and an adaptive lattice filter. Experimental results presented illustrate the capability of the new adaptive controller to predict
Bending light on demand by holographic sculpturing its wavefront
Latychevskaia, Tatiana
2015-01-01
A classical light beam propagates along a straight line and does not bend unless in a medium of variable refractive index. It is well known that by modifying the wavefront in a certain manner, the light intensity can be turned into a certain shape. Examples are optical lenses or Fresnel Zone Plates for focusing an incident wave to a point at the focal plane. Another example are Airy beams created by modifying the phase distribution of the wavefront into an Airy function resulting in a bending of the light intensity while propagating. A further example is holography, where the phase of the wavefront passing through a hologram is changed to mimic the object wavefront, thus providing the illusion that the original object is present in space. However, all these known techniques allow for limited light modifications: either focusing within a limited region in space2 or shaping a certain class of parametric curves along the optical axis or creating a bend in a quadratic-dependent declination as in the case of Airy ...
Liquid deformable mirror for high-order wavefront correction
Vuelban, E.M.; Bhattacharya, N.; Braat, J.J.M.
2006-01-01
We propose and demonstrate a novel liquid deformable mirror, based on electrocapillary actuation, for highorder wavefront correction. The device consists of a two-dimensional array of vertically oriented microchannels filled with two immiscible liquids, an aqueous electrolyte, and a viscous dielectr
Describing the Corneal Shape after Wavefront-Optimized Photorefractive Keratectomy
de Jong, Tim; Wijdh, Robert H. J.; Koopmans, Steven A.; Jansonius, Nomdo M.
2014-01-01
PURPOSE: To develop a procedure for describing wavefront-optimized photorefractive keratectomy (PRK) corneas and to characterize PRK-induced changes in shape. METHODS: We analyzed preoperative and postoperative corneal elevation data of 41 eyes of 41 patients (mean [±SD] age, 38 [±11] years) who und
Note on wavefront dislocation in surface water waves
Karjanto, Natanael; Groesen, van E.
2007-01-01
At singular points of a wave field, where the amplitude vanishes, the phase may become singular and wavefront dislocation may occur. In this Letter we investigate for wave fields in one spatial dimension the appearance of these essentially linear phenomena. We introduce the Chu–Mei quotient as it is
11 A METHOD FOR WAVEFRONT CURVATURE RANGING OF ...
African Journals Online (AJOL)
algorithm estimates the curvature of the incident wavefront of the source with ... A narrow-band (NB) filter is used to increase the SNR of the measured signal ..... oCher-scua:s cootn'bute to the varimce about this mean. This property forms the ...
Linear-constraint wavefront control for exoplanet coronagraphic imaging systems
Sun, He; Eldorado Riggs, A. J.; Kasdin, N. Jeremy; Vanderbei, Robert J.; Groff, Tyler Dean
2017-01-01
A coronagraph is a leading technology for achieving high-contrast imaging of exoplanets in a space telescope. It uses a system of several masks to modify the diffraction and achieve extremely high contrast in the image plane around target stars. However, coronagraphic imaging systems are very sensitive to optical aberrations, so wavefront correction using deformable mirrors (DMs) is necessary to avoid contrast degradation in the image plane. Electric field conjugation (EFC) and Stroke minimization (SM) are two primary high-contrast wavefront controllers explored in the past decade. EFC minimizes the average contrast in the search areas while regularizing the strength of the control inputs. Stroke minimization calculates the minimum DM commands under the constraint that a target average contrast is achieved. Recently in the High Contrast Imaging Lab at Princeton University (HCIL), a new linear-constraint wavefront controller based on stroke minimization was developed and demonstrated using numerical simulation. Instead of only constraining the average contrast over the entire search area, the new controller constrains the electric field of each single pixel using linear programming, which could led to significant increases in speed of the wavefront correction and also create more uniform dark holes. As a follow-up of this work, another linear-constraint controller modified from EFC is demonstrated theoretically and numerically and the lab verification of the linear-constraint controllers is reported. Based on the simulation and lab results, the pros and cons of linear-constraint controllers are carefully compared with EFC and stroke minimization.
Wavefronts and caustic associated with Durnin’s beams
de Jesús Cabrera-Rosas, Omar; Espíndola-Ramos, Ernesto; Alejandro Juárez-Reyes, Salvador; Julián-Macías, Israel; Ortega-Vidals, Paula; Silva-Ortigoza, Gilberto; Silva-Ortigoza, Ramón; Sosa-Sánchez, Citlalli Teresa
2017-01-01
The aim of the present work is to give a geometrical characterization of Durnin’s beams. That is, we compute the wavefronts and caustic associated with the nondiffracting solutions to the scalar wave equation introduced by Durnin. To this end, first we show that in an isotropic optical medium \\psi ({r},t)={{{e}}}{{i}[{k}0S({r})-ω t]} is an exact solution of the wave equation, if and only if, S is a solution of both the eikonal and Laplace equations, then from one and two-parameter families of this type of solution and the superposition principle we define new solutions of the wave equation, in particular we show that the ideal nondiffracting beams are one example of this type of construction in free space. Using this fact, the wavefronts and caustic associated with those beams are computed. We find that their caustic has only one branch, which is invariant under translations along the direction of evolution of the beam. Finally, the Bessel beam of order m is worked out explicitly and we find that it is characterized by wavefronts that are deformations of conical ones and the caustic is an infinite cylinder of radius proportional to m. In the case m = 0, the wavefronts are cones and the caustic degenerates into an infinite line.
The stochastic integrable AKNS hierarchy
Arnaudon, Alexis
2015-01-01
We derive a stochastic AKNS hierarchy using geometrical methods. The integrability is shown via a stochastic zero curvature relation associated with a stochastic isospectral problem. We expose some of the stochastic integrable partial differential equations which extend the stochastic KdV equation discovered by M. Wadati in 1983 for all the AKNS flows. We also show how to find stochastic solitons from the stochastic evolution of the scattering data of the stochastic IST. We finally expose som...
Moawia Alghalith
2012-01-01
We present new stochastic differential equations, that are more general and simpler than the existing Ito-based stochastic differential equations. As an example, we apply our approach to the investment (portfolio) model.
Stochastic processes - quantum physics
Energy Technology Data Exchange (ETDEWEB)
Streit, L. (Bielefeld Univ. (Germany, F.R.))
1984-01-01
The author presents an elementary introduction to stochastic processes. He starts from simple quantum mechanics and considers problems in probability, finally presenting quantum dynamics in terms of stochastic processes.
Stochastic tools in turbulence
Lumey, John L
2012-01-01
Stochastic Tools in Turbulence discusses the available mathematical tools to describe stochastic vector fields to solve problems related to these fields. The book deals with the needs of turbulence in relation to stochastic vector fields, particularly, on three-dimensional aspects, linear problems, and stochastic model building. The text describes probability distributions and densities, including Lebesgue integration, conditional probabilities, conditional expectations, statistical independence, lack of correlation. The book also explains the significance of the moments, the properties of the
Energy Technology Data Exchange (ETDEWEB)
Brennan,J.M.; Blaskiewicz, M. M.; Severino, F.
2009-05-04
After the success of longitudinal stochastic cooling of bunched heavy ion beam in RHIC, transverse stochastic cooling in the vertical plane of Yellow ring was installed and is being commissioned with proton beam. This report presents the status of the effort and gives an estimate, based on simulation, of the RHIC luminosity with stochastic cooling in all planes.
Design of the wavefront sensor unit of ARGOS, the LBT laser guide star system
Bonaglia, Marco
2012-01-01
ARGOS is the laser guide star ground layer adaptive optics system of the LBT. ARGOS is designed to bring a moderate but uniform reduction of the PSF size over a FoV as large as 4x4arcmin, allowing a significative increase of the science throughput of LUCI, the LBT NIR imager and MOS. ARGOS relays on 3 Rayleigh beacons to sense the lower layers of the atmosphere achieving almost 100% sky coverage. The ground layer AO correction is allowed by the 2 adaptive secondaries of the LBT. This PhD thesis first discusses a study based on numerical simulations and aimed to evaluate the performance of ARGOS. This work has been carried out using CAOS and representing in the code most of the features that characterize the system itself: as the laser beacon propagation in the atmosphere, the SH type wavefront sensing, the AO reconstruction and closed loop delays and the atmosphere tip-tilt sensing done using a NGS and a quad-cell type sensor. The results obtained in this study are in agreement and definitively confirm the pe...
Stochastic differential equations and a biological system
DEFF Research Database (Denmark)
Wang, Chunyan
1994-01-01
on experimental data is considered. As an example, the growth of bacteria Pseudomonas fluorescens is taken. Due to the specific features of stochastic differential equations, namely that their solutions do not exist in the general sense, two new integrals - the Ito integral and the Stratonovich integral - have......The purpose of this Ph.D. study is to explore the property of a growth process. The study includes solving and simulating of the growth process which is described in terms of stochastic differential equations. The identification of the growth and variability parameters of the process based......, Milstein and Runge-Kutta methods are used. Because of the specific feature of the model for the growth process, that its solution does not exist in the general sense, we combine these numerical integration methods with a transformation technique, and the solutions are derived in the Ito sense...
Balibrea-Iniesta, Francisco; Lopesino, Carlos; Wiggins, Stephen; Mancho, Ana M.
2016-12-01
In this paper, we introduce a new technique for depicting the phase portrait of stochastic differential equations. Following previous work for deterministic systems, we represent the phase space by means of a generalization of the method of Lagrangian descriptors to stochastic differential equations. Analogously to the deterministic differential equations setting, the Lagrangian descriptors graphically provide the distinguished trajectories and hyperbolic structures arising within the stochastic dynamics, such as random fixed points and their stable and unstable manifolds. We analyze the sense in which structures form barriers to transport in stochastic systems. We apply the method to several benchmark examples where the deterministic phase space structures are well-understood. In particular, we apply our method to the noisy saddle, the stochastically forced Duffing equation, and the stochastic double gyre model that is a benchmark for analyzing fluid transport.
A NOTE ON THE STOCHASTIC ROOTS OF STOCHASTIC MATRICES
Institute of Scientific and Technical Information of China (English)
Qi-Ming HE; Eldon GUNN
2003-01-01
In this paper, we study the stochastic root matrices of stochastic matrices. All stochastic roots of 2×2 stochastic matrices are found explicitly. A method based on characteristic polynomial of matrix is developed to find all real root matrices that are functions of the original 3×3 matrix, including all possible (function) stochastic root matrices. In addition, we comment on some numerical methods for computing stochastic root matrices of stochastic matrices.
Ogawa, Shigeyoshi
2017-01-01
This book presents an elementary introduction to the theory of noncausal stochastic calculus that arises as a natural alternative to the standard theory of stochastic calculus founded in 1944 by Professor Kiyoshi Itô. As is generally known, Itô Calculus is essentially based on the "hypothesis of causality", asking random functions to be adapted to a natural filtration generated by Brownian motion or more generally by square integrable martingale. The intention in this book is to establish a stochastic calculus that is free from this "hypothesis of causality". To be more precise, a noncausal theory of stochastic calculus is developed in this book, based on the noncausal integral introduced by the author in 1979. After studying basic properties of the noncausal stochastic integral, various concrete problems of noncausal nature are considered, mostly concerning stochastic functional equations such as SDE, SIE, SPDE, and others, to show not only the necessity of such theory of noncausal stochastic calculus but ...
Stochastic Lie group integrators
Malham, Simon J A
2007-01-01
We present Lie group integrators for nonlinear stochastic differential equations with non-commutative vector fields whose solution evolves on a smooth finite dimensional manifold. Given a Lie group action that generates transport along the manifold, we pull back the stochastic flow on the manifold to the Lie group via the action, and subsequently pull back the flow to the corresponding Lie algebra via the exponential map. We construct an approximation to the stochastic flow in the Lie algebra via closed operations and then push back to the Lie group and then to the manifold, thus ensuring our approximation lies in the manifold. We call such schemes stochastic Munthe-Kaas methods after their deterministic counterparts. We also present stochastic Lie group integration schemes based on Castell--Gaines methods. These involve using an underlying ordinary differential integrator to approximate the flow generated by a truncated stochastic exponential Lie series. They become stochastic Lie group integrator schemes if...
Real-time phasing and co-phasing of a ground-based interferometer with a pyramid wavefront sensor.
Vérinaud, Christophe; Esposito, Simone
The feasibility and remarkable performances of pyramid wavefront sensing in adaptive optics have already been demonstrated. In this paper, we investigate another potential of the pyramid wavefront sensor which is differential piston sensing in interferometry: this can be done by using a glass pyramid placed in a combined focal plane of the interferometer, and a CCD sampling the usual four diffracted images of the pupil, composed here by the interferometer apertures. From a purely geometrical point of view, no information about the differential phase between two pupils could be retrieved. However, as the sensor main component, the pyramid, is located directly in the interference pattern of the interferometer, the piston information present in the electric field of the combined focal plane modifies, after diffraction by the pyramid, the intensity distribution in the pupil plane. Thus, with only one sensor, the differential piston can be measured, in addition to the classical local tilts determination. In this paper we present the concept and give some simulation results showing the performances of a closed-loop adaptive optics correction for a ground-based two-telescope interferometer like the Large Binocular Telescope.
Terahertz wavefront control by tunable metasurface made of graphene ribbons
Energy Technology Data Exchange (ETDEWEB)
Yatooshi, Takumi; Ishikawa, Atsushi, E-mail: a-ishikawa@okayama-u.ac.jp; Tsuruta, Kenji [Department of Electrical and Electronic Engineering, Okayama University, 3-1-1 Tsushimanaka, Kitaku, Okayama 700-8530 (Japan)
2015-08-03
We propose a tunable metasurface consisting of an array of graphene ribbons on a silver mirror with a SiO{sub 2} gap layer to control reflected wavefront at terahertz frequencies. The graphene ribbons exhibit localized plasmon resonances depending on their Fermi levels to introduce abrupt phase shifts along the metasurface. With interference of the Fabry-Perot resonances in the SiO{sub 2} layer, phase shift through the system is largely accumulated, covering the 0-to-2π range for full control of the wavefront. Numerical simulations prove that wide-angle beam steering up to 53° with a high reflection efficiency of 60% is achieved at 5 THz within a switching time shorter than 0.6 ps.
10 um wavefront spatial filtering first results with chalcogenide fibers
Bordé, P J; Nguyen, T; Amy-Klein, A; Daussy, C; Raynal, P; Léger, A; Mazé, G; Borde, Pascal; Perrin, Guy; Nguyen, Thanh; Amy-Klein, Anne; Daussy, Christophe; Raynal, Pierre-Ivan; Leger, Alain; Maze, Gwenael
2003-01-01
Wavefront cleaning by single-mode fibers has proved to be efficient in optical-infrared interferometry to improve calibration quality. For instance, the FLUOR instrument has demonstrated the capability of fluoride glass single-mode fibers in this respect in the K and L bands. New interferometric instruments developped for the mid-infrared require the same capability for the 8-12 um range. We have initiated a program to develop single-mode fibers in the prospect of the VLTI mid-infrared instrument MIDI and of the ESA/DARWIN and NASA/TPF missions that require excellent wavefront quality. In order to characterize the performances of chalcogenide fibers we are developping, we have set up an experiment to measure the far-field pattern radiated at 10 um. In this paper, we report the first and promising results obtained with this new component.
Discontinuous Electromagnetic Fields Using Huygens Sources For Wavefront Manipulation
Selvanayagam, Michael
2013-01-01
We introduce the idea of discontinuous electric and magnetic fields at a boundary to design and shape wavefronts in an arbitrary manner. To create this discontinuity in the field we use electric and magnetic currents which act like a Huygens source to radiate the desired wavefront. These currents can be synthesized either by an array of electric and magnetic dipoles or by a combined impedance and admittance surface. A dipole array is an active implementation to impose discontinuous fields while the impedance/admittance surface acts as a passive one. We then expand on our previous work showing how electric and magnetic dipole arrays can be used to cloak an object demonstrating two novel cloaking schemes. We also show how to arbitrarily refract a beam using a set of impedance and admittance surfaces. Refraction using the idea of discontinuous fields is shown to be a more general case of refraction using phase discontinuities.
Wavefront modulation of water surface wave by a metasurface
Institute of Scientific and Technical Information of China (English)
孙海涛; 程营; 王敬时; 刘晓峻
2015-01-01
We design a planar metasurface to modulate the wavefront of a water surface wave (WSW) on a deep sub-wavelength scale. The metasurface is composed of an array of coiling-up-space units with specially designed parameters, and can take on the work of steering the wavefront when it is pierced into water. Like their acoustic counterparts, the modulation of WSW is ascribed to the gradient phase shift of the coiling-up-space units, which can be perfectly tuned by changing the coiling plate length and channel number inside the units. According to the generalized Snell’s law, negative refraction and‘driven’ surface mode of WSW are also demonstrated at certain incidences. Specially, the transmitted WSW could be efficiently guided out by linking a symmetrically-corrugated channel in‘driven’ surface mode. This work may have potential applications in water wave energy extraction and coastal protection.
Specification and Measurement of Mid-Frequency Wavefront Errors
Institute of Scientific and Technical Information of China (English)
XUAN Bin; XIE Jing-jiang
2006-01-01
Mid-frequency wavefront errors can be of the most importance for some optical components, but they're not explicitly covered by corresponding international standards such as ISO 10110. The testing methods for the errors also have a lot of aspects to be improved. This paper gives an overview of the specifications especially of PSD. NIF,developed by America, and XMM, developed by Europe, have both discovered some new testing methods.
Wavefront Reconstruction and Mirror Surface Optimizationfor Adaptive Optics
2014-06-01
correction. A DM has a reflective surface with actuators along the back struc- ture that apply forces causing the mirror surface to adapt to a desired shape...actuators. The actuators cause forces along the back of the mirror structure and the mirror surface deflects to form the conjugate shape of the wavefront...optical axis of the primary mirror. The interferometer and null corrector are mounted to remove the 81 Interferometer Null corrector Hexapod ❋✐❣✉r
Study of the wavefront aberrations in children with amblyopia
Institute of Scientific and Technical Information of China (English)
ZHAO Peng-fei; ZHOU Yue-hua; WANG Ning-li; ZHANG Jing
2010-01-01
Background Amblyopia is a common ophthalmological condition and the wavefront aberrometer is a relatively new diagnostic tool used globally to measure optical characteristics of human eyes as well as to study refractive errors in amblyopic eyes. We studied the wavefront aberration of the amblyopic children's eyes and analyzed the mechanism of the wavefront aberration in the formation of the amblyopia, try to investigate the new evidence of the treatment of the amblyopia, especially in the refractory amblyopia.Methods The WaveScan Wavefront System (VISX, USA) aberrometer was used to investigate four groups of children under dark accommodation and cilliary muscle paralysis. There were 45 cases in the metropic group, 87 in the amblyopic group, 92 in the corrected-amblyopic group and 38 in the refractory amblyopic group. One-way analysis of variance (ANOVA), t-test and multivariate linear regression were used to analyze all the data.Results Third order to 6th order aberrations showed a decreasing trend whereas in the higher order aberrations the main ones were 3rd order coma (Z3-1-Z31), trefoil (Z3-3-Z33) and 4th order aberration (Z40); and 3rd order coma represented the highest percentage of all three main aberrations. Within 3rd order coma, vertical coma (Z3-1) accounted for a greater percentage than horizontal coma (Z31). Significant differences of vertical coma were found among all clinical groups of children: vertical coma in the amblyopic group (0.17±0.15) was significantly higher than in the metropic group (0.11±0.13, P0.05).Conclusions Although lower order aberrations such as defocus (myopia and hyperopia) and astigmatism are major factors determining the quality of the retinal image, higher order aberrations also need to be considered in amblyopic eyes as their effects are significant.
Novel technology for reducing wavefront image processing latency
Barr, David; Schwartz, Noah; Vick, Andy; Coughlan, John; Halsall, Rob; Basden, Alastair; Dipper, Nigel
2016-07-01
Adaptive optics is essential for the successful operation of the future Extremely Large Telescopes (ELTs). At the heart of these AO system lies the real-time control which has become computationally challenging. A majority of the previous efforts has been aimed at reducing the wavefront reconstruction latency by using many-core hardware accelerators such as Xeon Phis and GPUs. These modern hardware solutions offer a large numbers of cores combined with high memory bandwidths but have restrictive input/output (I/O). The lack of efficient I/O capability makes the data handling very inefficient and adds both to the overall latency and jitter. For example a single wavefront sensor for an ELT scale adaptive optics system can produce hundreds of millions of pixels per second that need to be processed. Passing all this data through a CPU and into GPUs or Xeon Phis, even by reducing memory copies by using systems such as GPUDirect, is highly inefficient. The Mellanox TILE series is a novel technology offering a high number of cores and multiple 10 Gbps Ethernet ports. We present results of the TILE-Gx36 as a front-end wavefront sensor processing unit. In doing so we are able to greatly reduce the amount of data needed to be transferred to the wavefront reconstruction hardware. We show that the performance of the Mellanox TILE-GX36 is in-line with typical requirements, in terms of mean calculation time and acceptable jitter, for E-ELT first-light instruments and that the Mellanox TILE series is a serious contender for all E-ELT instruments.
The speed of reaction-diffusion wavefronts in nonsteady media
Energy Technology Data Exchange (ETDEWEB)
Mendez, Vicenc [Departament de Medicina, Facultat de Ciencies de la Salut, Universitat Internacional de Catalunya. c/Gomera s/n, 08190-Sant Cugat del Valles (Barcelona) (Spain); Fort, Joaquim [Departament de Fisica, Universitat de Girona, Campus Montilivi, 17071 Girona, Catalonia (Spain); Pujol, Toni [Departament de Fisica, Universitat de Girona, Campus Montilivi, 17071 Girona, Catalonia (Spain)
2003-04-11
The evolution of the speed of wavefronts for reaction-diffusion equations with time-varying parameters is analysed. We make use of singular perturbative analysis to study the temporal evolution of the speed for pushed fronts. The analogy with Hamilton-Jacobi dynamics allows us to consider the problem for pulled fronts, which is described by Kolmogorov-Petrovskii-Piskunov (KPP) reaction kinetics. Both analytical studies are in good agreement with the results of numerical solutions.
The speed of reaction-diffusion wavefronts in nonsteady media
Méndez, V; Pujol, T
2003-01-01
The evolution of the speed of wavefronts for reaction-diffusion equations with time-varying parameters is analysed. We make use of singular perturbative analysis to study the temporal evolution of the speed for pushed fronts. The analogy with Hamilton-Jacobi dynamics allows us to consider the problem for pulled fronts, which is described by Kolmogorov-Petrovskii-Piskunov (KPP) reaction kinetics. Both analytical studies are in good agreement with the results of numerical solutions.
Research on technique of wavefront retrieval based on Foucault test
Yuan, Lvjun; Wu, Zhonghua
2010-05-01
During finely grinding the best fit sphere and initial stage of polishing, surface error of large aperture aspheric mirrors is too big to test using common interferometer. Foucault test is widely used in fabricating large aperture mirrors. However, the optical path is disturbed seriously by air turbulence, and changes of light and dark zones can not be identified, which often lowers people's judging ability and results in making mistake to diagnose surface error of the whole mirror. To solve the problem, the research presents wavefront retrieval based on Foucault test through digital image processing and quantitative calculation. Firstly, real Foucault image can be gained through collecting a variety of images by CCD, and then average these image to eliminate air turbulence. Secondly, gray values are converted into surface error values through principle derivation, mathematical modeling, and software programming. Thirdly, linear deviation brought by defocus should be removed by least-square method to get real surface error. At last, according to real surface error, plot wavefront map, gray contour map and corresponding pseudo color contour map. The experimental results indicates that the three-dimensional wavefront map and two-dimensional contour map are able to accurately and intuitively show surface error on the whole mirrors under test, and they are beneficial to grasp surface error as a whole. The technique can be used to guide the fabrication of large aperture and long focal mirrors during grinding and initial stage of polishing the aspheric surface, which improves fabricating efficiency and precision greatly.
X-ray pulse wavefront metrology using speckle tracking
Energy Technology Data Exchange (ETDEWEB)
Berujon, Sebastien, E-mail: berujon@esrf.eu; Ziegler, Eric; Cloetens, Peter [European Synchrotron Radiation Facility, BP-220, F-38043 Grenoble (France)
2015-05-09
The theoretical description and experimental implementation of a speckle-tracking-based instrument which permits the characterisation of X-ray pulse wavefronts. An instrument allowing the quantitative analysis of X-ray pulsed wavefronts is presented and its processing method explained. The system relies on the X-ray speckle tracking principle to accurately measure the phase gradient of the X-ray beam from which beam optical aberrations can be deduced. The key component of this instrument, a semi-transparent scintillator emitting visible light while transmitting X-rays, allows simultaneous recording of two speckle images at two different propagation distances from the X-ray source. The speckle tracking procedure for a reference-less metrology mode is described with a detailed account on the advanced processing schemes used. A method to characterize and compensate for the imaging detector distortion, whose principle is also based on speckle, is included. The presented instrument is expected to find interest at synchrotrons and at the new X-ray free-electron laser sources under development worldwide where successful exploitation of beams relies on the availability of an accurate wavefront metrology.
Lee, Hun; Park, Si Yoon; Yong Kang, David Sung; Ha, Byoung Jin; Choi, Jin Young; Kim, Eung Kweon; Seo, Kyoung Yul; Kim, Tae-Im
2016-06-01
To evaluate the effects of photorefractive keratectomy (PRK) combined with corneal wavefront-guided ablation profiles and hyperaspheric ablation profiles on changes in higher-order aberrations (HOAs). Yonsei University College of Medicine and Eyereum Clinic, Seoul, South Korea. Comparative observational case series. Medical records of patients who had corneal wavefront-guided hyperaspheric PRK, corneal wavefront-guided mild-aspheric PRK, or non-corneal wavefront-guided mild-aspheric PRK were analyzed. The logMAR uncorrected distance visual acuity (UDVA), manifest refraction spherical equivalent (MRSE), and changes in corneal aberrations (root-mean-square [RMS] HOAs, spherical aberration, coma) were evaluated 1, 3, and 6 months postoperatively. The records of 61 patients (96 eyes) were reviewed. There was no statistically significant difference in logMAR UDVA or MRSE between the 3 groups at any timepoint. Corneal RMS HOAs were significantly smaller in the corneal wavefront-guided hyperaspheric group and the corneal wavefront-guided mild-aspheric group than in the noncorneal wavefront-guided mild-aspheric group at each timepoint. Corneal spherical aberration was significantly smaller for corneal wavefront-guided hyperaspheric PRK than for noncorneal wavefront-guided mild-aspheric PRK 6 months postoperatively. Changes in corneal spherical aberration (preoperatively and 6 months postoperatively) in corneal wavefront-guided hyperaspheric PRK were significantly smaller than in corneal wavefront-guided mild-aspheric PRK (P = .046). Corneal coma was significantly smaller with corneal wavefront-guided hyperaspheric PRK and corneal wavefront-guided mild-aspheric PRK than with noncorneal wavefront-guided mild-aspheric PRK 3 months and 6 months postoperatively. Corneal wavefront-guided hyperaspheric PRK induced less corneal spherical aberration 6 months postoperatively than corneal wavefront-guided mild-aspheric PRK and noncorneal wavefront-guided mild-aspheric PRK
Chen, Hua; Hou, Lv; Zhou, Xinglin
2016-08-20
We present a new apparatus for active compensation of wavefront aberrations by controllable heating of a lens using a film heater matrix. The annular electric film heater matrix, comprising 24 individual heaters, is attached to the periphery of a lens. Utilizing the linear superposition, and wavefront change proportional to the heating energy properties induced by heating, a controllable wavefront can be defined by solving a linear function. The two properties of wavefront change of a lens have been confirmed through a specially designed experiment. The feasibility of the compensation method is validated by compensating the wavefront of a plate lens. The results show that the wavefront of the lens changes from 12.52 to 2.95 nm rms after compensation. With a more precise electric controlling board, better results could be achieved.
Simulation of wavefront reconstruction in beam reshaping system for rectangular laser beam
Zhou, Qiong; Liu, Wenguang; Jiang, Zongfu
2014-05-01
A new method to calculating the wavefront of slap laser is studied in this paper. The method is based on the ray trace theory of geometrical optics. By using the Zemax simulation software and Matlab calculation software, the wavefront of rectangular beam in beam reshaping system is reconstructed. Firstly, with the x- and y-slope measurement of reshaping beam the direction cosine of wavefront can be calculated. Then, the inverse beam path of beam reshaping system is built by using Zemax simulation software and the direction cosine of rectangular beam can be given, too. Finally, Southwell zonal model is used to reconstruct the wavefront of rectangular beam in computer simulation. Once the wavefront is received, the aberration of laser can be eliminated by using the proper configuration of beam reshaping system. It is shown that this method to reconstruct the wavefront of rectangular beam can evidently reduce the negative influence of additional aberration induced by beam reshaping system.
Algorithm study of wavefront reconstruction based on the cyclic radial shear interferometer
Li Da Hai; Chen Huai Xin; Chen Zhen Pei; Chen Bo Fei; Jing Feng
2002-01-01
The author presents a new algorithm of wavefront reconstruction based on the cyclic radial shear interferometer. The algorithm is a technique that the actual wavefront can be reconstructed directly and accurately from the distribution of phase difference which is obtained from the radial shearing pattern by Fourier transform. It can help to measure accurately the distorted wavefront of ICF in-process. An experiment is presented to test the algorithm
Yang, Bin; Wei, Yin; Chen, Xinhua; Tang, Minxue
2014-11-01
Membrane mirror with flexible polymer film substrate is a new-concept ultra lightweight mirror for space applications. Compared with traditional mirrors, membrane mirror has the advantages of lightweight, folding and deployable, low cost and etc. Due to the surface shape of flexible membrane mirror is easy to deviate from the design surface shape, it will bring wavefront aberration to the optical system. In order to solve this problem, a method of membrane mirror wavefront aberration correction based on the liquid crystal spatial light modulator (LCSLM) will be studied in this paper. The wavefront aberration correction principle of LCSLM is described and the phase modulation property of a LCSLM is measured and analyzed firstly. Then the membrane mirror wavefront aberration correction system is designed and established according to the optical properties of a membrane mirror. The LCSLM and a Hartmann-Shack sensor are used as a wavefront corrector and a wavefront detector, respectively. The detected wavefront aberration is calculated and converted into voltage value on LCSLM for the mirror wavefront aberration correction by programming in Matlab. When in experiment, the wavefront aberration of a glass plane mirror with a diameter of 70 mm is measured and corrected for verifying the feasibility of the experiment system and the correctness of the program. The PV value and RMS value of distorted wavefront are reduced and near diffraction limited optical performance is achieved. On this basis, the wavefront aberration of the aperture center Φ25 mm in a membrane mirror with a diameter of 200 mm is corrected and the errors are analyzed. It provides a means of correcting the wavefront aberration of membrane mirror.
Fundamentals of Stochastic Networks
Ibe, Oliver C
2011-01-01
An interdisciplinary approach to understanding queueing and graphical networks In today's era of interdisciplinary studies and research activities, network models are becoming increasingly important in various areas where they have not regularly been used. Combining techniques from stochastic processes and graph theory to analyze the behavior of networks, Fundamentals of Stochastic Networks provides an interdisciplinary approach by including practical applications of these stochastic networks in various fields of study, from engineering and operations management to communications and the physi
Fluctuations as stochastic deformation
Kazinski, P. O.
2008-04-01
A notion of stochastic deformation is introduced and the corresponding algebraic deformation procedure is developed. This procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an imaginary deformation parameter (the Planck constant). This method is demonstrated on diverse relativistic and nonrelativistic models with finite and infinite degrees of freedom. It is shown that under stochastic deformation the model of a nonrelativistic particle interacting with the electromagnetic field on a curved background passes into the stochastic model described by the Fokker-Planck equation with the diffusion tensor being the inverse metric tensor. The first stochastic correction to the Newton equations for this system is found. The Klein-Kramers equation is also derived as the stochastic deformation of a certain classical model. Relativistic generalizations of the Fokker-Planck and Klein-Kramers equations are obtained by applying the procedure of stochastic deformation to appropriate relativistic classical models. The analog of the Fokker-Planck equation associated with the stochastic Lorentz-Dirac equation is derived too. The stochastic deformation of the models of a free scalar field and an electromagnetic field is investigated. It turns out that in the latter case the obtained stochastic model describes a fluctuating electromagnetic field in a transparent medium.
Singular stochastic differential equations
Cherny, Alexander S
2005-01-01
The authors introduce, in this research monograph on stochastic differential equations, a class of points termed isolated singular points. Stochastic differential equations possessing such points (called singular stochastic differential equations here) arise often in theory and in applications. However, known conditions for the existence and uniqueness of a solution typically fail for such equations. The book concentrates on the study of the existence, the uniqueness, and, what is most important, on the qualitative behaviour of solutions of singular stochastic differential equations. This is done by providing a qualitative classification of isolated singular points, into 48 possible types.
Numerical estimation of the curvature of a light wavefront in a weak gravitational field
Miguel, A San; Pascual-Sanchez, J -F
2009-01-01
The geometry of a light wavefront evolving in the 3--space associated with a post-Newtonian relativistic spacetime from a flat wavefront is studied numerically by means of the ray tracing method. For a discretization of the bidimensional wavefront the surface fitting technique is used to determine the curvature of this surface at each vertex of the mesh. The relationship between the curvature of a wavefront and the change of the arrival time at different points on the Earth is also numerically discussed.
Laundy, David; Alcock, Simon G.; Alianelli, Lucia; Sutter, John P.; Sawhney, Kawal J. S.; Chubar, Oleg
2014-09-01
A full wave propagation of X-rays from source to sample at a storage ring beamline requires simulation of the electron beam source and optical elements in the beamline. The finite emittance source causes the appearance of partial coherence in the wave field. Consequently, the wavefront cannot be treated exactly with fully coherent wave propagation or fully incoherent ray tracing. We have used the wavefront code Synchrotron Radiation Workshop (SRW) to perform partially coherent wavefront propagation using a parallel computing cluster at the Diamond Light Source. Measured mirror profiles have been used to correct the wavefront for surface errors.
Janin-Potiron, P.; N'Diaye, M.; Martinez, P.; Vigan, A.; Dohlen, K.; Carbillet, M.
2017-07-01
Context. Segmented aperture telescopes require an alignment procedure with successive steps from coarse alignment to monitoring process in order to provide very high optical quality images for stringent science operations such as exoplanet imaging. The final step, referred to as fine phasing, calls for a high sensitivity wavefront sensing and control system in a diffraction-limited regime to achieve segment alignment with nanometric accuracy. In this context, Zernike wavefront sensors represent promising options for such a calibration. A concept called the Zernike unit for segment phasing (ZEUS) was previously developed for ground-based applications to operate under seeing-limited images. Such a concept is, however, not suitable for fine cophasing with diffraction-limited images. Aims: We revisit ZELDA, a Zernike sensor that was developed for the measurement of residual aberrations in exoplanet direct imagers, to measure segment piston, tip, and tilt in the diffraction-limited regime. Methods: We introduce a novel analysis scheme of the sensor signal that relies on piston, tip, and tilt estimators for each segment, and provide probabilistic insights to predict the success of a closed-loop correction as a function of the initial wavefront error. Results: The sensor unambiguously and simultaneously retrieves segment piston and tip-tilt misalignment. Our scheme allows for correction of these errors in closed-loop operation down to nearly zero residuals in a few iterations. This sensor also shows low sensitivity to misalignment of its parts and high ability for operation with a relatively bright natural guide star. Conclusions: Our cophasing sensor relies on existing mask technologies that make the concept already available for segmented apertures in future space missions.
K. Wei (Katy); M. Moinat (Maxim); T.R. Maarleveld (Timo); F.J. Bruggeman (Frank)
2014-01-01
htmlabstractSignal transduction by prokaryotes almost exclusively relies on two-component systems for sensing and responding to (extracellular) signals. Here, we use stochastic models of two-component systems to better understand the impact of stochasticity on the fidelity and robustness of signal
On stochastic and discontinuous optimization methods
Energy Technology Data Exchange (ETDEWEB)
Ermoliev, Y.
1994-12-31
The talk is based on a joint article by Y. Ermoliev, V. Norkin and R. Wets. A new notion of subgradient is introduced which allows to develop easily implementable procedures of discontinuous optimization, in particular, finite-difference approximation schemes. The approach relies on the notion of differentiability in the sense of distributions converting a discontinuous optimization problem into a problem of the stochastic optimization. Applications involving risks and abrupt transitions are discussed.
Parameter Estimation in Stochastic Differential Equations; An Overview
DEFF Research Database (Denmark)
Nielsen, Jan Nygaard; Madsen, Henrik; Young, P. C.
2000-01-01
This paper presents an overview of the progress of research on parameter estimation methods for stochastic differential equations (mostly in the sense of Ito calculus) over the period 1981-1999. These are considered both without measurement noise and with measurement noise, where the discretely...... observed stochastic differential equations are embedded in a continuous-discrete time state space model. Every attempts has been made to include results from other scientific disciplines. Maximum likelihood estimation of parameters in nonlinear stochastic differential equations is in general not possible...
A Stochastic Employment Problem
Wu, Teng
2013-01-01
The Stochastic Employment Problem(SEP) is a variation of the Stochastic Assignment Problem which analyzes the scenario that one assigns balls into boxes. Balls arrive sequentially with each one having a binary vector X = (X[subscript 1], X[subscript 2],...,X[subscript n]) attached, with the interpretation being that if X[subscript i] = 1 the ball…
Stochastic Convection Parameterizations
Teixeira, Joao; Reynolds, Carolyn; Suselj, Kay; Matheou, Georgios
2012-01-01
computational fluid dynamics, radiation, clouds, turbulence, convection, gravity waves, surface interaction, radiation interaction, cloud and aerosol microphysics, complexity (vegetation, biogeochemistry, radiation versus turbulence/convection stochastic approach, non-linearities, Monte Carlo, high resolutions, large-Eddy Simulations, cloud structure, plumes, saturation in tropics, forecasting, parameterizations, stochastic, radiation-clod interaction, hurricane forecasts
Instantaneous stochastic perturbation theory
Lüscher, Martin
2015-01-01
A form of stochastic perturbation theory is described, where the representative stochastic fields are generated instantaneously rather than through a Markov process. The correctness of the procedure is established to all orders of the expansion and for a wide class of field theories that includes all common formulations of lattice QCD.
Verhoosel, C.V.; Gutiérrez, M.A.; Hulshoff, S.J.
2006-01-01
The field of fluid-structure interaction is combined with the field of stochastics to perform a stochastic flutter analysis. Various methods to directly incorporate the effects of uncertainties in the flutter analysis are investigated. The panel problem with a supersonic fluid flowing over it is con
Greenwood, Priscilla E
2016-01-01
This book describes a large number of open problems in the theory of stochastic neural systems, with the aim of enticing probabilists to work on them. This includes problems arising from stochastic models of individual neurons as well as those arising from stochastic models of the activities of small and large networks of interconnected neurons. The necessary neuroscience background to these problems is outlined within the text, so readers can grasp the context in which they arise. This book will be useful for graduate students and instructors providing material and references for applying probability to stochastic neuron modeling. Methods and results are presented, but the emphasis is on questions where additional stochastic analysis may contribute neuroscience insight. An extensive bibliography is included. Dr. Priscilla E. Greenwood is a Professor Emerita in the Department of Mathematics at the University of British Columbia. Dr. Lawrence M. Ward is a Professor in the Department of Psychology and the Brain...
Stochastic volatility selected readings
Shephard, Neil
2005-01-01
Neil Shephard has brought together a set of classic and central papers that have contributed to our understanding of financial volatility. They cover stocks, bonds and currencies and range from 1973 up to 2001. Shephard, a leading researcher in the field, provides a substantial introduction in which he discusses all major issues involved. General Introduction N. Shephard. Part I: Model Building. 1. A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices, (P. K. Clark). 2. Financial Returns Modelled by the Product of Two Stochastic Processes: A Study of Daily Sugar Prices, 1961-7, S. J. Taylor. 3. The Behavior of Random Variables with Nonstationary Variance and the Distribution of Security Prices, B. Rosenberg. 4. The Pricing of Options on Assets with Stochastic Volatilities, J. Hull and A. White. 5. The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor ARCH Model, F. X. Diebold and M. Nerlove. 6. Multivariate Stochastic Variance Models. 7. Stochastic Autoregressive...
Arcidiacono, Carmelo; Viotto, Valentina; Bergomi, Maria; Farinato, Jacopo; Magrin, Demetrio; Dima, Marco; Gullieuszik, Marco; Marafatto, Luca
2016-01-01
Dark wavefront sensing in its simplest and more crude form is a quad-cell with a round spot of dark ink acting as occulting disk at the center. This sensor exhibits fainter limiting magnitude than a conventional quad-cell, providing that the size of the occulting disk is slightly smaller than the size of the spot and smaller than the residual jitter movement in closed loop. We present simulations focusing a generic Adaptive Optics system using Natural Guide Stars to provide the tip-tilt signal. We consider a jitter spectrum of the residual correction including amplitudes exceeding the dark disk size.
Plantet, C; Meimon, S; Conan, J-M; Fusco, T
2015-11-01
Exoplanet direct imaging with large ground based telescopes requires eXtreme Adaptive Optics that couples high-order adaptive optics and coronagraphy. A key element of such systems is the high-order wavefront sensor. We study here several high-order wavefront sensing approaches, and more precisely compare their sensitivity to noise. Three techniques are considered: the classical Shack-Hartmann sensor, the pyramid sensor and the recently proposed LIFTed Shack-Hartmann sensor. They are compared in a unified framework based on precise diffractive models and on the Fisher information matrix, which conveys the information present in the data whatever the estimation method. The diagonal elements of the inverse of the Fisher information matrix, which we use as a figure of merit, are similar to noise propagation coefficients. With these diagonal elements, so called "Fisher coefficients", we show that the LIFTed Shack-Hartmann and pyramid sensors outperform the classical Shack-Hartmann sensor. In photon noise regime, the LIFTed Shack-Hartmann and modulated pyramid sensors obtain a similar overall noise propagation. The LIFTed Shack-Hartmann sensor however provides attractive noise properties on high orders.
Arbitrary optical wavefront shaping via spin-to-orbit coupling
Larocque, Hugo; Bouchard, Frédéric; Fickler, Robert; Upham, Jeremy; Boyd, Robert W; Karimi, Ebrahim
2016-01-01
Converting spin angular momentum to orbital angular momentum has been shown to be a practical and efficient method for generating optical beams carrying orbital angular momentum and possessing a space-varying polarized field. Here, we present novel liquid crystal devices for tailoring the wavefront of optical beams through the Pancharatnam-Berry phase concept. We demonstrate the versatility of these devices by generating an extensive range of optical beams such as beams carrying $\\pm200$ units of orbital angular momentum along with Bessel, Airy and Ince-Gauss beams. We characterize both the phase and the polarization properties of the generated beams, confirming our devices' performance.
Towards feasible and effective predictive wavefront control for adaptive optics
Energy Technology Data Exchange (ETDEWEB)
Poyneer, L A; Veran, J
2008-06-04
We have recently proposed Predictive Fourier Control, a computationally efficient and adaptive algorithm for predictive wavefront control that assumes frozen flow turbulence. We summarize refinements to the state-space model that allow operation with arbitrary computational delays and reduce the computational cost of solving for new control. We present initial atmospheric characterization using observations with Gemini North's Altair AO system. These observations, taken over 1 year, indicate that frozen flow is exists, contains substantial power, and is strongly detected 94% of the time.
Towards feasible and effective predictive wavefront control for adaptive optics
Energy Technology Data Exchange (ETDEWEB)
Poyneer, L A; Veran, J
2008-06-04
We have recently proposed Predictive Fourier Control, a computationally efficient and adaptive algorithm for predictive wavefront control that assumes frozen flow turbulence. We summarize refinements to the state-space model that allow operation with arbitrary computational delays and reduce the computational cost of solving for new control. We present initial atmospheric characterization using observations with Gemini North's Altair AO system. These observations, taken over 1 year, indicate that frozen flow is exists, contains substantial power, and is strongly detected 94% of the time.
Deformable Membrane Mirror for Wavefront Correction (Short Communication
Directory of Open Access Journals (Sweden)
Amita Gupta
2009-11-01
Full Text Available Deformable or adaptive mirrors are used in modern adaptive optics systems for direct correction of the aberrations in the light wavefront. Conventional deformable mirrors used for this purpose are expensive electromechanical devices. Deformable membrane mirror fabricated using microelectromechanical systems (MEMS technology is a low cost, compact adaptive optical element for correction of the lower-order optical aberrations such as defocus and astigmatism. In this paper, important aspects of device design and simulation, fabrication techniques, and test results are discussed.Defence Science Journal, 2009, 59(6, pp.590-594, DOI:http://dx.doi.org/10.14429/dsj.59.1563
Meskers, A.J.H.; Voigt, D.; Spronck, J.W.
2013-01-01
Many error sources can affect the accuracy of displacement measuring interferometer systems. In heterodyne interferometry two laser source frequencies constitute the finally detected wavefront. When the wavefronts of these source frequencies are non-ideal and one of them walks off the detector, the
Extracting hysteresis from nonlinear measurement of wavefront-sensorless adaptive optics system
Song, H.; Vdovin, G.; Fraanje, R.; Schitter, G.; Verhaegen, M.
2008-01-01
In many scientific and medical applications wavefront-sensorless adaptive optics (AO) systems are used to correct the wavefront aberration by optimizing a certain target parameter, which is nonlinear with respect to the control signal to the deformable mirror (DM). Hysteresis is the most common nonl
Expected gain in the pyramid wavefront sensor with limited Strehl ratio
Viotto, V.; Ragazzoni, R.; Bergomi, M.; Magrin, D.; Farinato, J.
2016-09-01
Context. One of the main properties of the pyramid wavefront sensor is that, once the loop is closed, and as the reference star image shrinks on the pyramid pin, the wavefront estimation signal-to-noise ratio can considerably improve. This has been shown to translate into a gain in limiting magnitude when compared with the Shack-Hartmann wavefront sensor, in which the sampling on the wavefront is performed before the light is split into four quadrants, which does not allow the quality of the focused spot to increase. Since this property is strictly related to the size of the re-imaged spot on the pyramid pin, the better the wavefront correction, the higher the gain. Aims: The goal of this paper is to extend the descriptive and analytical computation of this gain that was given in a previous paper, to partial wavefront correction conditions, which are representative for most of the wide field correction adaptive optics systems. Methods: After focusing on the low Strehl ratio regime, we analyze the minimum spatial sampling required for the wavefront sensor correction to still experience a considerable gain in sensitivity between the pyramid and the Shack-Hartmann wavefront sensors. Results: We find that the gain can be described as a function of the sampling in terms of the Fried parameter.
Dai, Guang-Ming
2006-02-15
The set of Fourier series is discussed following some discussion of Zernike polynomials. Fourier transforms of Zernike polynomials are derived that allow for relating Fourier series expansion coefficients to Zernike polynomial expansion coefficients. With iterative Fourier reconstruction, Zernike representations of wavefront aberrations can easily be obtained from wavefront derivative measurements.
Maurer, Tana; Deaver, Dawne; Howell, Christopher; Moyer, Steve; Nguyen, Oanh; Mueller, Greg; Ryan, Denise; Sia, Rose K.; Stutzman, Richard; Pasternak, Joseph; Bower, Kraig
2014-06-01
Major decisions regarding life and death are routinely made on the modern battlefield, where visual function of the individual soldier can be of critical importance in the decision-making process. Glasses in the combat environment have considerable disadvantages: degradation of short term visual performance can occur as dust and sweat accumulate on lenses during a mission or patrol; long term visual performance can diminish as lenses become increasingly scratched and pitted; during periods of intense physical trauma, glasses can be knocked off the soldier's face and lost or broken. Although refractive surgery offers certain benefits on the battlefield when compared to wearing glasses, it is not without potential disadvantages. As a byproduct of refractive surgery, elevated optical aberrations can be induced, causing decreases in contrast sensitivity and increases in the symptoms of glare, halos, and starbursts. Typically, these symptoms occur under low light level conditions, the same conditions under which most military operations are initiated. With the advent of wavefront aberrometry, we are now seeing correction not only of myopia and astigmatism but of other, smaller optical aberrations that can cause the above symptoms. In collaboration with the Warfighter Refractive Eye Surgery Program and Research Center (WRESP-RC) at Fort Belvoir and Walter Reed National Military Medical Center (WRNMMC), the overall objective of this study is to determine the impact of wavefront guided (WFG) versus wavefront-optimized (WFO) photorefractive keratectomy (PRK) on military task visual performance. Psychophysical perception testing was conducted before and after surgery to measure each participant's performance regarding target detection and identification using thermal imagery. The results are presented here.
Stochastic Chaos with Its Control and Synchronization
Institute of Scientific and Technical Information of China (English)
Zhang Ying; Xu Wei; Zhang Tianshu; Yang Xiaoli; Wu Cunli; Fang Tong
2008-01-01
conditions but also to different samples of the random parameter or the random excitation. Thus, the unique common feature of deterministic chaos and stochastic chaos is that they all have at least one positive top Lyapunov exponent for their chaotic motion. For analysis of random phenomena, one used to look for the PDFs (Probability Density Functions) of the ensemble random responses. However, it is a pity that PDF information is not favorable to studying repellency of the neighboring chaotic responses nor to calculating the related TLE, so we would rather study stochastic chaos through its sample responses. Moreover, since any sample of stochastic chaos is a deterministic one, we need not supplement any additional definition on stochastic chaos, just mentioning that every sample of stochastic chaos should be deterministic chaos.We are mainly concerned with the following two basic kinds of nonlinear stochastie systems, i.e. one with random variables as its parameters and one with ergodical random processes as its excitations. To solve the stoehastie chaos problems of these two kinds of systems, we first transform the original stochastie system into their equivalent deterministic ones. Namely, we can transform the former stochastic system into an equivalent deterministic system in the sense of mean square approximation with respect to the random parameter space by the orthogonal polynomial approximation, and transform the latter one simply through replacing its ergodical random excitations by their representative deterministic samples.Having transformed the original stochastic chaos problem into the deterministic chaos problem of equivalent systems, we can use all the available effective methods for further ehaos analysis. In this paper, we aim to review the state of art of studying stochastic chaos with its control and synchronization by the above-mentioned strategy.
Wavefront-error evaluation by mathematical analysis of experimental Foucault-test data
Wilson, R. G.
1975-01-01
The diffraction theory of the Foucault test provides an integral formula expressing the complex amplitude and irradiance distribution in the Foucault pattern of a test mirror (lens) as a function of wavefront error. Recent literature presents methods of inverting this formula to express wavefront error in terms of irradiance in the Foucault pattern. The present paper describes a study in which the inversion formulation was applied to photometric Foucault-test measurements on a nearly diffraction-limited mirror to determine wavefront errors for direct comparison with ones determined from scatter-plate interferometer measurements. The results affirm the practicability of the Foucault test for quantitative wavefront analysis of very small errors, and they reveal the fallacy of the prevalent belief that the test is limited to qualitative use only. Implications of the results with regard to optical testing and the potential use of the Foucault test for wavefront analysis in orbital space telescopes are discussed.
Real-time wavefront-shaping through scattering media by all optical feedback
Nixon, Micha; Small, Eran; Bromberg, Yaron; Friesem, Asher A; Silberberg, Yaron; Davidson, Nir
2013-01-01
Focusing light through dynamically varying heterogeneous media is a sought-after goal with important applications ranging from free-space communication to nano-surgery. The underlying challenge is to control the optical wavefront with a large number of degrees-of-freedom (DOF) at timescales shorter than the medium dynamics. Recently, many advancements have been reported following the demonstration of focusing through turbid samples by wavefront-shaping, using spatial light modulators (SLMs) having >1000 DOF. Unfortunately, SLM-based wavefront-shaping requires feedback from a detector/camera and is limited to slowly-varying samples. Here, we demonstrate a novel approach for wavefront-shaping using all-optical feedback. We show that the complex wavefront required to focus through highly scattering samples, including thin biological tissues, can be generated at sub-microsecond timescales by the process of field self-organization inside a multimode laser cavity, without requiring electronic feedback or SLMs. This...
Near infrared reflective shearing point diffraction interferometer for dynamic wavefront measurement
Zhu, Wenhua; Chen, Lei; Zheng, Donghui
2016-09-01
A near infrared reflective shearing point diffraction interferometer (NIRSPDI) is designed for large-aperture dynamic wave-front measurement. The PDI is integrated on the small substrate with properly designed thin film. The wave-front under test is reflected by the front and rear surfaces of the substrate respectively to generate an interferogram with high linear-carrier frequency, which is used to reconstruct the wave-front by means of the Fourier transform algorithm. In this article, the system error and the major parameters of NIRSPDI are discussed. In addition, we give an effective method to adjust NIRSPDI for fast measurement. Experimentally NIRSPDI was calibrated by a standard spherical surface and then it was applied to the dynamic wave-front with a diameter of 400mm. The measured results show the error of whole system which verifies that the proposed NIRSPDI is a powerful tool for large-aperture dynamic wave-front measurement.
Stochastic control with rough paths
Energy Technology Data Exchange (ETDEWEB)
Diehl, Joscha [University of California San Diego (United States); Friz, Peter K., E-mail: friz@math.tu-berlin.de [TU & WIAS Berlin (Germany); Gassiat, Paul [CEREMADE, Université Paris-Dauphine, PSL Research University (France)
2017-04-15
We study a class of controlled differential equations driven by rough paths (or rough path realizations of Brownian motion) in the sense of Lyons. It is shown that the value function satisfies a HJB type equation; we also establish a form of the Pontryagin maximum principle. Deterministic problems of this type arise in the duality theory for controlled diffusion processes and typically involve anticipating stochastic analysis. We make the link to old work of Davis and Burstein (Stoch Stoch Rep 40:203–256, 1992) and then prove a continuous-time generalization of Roger’s duality formula [SIAM J Control Optim 46:1116–1132, 2007]. The generic case of controlled volatility is seen to give trivial duality bounds, and explains the focus in Burstein–Davis’ (and this) work on controlled drift. Our study of controlled rough differential equations also relates to work of Mazliak and Nourdin (Stoch Dyn 08:23, 2008).
Model-based aberration correction in a closed-loop wavefront-sensor-less adaptive optics system
Song, H.; Fraanje, R.; Schitter, G.; Kroese, H.; Vdovin, G.; Verhaegen, M.
2010-01-01
In many scientific and medical applications, such as laser systems and microscopes, wavefront-sensor-less (WFSless) adaptive optics (AO) systems are used to improve the laser beam quality or the image resolution by correcting the wavefront aberration in the optical path. The lack of direct wavefront
Wavefront modulation of water surface wave by a metasurface
Sun, Hai-Tao; Cheng, Ying; Wang, Jing-Shi; Liu, Xiao-Jun
2015-10-01
We design a planar metasurface to modulate the wavefront of a water surface wave (WSW) on a deep sub-wavelength scale. The metasurface is composed of an array of coiling-up-space units with specially designed parameters, and can take on the work of steering the wavefront when it is pierced into water. Like their acoustic counterparts, the modulation of WSW is ascribed to the gradient phase shift of the coiling-up-space units, which can be perfectly tuned by changing the coiling plate length and channel number inside the units. According to the generalized Snell’s law, negative refraction and ‘driven’ surface mode of WSW are also demonstrated at certain incidences. Specially, the transmitted WSW could be efficiently guided out by linking a symmetrically-corrugated channel in ‘driven’ surface mode. This work may have potential applications in water wave energy extraction and coastal protection. Project supported by the National Basic Research Program of China (Grant No. 2012CB921504), the National Natural Science Foundation of China (Grant Nos. 11474162, 11274171, 11274099, and 11204145), and the Specialized Research Fund for the Doctoral Program of Higher Education, China (Grant Nos. 20110091120040 and 20120091110001).
Wavefront shaping based on three-dimensional optoacoustic feedback
Deán-Ben, X. L.; Estrada, Héctor; Ozbek, Ali; Razansky, Daniel
2015-07-01
Wavefront shaping techniques have recently evolved as a promising tool to control the light distribution in optically-scattering media. These techniques are based on spatially-modulating the phase of an incident light beam to create positive interference (focusing) at specific locations in the speckle pattern of the scattered wavefield. The optimum phase distribution (mask) of the spatial light modulator that allows focusing at the target location(s) is determined iteratively by monitoring the light intensity at such target. In this regard, optoacoustic (photoacoustic) imaging may provide the convenient advantage of simultaneous feedback information on light distribution in an entire region of interest. Herein, we showcase that volumetric optoacoustic images can effectively be used as a feedback mechanism in an iterative optimization algorithm allowing controlling the light distribution after propagation through a scattering sample. Experiments performed with absorbing microparticles distributed in a three-dimensional region showcase the feasibility of enhancing the light intensity at specific points. The advantages provided by optoacoustic imaging in terms of spatial and temporal resolution anticipate new capabilities of wavefront shaping techniques in biomedical optics.
Wavefront construction Kirchhoff migration with ray-amplitude corrections
Energy Technology Data Exchange (ETDEWEB)
Fehler, Michael C.; Hildebrand, S. T. (Steve T.); Huang, L. (Lian-Jie); Alde, D. M. (Douglas M.)
2002-01-01
Kirchhoff migration using ray tracing travel times has been a popular imaging method for many years. There are significant limitations in the ability of Kirchhoff migration using only first arrivals to reliably image regions of complex structure. Thus, new methods for imaging have been sought. One approach for improving imaging capability is to use ray tracing methods that allow the calculation of multiple-valued travel time tables to be used in migration. Additional improvements in ray-based imaging methods may be obtained by including amplitudes and phases of rays calculated using some ray tracing approach. One approach for calculating multiple-valued travel time tables along with estimates of amplitudes and phases is the use of wavefront construction ray tracing. We introduce our wavefront construction-based migration algorithm and present some example images obtained using the method. We compare the images obtained with those obtained using a dual-domain wave-equation migration method that we call Extended Local Rytov Fourier migration method.
X-ray pulse wavefront metrology using speckle tracking.
Berujon, Sebastien; Ziegler, Eric; Cloetens, Peter
2015-07-01
An instrument allowing the quantitative analysis of X-ray pulsed wavefronts is presented and its processing method explained. The system relies on the X-ray speckle tracking principle to accurately measure the phase gradient of the X-ray beam from which beam optical aberrations can be deduced. The key component of this instrument, a semi-transparent scintillator emitting visible light while transmitting X-rays, allows simultaneous recording of two speckle images at two different propagation distances from the X-ray source. The speckle tracking procedure for a reference-less metrology mode is described with a detailed account on the advanced processing schemes used. A method to characterize and compensate for the imaging detector distortion, whose principle is also based on speckle, is included. The presented instrument is expected to find interest at synchrotrons and at the new X-ray free-electron laser sources under development worldwide where successful exploitation of beams relies on the availability of an accurate wavefront metrology.
X-ray wavefront modeling of Bragg diffraction from crystals
Sutter, John P.
2011-09-01
The diffraction of an X-ray wavefront from a slightly distorted crystal can be modeled by the Takagi-Taupin theory, an extension of the well-known dynamical diffraction theory for perfect crystals. Maxwell's equations applied to a perturbed periodic medium yield two coupled differential equations in the incident and diffracted amplitude. These equations are discretized for numerical calculation into the determination of the two amplitudes on the points of an integration mesh, beginning with the incident amplitudes at the crystal's top surface. The result is a set of diffracted amplitudes on the top surface (in the Bragg geometry) or the bottom surface (in the Laue geometry), forming a wavefront that in turn can be propagated through free space using the Fresnel- Huygens equations. The performance of the Diamond Light Source I20 dispersive spectrometer has here been simulated using this method. Methods are shown for transforming displacements calculated by finite element analysis into local lattice distortions, and for efficiently performing 3-D linear interpolations from these onto the Takagi-Taupin integration mesh, allowing this method to be extended to crystals under thermal load or novel mechanical bender designs.
Correia, Carlos M; Teixeira, Joel
2014-12-01
Computationally efficient wave-front reconstruction techniques for astronomical adaptive-optics (AO) systems have seen great development in the past decade. Algorithms developed in the spatial-frequency (Fourier) domain have gathered much attention, especially for high-contrast imaging systems. In this paper we present the Wiener filter (resulting in the maximization of the Strehl ratio) and further develop formulae for the anti-aliasing (AA) Wiener filter that optimally takes into account high-order wave-front terms folded in-band during the sensing (i.e., discrete sampling) process. We employ a continuous spatial-frequency representation for the forward measurement operators and derive the Wiener filter when aliasing is explicitly taken into account. We further investigate and compare to classical estimates using least-squares filters the reconstructed wave-front, measurement noise, and aliasing propagation coefficients as a function of the system order. Regarding high-contrast systems, we provide achievable performance results as a function of an ensemble of forward models for the Shack-Hartmann wave-front sensor (using sparse and nonsparse representations) and compute point-spread-function raw intensities. We find that for a 32×32 single-conjugated AOs system the aliasing propagation coefficient is roughly 60% of the least-squares filters, whereas the noise propagation is around 80%. Contrast improvements of factors of up to 2 are achievable across the field in the H band. For current and next-generation high-contrast imagers, despite better aliasing mitigation, AA Wiener filtering cannot be used as a standalone method and must therefore be used in combination with optical spatial filters deployed before image formation actually takes place.
Sequential stochastic optimization
Cairoli, Renzo
1996-01-01
Sequential Stochastic Optimization provides mathematicians and applied researchers with a well-developed framework in which stochastic optimization problems can be formulated and solved. Offering much material that is either new or has never before appeared in book form, it lucidly presents a unified theory of optimal stopping and optimal sequential control of stochastic processes. This book has been carefully organized so that little prior knowledge of the subject is assumed; its only prerequisites are a standard graduate course in probability theory and some familiarity with discrete-paramet
Fundamentals of Stochastic Filtering
Crisan, Dan
2008-01-01
The objective of stochastic filtering is to determine the best estimate for the state of a stochastic dynamical system from partial observations. The solution of this problem in the linear case is the well known Kalman-Bucy filter which has found widespread practical application. The purpose of this book is to provide a rigorous mathematical treatment of the non-linear stochastic filtering problem using modern methods. Particular emphasis is placed on the theoretical analysis of numerical methods for the solution of the filtering problem via particle methods. The book should provide sufficient
Asymptotic problems for stochastic partial differential equations
Salins, Michael
Stochastic partial differential equations (SPDEs) can be used to model systems in a wide variety of fields including physics, chemistry, and engineering. The main SPDEs of interest in this dissertation are the semilinear stochastic wave equations which model the movement of a material with constant mass density that is exposed to both determinstic and random forcing. Cerrai and Freidlin have shown that on fixed time intervals, as the mass density of the material approaches zero, the solutions of the stochastic wave equation converge uniformly to the solutions of a stochastic heat equation, in probability. This is called the Smoluchowski-Kramers approximation. In Chapter 2, we investigate some of the multi-scale behaviors that these wave equations exhibit. In particular, we show that the Freidlin-Wentzell exit place and exit time asymptotics for the stochastic wave equation in the small noise regime can be approximated by the exit place and exit time asymptotics for the stochastic heat equation. We prove that the exit time and exit place asymptotics are characterized by quantities called quasipotentials and we prove that the quasipotentials converge. We then investigate the special case where the equation has a gradient structure and show that we can explicitly solve for the quasipotentials, and that the quasipotentials for the heat equation and wave equation are equal. In Chapter 3, we study the Smoluchowski-Kramers approximation in the case where the material is electrically charged and exposed to a magnetic field. Interestingly, if the system is frictionless, then the Smoluchowski-Kramers approximation does not hold. We prove that the Smoluchowski-Kramers approximation is valid for systems exposed to both a magnetic field and friction. Notably, we prove that the solutions to the second-order equations converge to the solutions of the first-order equation in an Lp sense. This strengthens previous results where convergence was proved in probability.
Stochastic differential equations and applications
Friedman, Avner
2006-01-01
This text develops the theory of systems of stochastic differential equations, and it presents applications in probability, partial differential equations, and stochastic control problems. Originally published in two volumes, it combines a book of basic theory and selected topics with a book of applications.The first part explores Markov processes and Brownian motion; the stochastic integral and stochastic differential equations; elliptic and parabolic partial differential equations and their relations to stochastic differential equations; the Cameron-Martin-Girsanov theorem; and asymptotic es
Frédéric, Pierret
2014-01-01
The equations of celestial mechanics that govern the variation of the orbital elements are completely derived for stochastic perturbation which generalized the classic perturbation equations which are used since Gauss, starting from Newton's equation and it's solution. The six most understandable orbital element, the semi-major axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle and the mean motion are express in term of the angular momentum vector $\\textbf{H}$ per unit of mass and the energy $E$ per unit of mass. We differentiate those expressions using It\\^o's theory of differential equations due to the stochastic nature of the perturbing force. The result is applied to the two-body problem perturbed by a stochastic dust cloud and also perturbed by a stochastic dynamical oblateness of the central body.
Doberkat, Ernst-Erich
2009-01-01
Combining coalgebraic reasoning, stochastic systems and logic, this volume presents the principles of coalgebraic logic from a categorical perspective. Modal logics are also discussed, including probabilistic interpretations and an analysis of Kripke models.
Stochastic modelling of turbulence
DEFF Research Database (Denmark)
Sørensen, Emil Hedevang Lohse
This thesis addresses stochastic modelling of turbulence with applications to wind energy in mind. The primary tool is ambit processes, a recently developed class of computationally tractable stochastic processes based on integration with respect to Lévy bases. The subject of ambit processes...... stochastic turbulence model based on ambit processes is proposed. It is shown how a prescribed isotropic covariance structure can be reproduced. Non-Gaussian turbulence models are obtained through non-Gaussian Lévy bases or through volatility modulation of Lévy bases. As opposed to spectral models operating...... is dissipated into heat due to the internal friction caused by viscosity. An existing stochastic model, also expressed in terms of ambit processes, is extended and shown to give a universal and parsimonious description of the turbulent energy dissipation. The volatility modulation, referred to above, has...
Stochastic calculus with infinitesimals
Herzberg, Frederik
2013-01-01
Stochastic analysis is not only a thriving area of pure mathematics with intriguing connections to partial differential equations and differential geometry. It also has numerous applications in the natural and social sciences (for instance in financial mathematics or theoretical quantum mechanics) and therefore appears in physics and economics curricula as well. However, existing approaches to stochastic analysis either presuppose various concepts from measure theory and functional analysis or lack full mathematical rigour. This short book proposes to solve the dilemma: By adopting E. Nelson's "radically elementary" theory of continuous-time stochastic processes, it is based on a demonstrably consistent use of infinitesimals and thus permits a radically simplified, yet perfectly rigorous approach to stochastic calculus and its fascinating applications, some of which (notably the Black-Scholes theory of option pricing and the Feynman path integral) are also discussed in the book.
Stochastic processes inference theory
Rao, Malempati M
2014-01-01
This is the revised and enlarged 2nd edition of the authors’ original text, which was intended to be a modest complement to Grenander's fundamental memoir on stochastic processes and related inference theory. The present volume gives a substantial account of regression analysis, both for stochastic processes and measures, and includes recent material on Ridge regression with some unexpected applications, for example in econometrics. The first three chapters can be used for a quarter or semester graduate course on inference on stochastic processes. The remaining chapters provide more advanced material on stochastic analysis suitable for graduate seminars and discussions, leading to dissertation or research work. In general, the book will be of interest to researchers in probability theory, mathematical statistics and electrical and information theory.
Notes on the Stochastic Exponential and Logarithm
Larsson, Martin; Ruf, Johannes
2017-01-01
Stochastic exponentials are defined for semimartingales on stochastic intervals, and stochastic logarithms are defined for nonnegative semimartingales, up to the first time the semimartingale hits zero continuously. In the case of (nonnegative) local supermartingales, these two stochastic transformations are inverse to each other. The reciprocal of a stochastic exponential is again a stochastic exponential on a stochastic interval.
Geometric Stochastic Resonance
Ghosh, Pulak Kumar; Savel'ev, Sergey E; Nori, Franco
2015-01-01
A Brownian particle moving across a porous membrane subject to an oscillating force exhibits stochastic resonance with properties which strongly depend on the geometry of the confining cavities on the two sides of the membrane. Such a manifestation of stochastic resonance requires neither energetic nor entropic barriers, and can thus be regarded as a purely geometric effect. The magnitude of this effect is sensitive to the geometry of both the cavities and the pores, thus leading to distinctive optimal synchronization conditions.
Stochastic Volatility and Option Pricing in Heath-Jarrow-Morton Term Structure Analysis
DEFF Research Database (Denmark)
Christensen, Bent Jesper; Konaris, George; Nicolato, Elisa
We consider a generalized Heath-Jarrow-Morton bond market model which allows both for jumps and stochastic volatility. Specifications with affine and quadratic volatility are studied and explicit option pricing formulas (in the Heston (1993) sense) are derived and implemented.......We consider a generalized Heath-Jarrow-Morton bond market model which allows both for jumps and stochastic volatility. Specifications with affine and quadratic volatility are studied and explicit option pricing formulas (in the Heston (1993) sense) are derived and implemented....
Compressive Sensing for Quantum Imaging
Howland, Gregory A.
. Entanglement imaging is demonstrated at 1024 dimensions-per-photon with channel capacities exceeding 8.4 bits-per-photon. In practice, the measurement time is reduced from 310 days for the standard technique to 8 hours for the compressive technique. An entropic steering inequality is violated to witness entanglement. The final application is a compressive wavefront sensor that unites compressive sensing with weak measurement. We show how a twisted-nematic spatial light modulator can be be used to weakly couple an optical field's position and polarization degrees of freedom. The complex nature of the weak value is used to directly measure random projections of the real and imaginary parts of the optical field, where polarization serves as an ancillary meter. We obtain 256 x 256 pixel wavefronts from only 10,000 random projections. Photon-counting detectors provide sub-picowatt sensitivity.
The construction of individual eye model based on eye's wavefront aberration measurement
Wang, Zhao-Qi; Guo, Huan-Qing
2005-08-01
Based on the widely used Gullstrand-Le Grand eye model, the individual human eye model has been established here, which has individual corneal data, anterior chamber depth and the eyeball depth. Furthermore the foremost thing is that the wavefront aberration calculated from the individual eye model is equal to the eye's wavefront aberration measured with the Hartmann-shack wavefront sensor. There were four main steps to build the model. Firstly, the corneal topography instrument was used to measure the corneal surfaces and depth. And in order to input cornea into the optical model, high order aspheric surface-Zernike Fringe Sag surface was chosen to fit the corneal surfaces. Secondly, the Hartmann-shack wavefront sensor, which can offer the Zernike polynomials to describe the wavefront aberration, was built to measure the wavefront aberration of the eye. Thirdly, the eye's axial lengths among every part were measured with A-ultrasonic technology. Then the data were input into the optical design software -ZEMAX and the crystalline lens's shapes were optimized with the aberration as the merit function. The individual eye model, which has the same wavefront aberrations with the real eye, is established.
Broadband reflected wavefronts manipulation using structured phase gradient metasurfaces
Wang, Xiao-Peng; Wan, Le-Le; Chen, Tian-Ning; Song, Ai-Ling; Du, Xiao-Wen
2016-06-01
Acoustic metasurface (AMS) is a good candidate to manipulate acoustic waves due to special acoustic performs that cannot be realized by traditional materials. In this paper, we design the AMS by using circular-holed cubic arrays. The advantages of our AMS are easy assemble, subwavelength thickness, and low energy loss for manipulating acoustic waves. According to the generalized Snell's law, acoustic waves can be manipulated arbitrarily by using AMS with different phase gradients. By selecting suitable hole diameter of circular-holed cube (CHC), some interesting phenomena are demonstrated by our simulations based on finite element method, such as the conversion of incoming waves into surface waves, anomalous reflections (including negative reflection), acoustic focusing lens, and acoustic carpet cloak. Our results can provide a simple approach to design AMSes and use them in wavefront manipulation and manufacturing of acoustic devices.
Multicore-Optimized Wavefront Diamond Blocking for Optimizing Stencil Updates
Malas, T.
2015-07-02
The importance of stencil-based algorithms in computational science has focused attention on optimized parallel implementations for multilevel cache-based processors. Temporal blocking schemes leverage the large bandwidth and low latency of caches to accelerate stencil updates and approach theoretical peak performance. A key ingredient is the reduction of data traffic across slow data paths, especially the main memory interface. In this work we combine the ideas of multicore wavefront temporal blocking and diamond tiling to arrive at stencil update schemes that show large reductions in memory pressure compared to existing approaches. The resulting schemes show performance advantages in bandwidth-starved situations, which are exacerbated by the high bytes per lattice update case of variable coefficients. Our thread groups concept provides a controllable trade-off between concurrency and memory usage, shifting the pressure between the memory interface and the CPU. We present performance results on a contemporary Intel processor.
Laboratory simulation of atmospheric turbulence-induced optical wavefront distortion
Taylor, Travis S.; Gregory, Don A.
2002-11-01
Real-time liquid crystal television-based technique for simulating optical wavefront distortion due to atmospheric turbulence is presented and demonstrated. A liquid crystal television (LCTV) operating in the "phase mostly" mode was used as an array of spatially correlated phase delays. A movie of the arrays in motion was then generated and displayed on the LCTV. The turbulence simulation system was verified by passing a collimated and doubled diode pumped Nd:YVO 4 laser beam (532 nm) through the transparent LCTV screen. The beam was then passed through a lens and the power spectra of the turbulence information carrying beam was detected as a measure of the far-field distribution. The same collimated laser beam, without the LCTV, was also transmitted down an open-air range and the power spectra detected as a measure of a real far-field distribution. Accepted turbulence parameters were measured for both arrangements and then compared.
Monotone traveling wavefronts of the KPP-Fisher delayed equation
Gomez, Adrian
2010-01-01
In the early 2000's, Gourley (2000), Wu et al. (2001), Ashwin et al. (2002) initiated the study of the positive wavefronts in the delayed Kolmogorov-Petrovskii-Piskunov-Fisher equation. Since then, this model has become one of the most popular objects in the studies of traveling waves for the monostable delayed reaction-diffusion equations. In this paper, we give a complete solution to the problem of existence and uniqueness of monotone waves in the KPP-Fisher equation. We show that each monotone traveling wave can be found via an iteration procedure. The proposed approach is based on the use of special monotone integral operators (which are different from the usual Wu-Zou operator) and appropriate upper and lower solutions associated to them. The analysis of the asymptotic expansions of the eventual traveling fronts at infinity is another key ingredient of our approach.
Fast wavefront optimization for focusing through biological tissue (Conference Presentation)
Blochet, Baptiste; Bourdieu, Laurent; Gigan, Sylvain
2017-02-01
The propagation of light in biological tissues is rapidly dominated by multiple scattering: ballistic light is exponentially attenuated, which limits the penetration depth of conventional microscopy techniques. For coherent light, the recombination of the different scattered paths creates a complex interference: speckle. Recently, different wavefront shaping techniques have been developed to coherently manipulate the speckle. It opens the possibility to focus light through complex media and ultimately to image in them, provided however that the medium can be considered as stationary. We have studied the possibility to focus in and through time-varying biological tissues. Their intrinsic temporal dynamics creates a fast decorrelation of the speckle pattern. Therefore, focusing through biological tissues requires fast wavefront shaping devices, sensors and algorithms. We have investigated the use of a MEMS-based spatial light modulator (SLM) and a fast photodetector, combined with FPGA electronics to implement a closed-loop optimization. Our optimization process is just limited by the temporal dynamics of the SLM (200µs) and the computation time (45µs), thus corresponding to a rate of 4 kHz. To our knowledge, it's the fastest closed loop optimization using phase modulators. We have studied the focusing through colloidal solutions of TiO2 particles in glycerol, allowing tunable temporal stability, and scattering properties similar to biological tissues. We have shown that our set-up fulfills the required characteristics (speed, enhancement) to focus through biological tissues. We are currently investigating the focusing through acute rat brain slices and the memory effect in dynamic scattering media.
Operation modes of a liquid-crystal modal wave-front corrector.
Loktev, Mikhail; Vdovin, Gleb; Guralnik, Igor
2004-04-10
Liquid-crystal modal wave-front correctors provide much better wave-front correction than do piston correctors with the same number of actuators; moreover, use of additional degrees of freedom of the driving ac voltage signals may further improve device performance. Some practical aspects of the operation of liquid-crystal modal wave-front correctors are discussed. Special attention is paid to the interference of various contact responses and to the formation of required phase shapes through wider control of signal frequencies and electric phase shifts. The study is based on an analytic approach and numerical investigation; major theoretical conclusions are verified experimentally.
Wavefront-sensor-based electron density measurements for laser-plasma accelerators
Energy Technology Data Exchange (ETDEWEB)
Plateau, Guillaume; Matlis, Nicholas; Geddes, Cameron; Gonsalves, Anthony; Shiraishi, Satomi; Lin, Chen; van Mourik, Reinier; Leemans, Wim
2010-02-20
Characterization of the electron density in laser produced plasmas is presented using direct wavefront analysis of a probe laser beam. The performance of a laser-driven plasma-wakefield accelerator depends on the plasma wavelength, hence on the electron density. Density measurements using a conventional folded-wave interferometer and using a commercial wavefront sensor are compared for different regimes of the laser-plasma accelerator. It is shown that direct wavefront measurements agree with interferometric measurements and, because of the robustness of the compact commercial device, have greater phase sensitivity, straightforward analysis, improving shot-to-shot plasma-density diagnostics.
Yu, Hyeonseung; Jo, YoungJu; Lee, KyeoReh; Tuchin, Valery V; Jeong, Yong; Park, YongKeun
2016-01-01
We demonstrate that simultaneous application of optical clearing agents (OCAs) and complex wavefront shaping in optical coherence tomography (OCT) can provide significant enhancement of the penetration depth and imaging quality. OCA reduces optical inhomogeneity of a highly scattering sample, and the wavefront shaping of illumination light controls multiple scattering, resulting in an enhancement of the penetration depth and signal-to-noise ratio. A tissue phantom study shows that concurrent applications of OCA and wavefront shaping successfully operate in OCT imaging. The penetration depth enhancement is further demonstrated for ex vivo mouse ears, revealing hidden structures inaccessible with conventional OCT imaging.
Robustness of Populations in Stochastic Environments
DEFF Research Database (Denmark)
Gießen, Christian; Kötzing, Timo
2014-01-01
We consider stochastic versions of OneMax and Leading-Ones and analyze the performance of evolutionary algorithms with and without populations on these problems. It is known that the (1+1) EA on OneMax performs well in the presence of very small noise, but poorly for higher noise levels. We extend...... these results to LeadingOnes and to many different noise models, showing how the application of drift theory can significantly simplify and generalize previous analyses. Most surprisingly, even small populations (of size _(log n)) can make evolutionary algorithms perform well for high noise levels, well outside...... the abilities of the (1+1) EA! Larger population sizes are even more beneficial; we consider both parent and o_spring populations. In this sense, populations are robust in these stochastic settings....
Robustness of Populations in Stochastic Environments
DEFF Research Database (Denmark)
Gießen, Christian; Kötzing, Timo
2016-01-01
We consider stochastic versions of OneMax and LeadingOnes and analyze the performance of evolutionary algorithms with and without populations on these problems. It is known that the (1+1) EA on OneMax performs well in the presence of very small noise, but poorly for higher noise levels. We extend...... these results to LeadingOnes and to many different noise models, showing how the application of drift theory can significantly simplify and generalize previous analyses. Most surprisingly, even small populations (of size Θ(logn)) can make evolutionary algorithms perform well for high noise levels, well outside...... the abilities of the (1+1) EA. Larger population sizes are even more beneficial; we consider both parent and offspring populations. In this sense, populations are robust in these stochastic settings....
Quantum Spontaneous Stochasticity
Eyink, Gregory L
2015-01-01
The quantum wave-function of a massive particle with small initial uncertainties (consistent with the uncertainty relation) is believed to spread very slowly, so that the dynamics is deterministic. This assumes that the classical motions for given initial data are unique. In fluid turbulence non-uniqueness due to "roughness" of the advecting velocity field is known to lead to stochastic motion of classical particles. Vanishingly small random perturbations are magnified by Richardson diffusion in a "nearly rough" velocity field so that motion remains stochastic as the noise disappears, or classical spontaneous stochasticity, . Analogies between stochastic particle motion in turbulence and quantum evolution suggest that there should be quantum spontaneous stochasticity (QSS). We show this for 1D models of a particle in a repulsive potential that is "nearly rough" with $V(x) \\sim C|x|^{1+\\alpha}$ at distances $|x|\\gg \\ell$ , for some UV cut-off $\\ell$, and for initial Gaussian wave-packet centered at 0. We consi...
Stochastic optimization methods
Marti, Kurt
2005-01-01
Optimization problems arising in practice involve random parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insensitive with respect to random parameter variations, deterministic substitute problems are needed. Based on the distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into deterministic substitute problems. Due to the occurring probabilities and expectations, approximative solution techniques must be applied. Deterministic and stochastic approximation methods and their analytical properties are provided: Taylor expansion, regression and response surface methods, probability inequalities, First Order Reliability Methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation methods, differentiation of probability and mean value functions. Convergence results of the resulting iterative solution procedures are given.
Stochastic dynamics and irreversibility
Tomé, Tânia
2015-01-01
This textbook presents an exposition of stochastic dynamics and irreversibility. It comprises the principles of probability theory and the stochastic dynamics in continuous spaces, described by Langevin and Fokker-Planck equations, and in discrete spaces, described by Markov chains and master equations. Special concern is given to the study of irreversibility, both in systems that evolve to equilibrium and in nonequilibrium stationary states. Attention is also given to the study of models displaying phase transitions and critical phenomema both in thermodynamic equilibrium and out of equilibrium. These models include the linear Glauber model, the Glauber-Ising model, lattice models with absorbing states such as the contact process and those used in population dynamic and spreading of epidemic, probabilistic cellular automata, reaction-diffusion processes, random sequential adsorption and dynamic percolation. A stochastic approach to chemical reaction is also presented.The textbook is intended for students of ...
Dong, Bing; Li, Yan; Han, Xin-li; Hu, Bin
2016-01-01
For high-speed aircraft, a conformal window is used to optimize the aerodynamic performance. However, the local shape of the conformal window leads to large amounts of dynamic aberrations varying with look angle. In this paper, deformable mirror (DM) and model-based wavefront sensorless adaptive optics (WSLAO) are used for dynamic aberration correction of an infrared remote sensor equipped with a conformal window and scanning mirror. In model-based WSLAO, aberration is captured using Lukosz mode, and we use the low spatial frequency content of the image spectral density as the metric function. Simulations show that aberrations induced by the conformal window are dominated by some low-order Lukosz modes. To optimize the dynamic correction, we can only correct dominant Lukosz modes and the image size can be minimized to reduce the time required to compute the metric function. In our experiment, a 37-channel DM is used to mimic the dynamic aberration of conformal window with scanning rate of 10 degrees per second. A 52-channel DM is used for correction. For a 128 × 128 image, the mean value of image sharpness during dynamic correction is 1.436 × 10−5 in optimized correction and is 1.427 × 10−5 in un-optimized correction. We also demonstrated that model-based WSLAO can achieve convergence two times faster than traditional stochastic parallel gradient descent (SPGD) method. PMID:27598161
Dong, Bing; Li, Yan; Han, Xin-Li; Hu, Bin
2016-09-02
For high-speed aircraft, a conformal window is used to optimize the aerodynamic performance. However, the local shape of the conformal window leads to large amounts of dynamic aberrations varying with look angle. In this paper, deformable mirror (DM) and model-based wavefront sensorless adaptive optics (WSLAO) are used for dynamic aberration correction of an infrared remote sensor equipped with a conformal window and scanning mirror. In model-based WSLAO, aberration is captured using Lukosz mode, and we use the low spatial frequency content of the image spectral density as the metric function. Simulations show that aberrations induced by the conformal window are dominated by some low-order Lukosz modes. To optimize the dynamic correction, we can only correct dominant Lukosz modes and the image size can be minimized to reduce the time required to compute the metric function. In our experiment, a 37-channel DM is used to mimic the dynamic aberration of conformal window with scanning rate of 10 degrees per second. A 52-channel DM is used for correction. For a 128 × 128 image, the mean value of image sharpness during dynamic correction is 1.436 × 10(-5) in optimized correction and is 1.427 × 10(-5) in un-optimized correction. We also demonstrated that model-based WSLAO can achieve convergence two times faster than traditional stochastic parallel gradient descent (SPGD) method.
Hartmann-Shack test with random masks for modal wavefront reconstruction.
Soloviev, Oleg; Vdovin, Gleb
2005-11-14
The paper discusses the influence of the geometry of a Hartmann-(Shack) wavefront sensor on the total error of modal wavefront reconstruction. A mathematical model is proposed, which describes the modal wavefront reconstruction in terms of linear operators. The model covers the most general case and is not limited by the orthogonality of decomposition basis or by the method chosen for decomposition. The total reconstruction error is calculated for any given statistics of the wavefront to be measured. Based on this estimate, the total reconstruction error is calculated for regular and randomised Hartmann masks. The calculations demonstrate that random masks with non-regular Fourier spectra provide absolute minimum error and allow to double the number of decomposition modes.
Chong, Katie E; Staude, Isabelle; James, Anthony; Dominguez, Jason; Liu, Sheng; Subramania, Ganapathi S; Decker, Manuel; Neshev, Dragomir N; Brener, Igal; Kivshar, Yuri S
2016-01-01
Subwavelength-thin metasurfaces have shown great promises for the control of optical wavefronts, thus opening new pathways for the development of efficient flat optics. In particular, Huygens' metasurfaces based on all-dielectric resonant meta-atoms have already shown a huge potential for practical applications with their polarization insensitivity and high transmittance efficiency. Here, we experimentally demonstrate a polarization insensitive holographic Huygens' metasurface based on dielectric resonant meta-atoms capable of complex wavefront control at telecom wavelengths. Our metasurface produces a hologram image in the far-field with 82% transmittance efficiency and 40% imaging efficiency. Such efficient complex wavefront control shows that Huygens' metasurfaces based on resonant dielectric meta-atoms are a big step towards practical applications of metasurfaces in wavefront design related technologies, including computer-generated holograms, ultra-thin optics, security and data storage devices.
Calibrating the interaction matrix for the LINC-NIRVANA high layer wavefront sensor.
Zhang, Xianyu; Arcidiacono, Carmelo; Conrad, Albert R; Herbst, Thomas M; Gaessler, Wolfgang; Bertram, Thomas; Ragazzoni, Roberto; Schreiber, Laura; Diolaiti, Emiliano; Kuerster, Martin; Bizenberger, Peter; Meschke, Daniel; Rix, Hans-Walter; Rao, Changhui; Mohr, Lars; Briegel, Florian; Kittmann, Frank; Berwein, Juergen; Trowitzsch, Jan
2012-03-26
LINC-NIRVANA is a near-infrared Fizeau interferometric imager that will operate at the Large Binocular Telescope. In preparation for the commissioning of this instrument, we conducted experiments for calibrating the high-layer wavefront sensor of the layer-oriented multi-conjugate adaptive optics system. For calibrating the multi-pyramid wavefront sensor, four light sources were used to simulate guide stars. Using this setup, we developed the push-pull method for calibrating the interaction matrix. The benefits of this method over the traditional push-only method are quantified, and also the effects of varying the number of push-pull frames over which aberrations are averaged is reported. Finally, we discuss a method for measuring mis-conjugation between the deformable mirror and the wavefront sensor, and the proper positioning of the wavefront sensor detector with respect to the four pupil positions.
Modeling the Effect of Wave-front Aberrations in Fiber-based Scanning Optical Microscopy
Verstraete, H.R.G.W.; Verhaegen, M.H.G.; Kalkman, J.
2013-01-01
In scanning microscopy and optical coherence tomography, aberrations of the wave-front cause a loss in intensity and resolution. Intensity and resolution are quantified using Fresnel propagation, Fraunhofer diffraction, and the calculation of overlap integrals.
Stochastic models, estimation, and control
Maybeck, Peter S
1982-01-01
This volume builds upon the foundations set in Volumes 1 and 2. Chapter 13 introduces the basic concepts of stochastic control and dynamic programming as the fundamental means of synthesizing optimal stochastic control laws.
STOCHASTIC COOLING FOR BUNCHED BEAMS.
Energy Technology Data Exchange (ETDEWEB)
BLASKIEWICZ, M.
2005-05-16
Problems associated with bunched beam stochastic cooling are reviewed. A longitudinal stochastic cooling system for RHIC is under construction and has been partially commissioned. The state of the system and future plans are discussed.
Pierret, Frédéric
2016-02-01
We derived the equations of Celestial Mechanics governing the variation of the orbital elements under a stochastic perturbation, thereby generalizing the classical Gauss equations. Explicit formulas are given for the semimajor axis, the eccentricity, the inclination, the longitude of the ascending node, the pericenter angle, and the mean anomaly, which are expressed in term of the angular momentum vector H per unit of mass and the energy E per unit of mass. Together, these formulas are called the stochastic Gauss equations, and they are illustrated numerically on an example from satellite dynamics.
Stochastic dynamics and control
Sun, Jian-Qiao; Zaslavsky, George
2006-01-01
This book is a result of many years of author's research and teaching on random vibration and control. It was used as lecture notes for a graduate course. It provides a systematic review of theory of probability, stochastic processes, and stochastic calculus. The feedback control is also reviewed in the book. Random vibration analyses of SDOF, MDOF and continuous structural systems are presented in a pedagogical order. The application of the random vibration theory to reliability and fatigue analysis is also discussed. Recent research results on fatigue analysis of non-Gaussian stress proc
Foundations of stochastic analysis
Rao, M M; Lukacs, E
1981-01-01
Foundations of Stochastic Analysis deals with the foundations of the theory of Kolmogorov and Bochner and its impact on the growth of stochastic analysis. Topics covered range from conditional expectations and probabilities to projective and direct limits, as well as martingales and likelihood ratios. Abstract martingales and their applications are also discussed. Comprised of five chapters, this volume begins with an overview of the basic Kolmogorov-Bochner theorem, followed by a discussion on conditional expectations and probabilities containing several characterizations of operators and mea
Stochastic Electrochemical Kinetics
Beruski, O
2016-01-01
A model enabling the extension of the Stochastic Simulation Algorithm to electrochemical systems is proposed. The physical justifications and constraints for the derivation of a chemical master equation are provided and discussed. The electrochemical driving forces are included in the mathematical framework, and equations are provided for the associated electric responses. The implementation for potentiostatic and galvanostatic systems is presented, with results pointing out the stochastic nature of the algorithm. The electric responses presented are in line with the expected results from the theory, providing a new tool for the modeling of electrochemical kinetics.
Markov stochasticity coordinates
Eliazar, Iddo
2017-01-01
Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method-termed Markov Stochasticity Coordinates-is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.
Markov stochasticity coordinates
Energy Technology Data Exchange (ETDEWEB)
Eliazar, Iddo, E-mail: iddo.eliazar@intel.com
2017-01-15
Markov dynamics constitute one of the most fundamental models of random motion between the states of a system of interest. Markov dynamics have diverse applications in many fields of science and engineering, and are particularly applicable in the context of random motion in networks. In this paper we present a two-dimensional gauging method of the randomness of Markov dynamics. The method–termed Markov Stochasticity Coordinates–is established, discussed, and exemplified. Also, the method is tweaked to quantify the stochasticity of the first-passage-times of Markov dynamics, and the socioeconomic equality and mobility in human societies.
Brousseau, Denis; Thibaul, Simon; Ritcey, Anna M; Parent, Jocelyn; Seddiki, Omar; Dery, Jean-Philippe; Faucher, Luc; Vassallo, Julien; Naderian, Azadeh
2008-01-01
We present the research status of a deformable mirror made of a magnetic liquid whose surface is actuated by a triangular array of small current carrying coils. We demonstrate that the mirror can correct a 11 microns low order aberrated wavefront to a residual RMS wavefront error 0.05 microns. Recent developments show that these deformable mirrors can reach a frequency response of several hundred hertz. A new method for linearizing the response of these mirrors is also presented.
Optogenetic signaling-pathway regulation through scattering skull using wavefront shaping
Yoon, Jonghee; Lee, KyeoReh; Kim, Nury; Kim, Jin Man; Park, Jongchan; Choi, Chulhee; Heo, Won Do; Park, YongKeun
2015-01-01
We introduce a non-invasive approach for optogenetic regulation in biological cells through highly scattering skull tissue using wavefront shaping. The wavefront of the incident light was systematically controlled using a spatial light modulator in order to overcome multiple light-scattering in a mouse skull layer and to focus light on the target cells. We demonstrate that illumination with shaped waves enables spatiotemporal regulation of intracellular Ca2+ level at the individual-cell level.
FGF4 and FGF8 comprise the wavefront activity that controls somitogenesis
L A Naiche; Holder, Nakisha; Lewandoski, Mark
2011-01-01
Somites form along the embryonic axis by sequential segmentation from the presomitic mesoderm (PSM) and differentiate into the segmented vertebral column as well as other unsegmented tissues. Somites are thought to form via the intersection of two activities known as the clock and the wavefront. Previous work has suggested that fibroblast growth factor (FGF) activity may be the wavefront signal, which maintains the PSM in an undifferentiated state. However, it is unclear which (if any) of the...
Stochastic integrals: a combinatorial approach
Rota, Gian-Carlo; Wallstrom, Timothy C.
1997-01-01
A combinatorial definition of multiple stochastic integrals is given in the setting of random measures. It is shown that some properties of such stochastic integrals, formerly known to hold in special cases, are instances of combinatorial identities on the lattice of partitions of a set. The notion of stochastic sequences of binomial type is introduced as a generalization of special polynomial sequences occuring in stochastic integration, such as Hermite, Poisson–Charlier an...
Hamiltonian mechanics of stochastic acceleration.
Burby, J W; Zhmoginov, A I; Qin, H
2013-11-08
We show how to find the physical Langevin equation describing the trajectories of particles undergoing collisionless stochastic acceleration. These stochastic differential equations retain not only one-, but two-particle statistics, and inherit the Hamiltonian nature of the underlying microscopic equations. This opens the door to using stochastic variational integrators to perform simulations of stochastic interactions such as Fermi acceleration. We illustrate the theory by applying it to two example problems.
Dispersed Fringe Sensing Analysis - DFSA
Sigrist, Norbert; Shi, Fang; Redding, David C.; Basinger, Scott A.; Ohara, Catherine M.; Seo, Byoung-Joon; Bikkannavar, Siddarayappa A.; Spechler, Joshua A.
2012-01-01
Dispersed Fringe Sensing (DFS) is a technique for measuring and phasing segmented telescope mirrors using a dispersed broadband light image. DFS is capable of breaking the monochromatic light ambiguity, measuring absolute piston errors between segments of large segmented primary mirrors to tens of nanometers accuracy over a range of 100 micrometers or more. The DFSA software tool analyzes DFS images to extract DFS encoded segment piston errors, which can be used to measure piston distances between primary mirror segments of ground and space telescopes. This information is necessary to control mirror segments to establish a smooth, continuous primary figure needed to achieve high optical quality. The DFSA tool is versatile, allowing precise piston measurements from a variety of different optical configurations. DFSA technology may be used for measuring wavefront pistons from sub-apertures defined by adjacent segments (such as Keck Telescope), or from separated sub-apertures used for testing large optical systems (such as sub-aperture wavefront testing for large primary mirrors using auto-collimating flats). An experimental demonstration of the coarse-phasing technology with verification of DFSA was performed at the Keck Telescope. DFSA includes image processing, wavelength and source spectral calibration, fringe extraction line determination, dispersed fringe analysis, and wavefront piston sign determination. The code is robust against internal optical system aberrations and against spectral variations of the source. In addition to the DFSA tool, the software package contains a simple but sophisticated MATLAB model to generate dispersed fringe images of optical system configurations in order to quickly estimate the coarse phasing performance given the optical and operational design requirements. Combining MATLAB (a high-level language and interactive environment developed by MathWorks), MACOS (JPL s software package for Modeling and Analysis for Controlled Optical
Stochastic integral equations without probability
Mikosch, T; Norvaisa, R
2000-01-01
A pathwise approach to stochastic integral equations is advocated. Linear extended Riemann-Stieltjes integral equations driven by certain stochastic processes are solved. Boundedness of the p-variation for some 0
stochastic process. Typical examples of such
Analysis of bilinear stochastic systems
Willsky, A. S.; Martin, D. N.; Marcus, S. I.
1975-01-01
Analysis of stochastic dynamical systems that involve multiplicative (bilinear) noise processes. After defining the systems of interest, consideration is given to the evolution of the moments of such systems, the question of stochastic stability, and estimation for bilinear stochastic systems. Both exact and approximate methods of analysis are introduced, and, in particular, the uses of Lie-theoretic concepts and harmonic analysis are discussed.
Rogers, J. M.; Walcott, G. P.; Gladden, J. D.; Melnick, S. B.; Ideker, R. E.; Kay, M. W.
2008-01-01
It has been proposed that ventricular fibrillation (VF) waves emanate from stable localized sources, often called 'mother rotors'. However, evidence for the existence of these rotors is conflicting. Using a new panoramic optical mapping system that can image nearly the entire ventricular epicardium, we recently excluded epicardial mother rotors as the drivers of Wiggers' stage II VF in the isolated swine heart. Furthermore, we were unable to find evidence that VF requires sustained intramural sources. The present study was designed to test the following hypotheses: (i) VF is driven by a specific region, and (ii) rotors that are long-lived, though not necessarily permanent, are the primary generators of VF wavefronts. Using panoramic optical mapping, we mapped VF wavefronts from six isolated swine hearts. Wavefronts were tracked to characterize their activation pathways and to locate their originating sources. We found that the wavefronts that participate in epicardial re-entry were not confined to a compact region; rather they activated the entire epicardial surface. New wavefronts feeding into the epicardial activation pattern were generated over the majority of the epicardium and almost all of them were associated with rotors or repetitive breakthrough patterns that lasted for less than 2 s. These findings indicate that epicardial wavefronts in this model are generated by many transitory epicardial sources distributed over the entire surface of the heart.
Large field-of-view wavefront control for deep brain imaging (Conference Presentation)
Park, Jung-Hoon; Cui, Meng
2016-03-01
The biggest obstacle for deep tissue imaging is the scattering of light due to the heterogeneous distribution of biological tissue. In this respect, multiphoton microscopy has an inherent advantage as the scattering is significantly reduced by the use of longer excitation wavelengths. However, as we go deeper into the brain, effects of scattering still accumulate resulting in a loss of resolution and increased background noise. Adaptive optics is an ideal tool of choice to correct for such distortions of the excitation wavefront; the incident light can be tuned to cancel out the wavefront distortion experienced while propagating into greater depths resulting in a diffraction limited focus at the depth of interest. However, the biggest limitation of adaptive optics for in vivo brain imaging is its limited corrected field-of-view (FOV). For typical multiphoton laser scanning microscopes, the wavefront corrector for adaptive optics is placed at the pupil plane. This means that a single correction wavefront is applied to the entire scanned FOV which results in inefficient correction as the correction is averaged over the entire FOV. In this work, we demonstrate a novel approach to measure and display different correction wavefronts over different segments of the FOV. The application of the different correction wavefronts for each segment is realized in parallel resulting in fast aberration corrected imaging over a large FOV for high resolution in vivo brain imaging.
Research on encoding multi-gray-scale phase hologram and wavefront reconstruction.
Zhang, Hongxin; Zhou, Hao; Li, Jingyao; Qiao, Yujing; Gao, Wei
2016-04-01
Application of computer-generated holography for wavefront generation is beneficial for optical interferometry and 3D image display. However, there is a noticeable encoding error in computer-generated holograms, which is encoded by using the object's wavefront function in a computer. The encoding error will be transmitted and amplified during fabrication of a hologram, which can cause a reconstructed error in the generated wavefront. A correction method of encoding errors based on the least-squares fitting is proposed. A validating experiment is completed by using a liquid crystal spatial light modulator to reconstruct a group of paraboloid wavefronts. The results show that encoding errors increase the reconstructed error of a wavefront less than optical system errors, and the root-mean-square value drops 0.022λ after the correction of the encoding error, but it falls 0.092λ after the correction of optical system errors. The total error has been reduced by 0.114λ. This research is helpful for prediction of encoding errors and improvement of wavefront reconstruction accuracy.
Telescope Alignment From Sparsely Sampled Wavefront Measurements Over Pupil Subapertures
Bloemhof, Eric E.; An, Xin; Kuan, Gary M.; Moore, Douglas M.; OShay, Joseph F.; Tang, Hong; Page, Norman A.
2012-01-01
Alignment of two-element telescopes is a classic problem. During recent integration and test of the Space Interferometry Mission s (SIM s) Astrometric Beam Combiner (ABC), the innovators were faced with aligning two such telescope subsystems in the presence of a further complication: only two small subapertures in each telescope s pupil were accessible for measuring the wavefront with a Fizeau interferometer. This meant that the familiar aberrations that might be interpreted to infer system misalignments could be viewed only over small sub-regions of the pupil, making them hard to recognize. Further, there was no contiguous surface of the pupil connecting these two subapertures, so relative phase piston information was lost; the underlying full-aperture aberrations therefore had an additional degree of ambiguity. The solution presented here is to recognize that, in the absence of phase piston, the Zygo measurements primarily provide phase tilt in the subaperture windows of interest. Because these windows are small and situated far from the center of the (inaccessible) unobscured full aperture, any aberrations that are higher-order than tilt will be extremely high-order on the full aperture, and so not necessary or helpful to the alignment. Knowledge of the telescope s optical prescription allows straightforward evaluation of sensitivities (subap mode strength per unit full-aperture aberration), and these can be used in a predictive matrix approach to move with assurance to an aligned state. The technique is novel in every operational way compared to the standard approach of alignment based on full-aperture aberrations or searching for best rms wavefront. This approach is closely grounded in the observable quantities most appropriate to the problem. It is also more intuitive than inverting full phase maps (or subaperture Zernike spectra) with a ray-tracing program, which must certainly work in principle, but in practice met with limited success. Even if such
The stochastic quality calculus
DEFF Research Database (Denmark)
Zeng, Kebin; Nielson, Flemming; Nielson, Hanne Riis
2014-01-01
We introduce the Stochastic Quality Calculus in order to model and reason about distributed processes that rely on each other in order to achieve their overall behaviour. The calculus supports broadcast communication in a truly concurrent setting. Generally distributed delays are associated...
Stochastic Control - External Models
DEFF Research Database (Denmark)
Poulsen, Niels Kjølstad
2005-01-01
This note is devoted to control of stochastic systems described in discrete time. We are concerned with external descriptions or transfer function model, where we have a dynamic model for the input output relation only (i.e.. no direct internal information). The methods are based on LTI systems...
D.F. Schrager
2006-01-01
We propose a new model for stochastic mortality. The model is based on the literature on affine term structure models. It satisfies three important requirements for application in practice: analytical tractibility, clear interpretation of the factors and compatibility with financial option pricing m
Wheeler, Tim Allan; Holder, Martin; Winner, Hermann; Kochenderfer, Mykel
2017-01-01
Accurate simulation and validation of advanced driver assistance systems requires accurate sensor models. Modeling automotive radar is complicated by effects such as multipath reflections, interference, reflective surfaces, discrete cells, and attenuation. Detailed radar simulations based on physical principles exist but are computationally intractable for realistic automotive scenes. This paper describes a methodology for the construction of stochastic automotive radar models based on deep l...
Energy Technology Data Exchange (ETDEWEB)
Tollestrup, A.V.; Dugan, G
1983-12-01
Major headings in this review include: proton sources; antiproton production; antiproton sources and Liouville, the role of the Debuncher; transverse stochastic cooling, time domain; the accumulator; frequency domain; pickups and kickers; Fokker-Planck equation; calculation of constants in the Fokker-Planck equation; and beam feedback. (GHT)
Multistage quadratic stochastic programming
Lau, Karen K.; Womersley, Robert S.
2001-04-01
Quadratic stochastic programming (QSP) in which each subproblem is a convex piecewise quadratic program with stochastic data, is a natural extension of stochastic linear programming. This allows the use of quadratic or piecewise quadratic objective functions which are essential for controlling risk in financial and project planning. Two-stage QSP is a special case of extended linear-quadratic programming (ELQP). The recourse functions in QSP are piecewise quadratic convex and Lipschitz continuous. Moreover, they have Lipschitz gradients if each QP subproblem is strictly convex and differentiable. Using these properties, a generalized Newton algorithm exhibiting global and superlinear convergence has been proposed recently for the two stage case. We extend the generalized Newton algorithm to multistage QSP and show that it is globally and finitely convergent under suitable conditions. We present numerical results on randomly generated data and modified publicly available stochastic linear programming test sets. Efficiency schemes on different scenario tree structures are discussed. The large-scale deterministic equivalent of the multistage QSP is also generated and their accuracy compared.
Fuzzy stochastic neural network model for structural system identification
Jiang, Xiaomo; Mahadevan, Sankaran; Yuan, Yong
2017-01-01
This paper presents a dynamic fuzzy stochastic neural network model for nonparametric system identification using ambient vibration data. The model is developed to handle two types of imprecision in the sensed data: fuzzy information and measurement uncertainties. The dimension of the input vector is determined by using the false nearest neighbor approach. A Bayesian information criterion is applied to obtain the optimum number of stochastic neurons in the model. A fuzzy C-means clustering algorithm is employed as a data mining tool to divide the sensed data into clusters with common features. The fuzzy stochastic model is created by combining the fuzzy clusters of input vectors with the radial basis activation functions in the stochastic neural network. A natural gradient method is developed based on the Kullback-Leibler distance criterion for quick convergence of the model training. The model is validated using a power density pseudospectrum approach and a Bayesian hypothesis testing-based metric. The proposed methodology is investigated with numerically simulated data from a Markov Chain model and a two-story planar frame, and experimentally sensed data from ambient vibration data of a benchmark structure.
Beamlet pulse-generation and wavefront-control system
Energy Technology Data Exchange (ETDEWEB)
Van Wonterghem, B.M.; Salmon, J.T.; Wilcox, R.W.
1996-06-01
The Beamlet pulse-generation system (or {open_quotes}front end{close_quotes}) refers to the laser hardware that generates the spatially and temporally shaped pulse that is injected into the main laser cavity. All large ICF lasers have pulse-generation systems that typically consist of a narrow-band oscillator, elector-optic modulators for temporal and bandwidth shaping, and one or more preamplifiers. Temporal shaping is used to provide the desired laser output pulse shape and also to compensate for gain saturation effects in the large-aperture amplifiers. Bandwidth is applied to fulfill specific target irradiation requirements and to avoid stimulated Brillouin scattering (SBS) in large-aperture laser components. Usually the sharp edge of the beam`s spatial intensity profile is apodized before injection in the main amplifier beam line. This prevents large-amplitude ripples on the intensity profile. Here the authors briefly review the front-end design and discuss improvements to the oscillator and modulator systems. Their main focus, however, is to describe Beamlet`s novel beam-shaping and wavefront-control systems that have recently been fully activated and tested.
Harmonic source wavefront aberration correction for ultrasound imaging
Dianis, Scott W.; von Ramm, Olaf T.
2011-01-01
A method is proposed which uses a lower-frequency transmit to create a known harmonic acoustical source in tissue suitable for wavefront correction without a priori assumptions of the target or requiring a transponder. The measurement and imaging steps of this method were implemented on the Duke phased array system with a two-dimensional (2-D) array. The method was tested with multiple electronic aberrators [0.39π to 1.16π radians root-mean-square (rms) at 4.17 MHz] and with a physical aberrator 0.17π radians rms at 4.17 MHz) in a variety of imaging situations. Corrections were quantified in terms of peak beam amplitude compared to the unaberrated case, with restoration between 0.6 and 36.6 dB of peak amplitude with a single correction. Standard phantom images before and after correction were obtained and showed both visible improvement and 14 dB contrast improvement after correction. This method, when combined with previous phase correction methods, may be an important step that leads to improved clinical images. PMID:21303031
Suppressing Anomalous Localized Waffle Behavior in Least Squares Wavefront Reconstructors
Energy Technology Data Exchange (ETDEWEB)
Gavel, D
2002-10-08
A major difficulty with wavefront slope sensors is their insensitivity to certain phase aberration patterns, the classic example being the waffle pattern in the Fried sampling geometry. As the number of degrees of freedom in AO systems grows larger, the possibility of troublesome waffle-like behavior over localized portions of the aperture is becoming evident. Reconstructor matrices have associated with them, either explicitly or implicitly, an orthogonal mode space over which they operate, called the singular mode space. If not properly preconditioned, the reconstructor's mode set can consist almost entirely of modes that each have some localized waffle-like behavior. In this paper we analyze the behavior of least-squares reconstructors with regard to their mode spaces. We introduce a new technique that is successful in producing a mode space that segregates the waffle-like behavior into a few ''high order'' modes, which can then be projected out of the reconstructor matrix. This technique can be adapted so as to remove any specific modes that are undesirable in the final reconstructor (such as piston, tip, and tilt for example) as well as suppress (the more nebulously defined) localized waffle behavior.
Continuous shearlet frames and resolution of the wavefront set
Grohs, Philipp
2010-12-04
In recent years directional multiscale transformations like the curvelet- or shearlet transformation have gained considerable attention. The reason for this is that these transforms are-unlike more traditional transforms like wavelets-able to efficiently handle data with features along edges. The main result in Kutyniok and Labate (Trans. Am. Math. Soc. 361:2719-2754, 2009) confirming this property for shearlets is due to Kutyniok and Labate where it is shown that for very special functions ψ with frequency support in a compact conical wegde the decay rate of the shearlet coefficients of a tempered distribution f with respect to the shearlet ψ can resolve the wavefront set of f. We demonstrate that the same result can be verified under much weaker assumptions on ψ, namely to possess sufficiently many anisotropic vanishing moments. We also show how to build frames for L2(ℝ2)from any such function. To prove our statements we develop a new approach based on an adaption of the Radon transform to the shearlet structure. © 2010 Springer-Verlag.
Monotone traveling wavefronts of the KPP-Fisher delayed equation
Gomez, Adrian; Trofimchuk, Sergei
In the early 2000's, Gourley (2000), Wu et al. (2001), Ashwin et al. (2002) initiated the study of the positive wavefronts in the delayed Kolmogorov-Petrovskii-Piskunov-Fisher equation u(t,x)=Δu(t,x)+u(t,x)(1-u(t-h,x)), u⩾0, x∈R. Since then, this model has become one of the most popular objects in the studies of traveling waves for the monostable delayed reaction-diffusion equations. In this paper, we give a complete solution to the problem of existence and uniqueness of monotone waves in Eq. (*). We show that each monotone traveling wave can be found via an iteration procedure. The proposed approach is based on the use of special monotone integral operators (which are different from the usual Wu-Zou operator) and appropriate upper and lower solutions associated to them. The analysis of the asymptotic expansions of the eventual traveling fronts at infinity is another key ingredient of our approach.
Wavefront aberrations of x-ray dynamical diffraction beams.
Liao, Keliang; Hong, Youli; Sheng, Weifan
2014-10-01
The effects of dynamical diffraction in x-ray diffractive optics with large numerical aperture render the wavefront aberrations difficult to describe using the aberration polynomials, yet knowledge of them plays an important role in a vast variety of scientific problems ranging from optical testing to adaptive optics. Although the diffraction theory of optical aberrations was established decades ago, its application in the area of x-ray dynamical diffraction theory (DDT) is still lacking. Here, we conduct a theoretical study on the aberration properties of x-ray dynamical diffraction beams. By treating the modulus of the complex envelope as the amplitude weight function in the orthogonalization procedure, we generalize the nonrecursive matrix method for the determination of orthonormal aberration polynomials, wherein Zernike DDT and Legendre DDT polynomials are proposed. As an example, we investigate the aberration evolution inside a tilted multilayer Laue lens. The corresponding Legendre DDT polynomials are obtained numerically, which represent balanced aberrations yielding minimum variance of the classical aberrations of an anamorphic optical system. The balancing of classical aberrations and their standard deviations are discussed. We also present the Strehl ratio of the primary and secondary balanced aberrations.
Limits for Stochastic Reaction Networks
DEFF Research Database (Denmark)
Cappelletti, Daniele
at a certain time are stochastically modelled by means of a continuous-time Markov chain. Our work concerns primarily stochastic reaction systems, and their asymptotic properties. In Paper I, we consider a reaction system with intermediate species, i.e. species that are produced and fast degraded along a path...... of the stochastic reaction systems. Specically, we build a theory for stochastic reaction systems that is parallel to the deciency zero theory for deterministic systems, which dates back to the 70s. A deciency theory for stochastic reaction systems was missing, and few results connecting deciency and stochastic....... Such species, in the deterministic modelling regime, assume always the same value at any positive steady state. In the stochastic setting, we prove that, if the initial condition is a point in the basin of attraction of a positive steady state of the corresponding deterministic model and tends to innity...
Stochastic processes in cell biology
Bressloff, Paul C
2014-01-01
This book develops the theory of continuous and discrete stochastic processes within the context of cell biology. A wide range of biological topics are covered including normal and anomalous diffusion in complex cellular environments, stochastic ion channels and excitable systems, stochastic calcium signaling, molecular motors, intracellular transport, signal transduction, bacterial chemotaxis, robustness in gene networks, genetic switches and oscillators, cell polarization, polymerization, cellular length control, and branching processes. The book also provides a pedagogical introduction to the theory of stochastic process – Fokker Planck equations, stochastic differential equations, master equations and jump Markov processes, diffusion approximations and the system size expansion, first passage time problems, stochastic hybrid systems, reaction-diffusion equations, exclusion processes, WKB methods, martingales and branching processes, stochastic calculus, and numerical methods. This text is primarily...
The wavefront of the radio signal emitted by cosmic ray air showers
Energy Technology Data Exchange (ETDEWEB)
Apel, W.D.; Bekk, K.; Blümer, J.; Bozdog, H.; Daumiller, K.; Doll, P.; Engel, R. [Institut für Kernphysik, Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen (Germany); Arteaga-Velázquez, J.C. [Instituto de Física y Matemáticas, Universidad Michoacana, Edificio C-3, Cd. Universitaria, C.P. 58040 Morelia, Michoacán (Mexico); Bähren, L.; Falcke, H. [ASTRON, Oude Hoogeveensedijk 4, 7991 PD Dwingeloo (Netherlands); Bertaina, M.; Cantoni, E.; Chiavassa, A.; Pierro, F. Di [Dipartimento di Fisica, Università degli Studi di Torino, Via Giuria 1, 10125 Torino (Italy); Biermann, P.L. [Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn (Germany); Brancus, I.M. [National Institute of Physics and Nuclear Engineering, Str. Reactorului no. 30, P.O. Box MG-6, Bucharest-Magurele (Romania); De Souza, V. [Instituto de Física de São Carlos, Universidade de São Paulo, Av. Trabalhador São-Carlense 400, Pq. Arnold Schmidt, São Carlos (Brazil); Fuchs, B. [Institut für Experimentelle Kernphysik, Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen (Germany); Gemmeke, H. [Institut für Prozessdatenverarbeitung und Elektronik, Karlsruhe Institute of Technology (KIT), Hermann-von-Helmholtz-Platz 1, 76344 Eggenstein-Leopoldshafen (Germany); Grupen, C., E-mail: frank.schroeder@kit.edu [Faculty of Natural Sciences and Engineering, Universität Siegen, Walter-Flex-Straße 3, 57072 Siegen (Germany); and others
2014-09-01
Analyzing measurements of the LOPES antenna array together with corresponding CoREAS simulations for more than 300 measured events with energy above 10{sup 17} eV and zenith angles smaller than 45{sup o}, we find that the radio wavefront of cosmic-ray air showers is of approximately hyperbolic shape. The simulations predict a slightly steeper wavefront towards East than towards West, but this asymmetry is negligible against the measurement uncertainties of LOPES. At axis distances ∼> 50 m, the wavefront can be approximated by a simple cone. According to the simulations, the cone angle is clearly correlated with the shower maximum. Thus, we confirm earlier predictions that arrival time measurements can be used to study the longitudinal shower development, but now using a realistic wavefront. Moreover, we show that the hyperbolic wavefront is compatible with our measurement, and we present several experimental indications that the cone angle is indeed sensitive to the shower development. Consequently, the wavefront can be used to statistically study the primary composition of ultra-high energy cosmic rays. At LOPES, the experimentally achieved precision for the shower maximum is limited by measurement uncertainties to approximately 140 g/c {sup 2}. But the simulations indicate that under better conditions this method might yield an accuracy for the atmospheric depth of the shower maximum, X{sub max}, better than 30 g/c {sup 2}. This would be competitive with the established air-fluorescence and air-Cherenkov techniques, where the radio technique offers the advantage of a significantly higher duty-cycle. Finally, the hyperbolic wavefront can be used to reconstruct the shower geometry more accurately, which potentially allows a better reconstruction of all other shower parameters, too.
Dynamic stochastic optimization
Ermoliev, Yuri; Pflug, Georg
2004-01-01
Uncertainties and changes are pervasive characteristics of modern systems involving interactions between humans, economics, nature and technology. These systems are often too complex to allow for precise evaluations and, as a result, the lack of proper management (control) may create significant risks. In order to develop robust strategies we need approaches which explic itly deal with uncertainties, risks and changing conditions. One rather general approach is to characterize (explicitly or implicitly) uncertainties by objec tive or subjective probabilities (measures of confidence or belief). This leads us to stochastic optimization problems which can rarely be solved by using the standard deterministic optimization and optimal control methods. In the stochastic optimization the accent is on problems with a large number of deci sion and random variables, and consequently the focus ofattention is directed to efficient solution procedures rather than to (analytical) closed-form solu tions. Objective an...
Directory of Open Access Journals (Sweden)
William Margulies
2004-11-01
Full Text Available In this paper, we study a specific stochastic differential equation depending on a parameter and obtain a representation of its probability density function in terms of Jacobi Functions. The equation arose in a control problem with a quadratic performance criteria. The quadratic performance is used to eliminate the control in the standard Hamilton-Jacobi variational technique. The resulting stochastic differential equation has a noise amplitude which complicates the solution. We then solve Kolmogorov's partial differential equation for the probability density function by using Jacobi Functions. A particular value of the parameter makes the solution a Martingale and in this case we prove that the solution goes to zero almost surely as time tends to infinity.
Stochastic porous media equations
Barbu, Viorel; Röckner, Michael
2016-01-01
Focusing on stochastic porous media equations, this book places an emphasis on existence theorems, asymptotic behavior and ergodic properties of the associated transition semigroup. Stochastic perturbations of the porous media equation have reviously been considered by physicists, but rigorous mathematical existence results have only recently been found. The porous media equation models a number of different physical phenomena, including the flow of an ideal gas and the diffusion of a compressible fluid through porous media, and also thermal propagation in plasma and plasma radiation. Another important application is to a model of the standard self-organized criticality process, called the "sand-pile model" or the "Bak-Tang-Wiesenfeld model". The book will be of interest to PhD students and researchers in mathematics, physics and biology.
Multistage stochastic optimization
Pflug, Georg Ch
2014-01-01
Multistage stochastic optimization problems appear in many ways in finance, insurance, energy production and trading, logistics and transportation, among other areas. They describe decision situations under uncertainty and with a longer planning horizon. This book contains a comprehensive treatment of today’s state of the art in multistage stochastic optimization. It covers the mathematical backgrounds of approximation theory as well as numerous practical algorithms and examples for the generation and handling of scenario trees. A special emphasis is put on estimation and bounding of the modeling error using novel distance concepts, on time consistency and the role of model ambiguity in the decision process. An extensive treatment of examples from electricity production, asset liability management and inventory control concludes the book
Samuelson, Paul A.
1971-01-01
Because a commodity like wheat can be carried forward from one period to the next, speculative arbitrage serves to link its prices at different points of time. Since, however, the size of the harvest depends on complicated probability processes impossible to forecast with certainty, the minimal model for understanding market behavior must involve stochastic processes. The present study, on the basis of the axiom that it is the expected rather than the known-for-certain prices which enter into all arbitrage relations and carryover decisions, determines the behavior of price as the solution to a stochastic-dynamic-programming problem. The resulting stationary time series possesses an ergodic state and normative properties like those often observed for real-world bourses. PMID:16591903
Essentials of stochastic processes
Durrett, Richard
2016-01-01
Building upon the previous editions, this textbook is a first course in stochastic processes taken by undergraduate and graduate students (MS and PhD students from math, statistics, economics, computer science, engineering, and finance departments) who have had a course in probability theory. It covers Markov chains in discrete and continuous time, Poisson processes, renewal processes, martingales, and option pricing. One can only learn a subject by seeing it in action, so there are a large number of examples and more than 300 carefully chosen exercises to deepen the reader’s understanding. Drawing from teaching experience and student feedback, there are many new examples and problems with solutions that use TI-83 to eliminate the tedious details of solving linear equations by hand, and the collection of exercises is much improved, with many more biological examples. Originally included in previous editions, material too advanced for this first course in stochastic processes has been eliminated while treatm...
Stochastic calculus and applications
Cohen, Samuel N
2015-01-01
Completely revised and greatly expanded, the new edition of this text takes readers who have been exposed to only basic courses in analysis through the modern general theory of random processes and stochastic integrals as used by systems theorists, electronic engineers and, more recently, those working in quantitative and mathematical finance. Building upon the original release of this title, this text will be of great interest to research mathematicians and graduate students working in those fields, as well as quants in the finance industry. New features of this edition include: End of chapter exercises; New chapters on basic measure theory and Backward SDEs; Reworked proofs, examples and explanatory material; Increased focus on motivating the mathematics; Extensive topical index. "Such a self-contained and complete exposition of stochastic calculus and applications fills an existing gap in the literature. The book can be recommended for first-year graduate studies. It will be useful for all who intend to wo...
Dynamics of stochastic systems
Klyatskin, Valery I
2005-01-01
Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. The well known example of Brownian particle suspended in fluid and subjected to random molecular bombardment laid the foundation for modern stochastic calculus and statistical physics. Other important examples include turbulent transport and diffusion of particle-tracers (pollutants), or continuous densities (''''oil slicks''''), wave propagation and scattering in randomly inhomogeneous media, for instance light or sound propagating in the turbulent atmosphere.Such models naturally render to statistical description, where the input parameters and solutions are expressed by random processes and fields.The fundamental problem of stochastic dynamics is to identify the essential characteristics of system (its state and evolution), and relate those to the input parameters of ...
Stochastic gravitoelectromagnetic inflation
Aguilar, J E M; Bellini, Mauricio
2006-01-01
Gravitoelectromagnetic inflation was recently introduced to describe, in an unified manner, electromagnetic, gravitatory and inflaton fields in the early (accelerated) inflationary universe from a 5D vacuum state. In this paper, we study a stochastic treatment for the gravitoelectromagnetic components $A_B=(A_{\\mu},\\phi)$, on cosmological scales. We focus our study on the seed magnetic fields on super Hubble scales, which could play an important role in large scale structure formation of the universe.
Holmes-Cerfon, Miranda
2016-11-01
We study a model of rolling particles subject to stochastic fluctuations, which may be relevant in systems of nano- or microscale particles where rolling is an approximation for strong static friction. We consider the simplest possible nontrivial system: a linear polymer of three disks constrained to remain in contact and immersed in an equilibrium heat bath so the internal angle of the polymer changes due to stochastic fluctuations. We compare two cases: one where the disks can slide relative to each other and the other where they are constrained to roll, like gears. Starting from the Langevin equations with arbitrary linear velocity constraints, we use formal homogenization theory to derive the overdamped equations that describe the process in configuration space only. The resulting dynamics have the formal structure of a Brownian motion on a Riemannian or sub-Riemannian manifold, depending on if the velocity constraints are holonomic or nonholonomic. We use this to compute the trimer's equilibrium distribution with and without the rolling constraints. Surprisingly, the two distributions are different. We suggest two possible interpretations of this result: either (i) dry friction (or other dissipative, nonequilibrium forces) changes basic thermodynamic quantities like the free energy of a system, a statement that could be tested experimentally, or (ii) as a lesson in modeling rolling or friction more generally as a velocity constraint when stochastic fluctuations are present. In the latter case, we speculate there could be a "roughness" entropy whose inclusion as an effective force could compensate the constraint and preserve classical Boltzmann statistics. Regardless of the interpretation, our calculation shows the word "rolling" must be used with care when stochastic fluctuations are present.
Identifiability in stochastic models
1992-01-01
The problem of identifiability is basic to all statistical methods and data analysis, occurring in such diverse areas as Reliability Theory, Survival Analysis, and Econometrics, where stochastic modeling is widely used. Mathematics dealing with identifiability per se is closely related to the so-called branch of ""characterization problems"" in Probability Theory. This book brings together relevant material on identifiability as it occurs in these diverse fields.
Stochastic Thermodynamics of Learning
Goldt, Sebastian; Seifert, Udo
2017-01-01
Virtually every organism gathers information about its noisy environment and builds models from those data, mostly using neural networks. Here, we use stochastic thermodynamics to analyze the learning of a classification rule by a neural network. We show that the information acquired by the network is bounded by the thermodynamic cost of learning and introduce a learning efficiency η ≤1 . We discuss the conditions for optimal learning and analyze Hebbian learning in the thermodynamic limit.
Stochastic Games. I. Foundations,
1982-04-01
stimulate discussion and critical coment. Requests for single copies of a Paper will be filled by the Cowles Foundation within the limits of the supply...underpinning for the theory of stochastic games. Section 2 is a reworking of the Bevley- Kohlberg result integrated with Shapley’s; the "black magic" of... Kohlberg : The values of the r-discount game, and the stationary optimal strategies, have Puiseaux expansions. L.. 11" 6 3. More generally, consider an
Stochastic gravitoelectromagnetic inflation
Madriz Aguilar, José Edgar; Bellini, Mauricio
2006-11-01
Gravitoelectromagnetic inflation was recently introduced to describe, in an unified manner, electromagnetic, gravitatory and inflaton fields in the early (accelerated) inflationary universe from a 5D vacuum state. In this Letter, we study a stochastic treatment for the gravitoelectromagnetic components A=(A,φ), on cosmological scales. We focus our study on the seed magnetic fields on super-Hubble scales, which could play an important role in large scale structure formation of the universe.
Stochastic power system operation
Power, Michael
2010-01-01
This paper outlines how to economically and reliably operate a power system with high levels of renewable generation which are stochastic in nature. It outlines the challenges for system operators, and suggests tools and methods for meeting this challenge, which is one of the most fundamental since large scale power networks were instituted. The Ireland power system, due to its nature and level of renewable generation, is considered as an example in this paper.
Stochastic Thermodynamics of Learning
Goldt, Sebastian
2016-01-01
Virtually every organism gathers information about its noisy environment and builds models from that data, mostly using neural networks. Here, we use stochastic thermodynamics to analyse the learning of a classification rule by a neural network. We show that the information acquired by the network is bounded by the thermodynamic cost of learning and introduce a learning efficiency $\\eta\\le1$. We discuss the conditions for optimal learning and analyse Hebbian learning in the thermodynamic limit.
Stochastic Nonlinear Aeroelasticity
2009-01-01
STOCHASTIC NONLINEAR AEROELASTICITY 5a. CONTRACT NUMBER In- house 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 0601102 6. AUTHOR(S) Philip S...ABSTRACT This report documents the culmination of in- house work in the area of uncertainty quantification and probabilistic techniques for... coff U∞ cs ea lw cw Figure 6: Wing and store geometry (left), wing box structural model (middle), flutter distribution (right
Stochasticity Modeling in Memristors
Naous, Rawan
2015-10-26
Diverse models have been proposed over the past years to explain the exhibiting behavior of memristors, the fourth fundamental circuit element. The models varied in complexity ranging from a description of physical mechanisms to a more generalized mathematical modeling. Nonetheless, stochasticity, a widespread observed phenomenon, has been immensely overlooked from the modeling perspective. This inherent variability within the operation of the memristor is a vital feature for the integration of this nonlinear device into the stochastic electronics realm of study. In this paper, experimentally observed innate stochasticity is modeled in a circuit compatible format. The model proposed is generic and could be incorporated into variants of threshold-based memristor models in which apparent variations in the output hysteresis convey the switching threshold shift. Further application as a noise injection alternative paves the way for novel approaches in the fields of neuromorphic engineering circuits design. On the other hand, extra caution needs to be paid to variability intolerant digital designs based on non-deterministic memristor logic.
Simulation of Stochastic Partial Differential Equations and Stochastic Active Contours
Lang, Annika
2007-01-01
This thesis discusses several aspects of the simulation of stochastic partial differential equations. First, two fast algorithms for the approximation of infinite dimensional Gaussian random fields with given covariance are introduced. Later Hilbert space-valued Wiener processes are constructed out of these random fields. A short introduction to infinite-dimensional stochastic analysis and stochastic differential equations is given. Furthermore different definitions of numerical stability for...
Effect of Pupil Size on Wavefront Refraction during Orthokeratology.
Faria-Ribeiro, Miguel; Navarro, Rafael; González-Méijome, José Manuel
2016-11-01
It has been hypothesized that central and peripheral refraction, in eyes treated with myopic overnight orthokeratology, might vary with changes in pupil diameter. The aim of this work was to evaluate the axial and peripheral refraction and optical quality after orthokeratology, using ray tracing software for different pupil sizes. Zemax-EE was used to generate a series of 29 semi-customized model eyes based on the corneal topography changes from 29 patients who had undergone myopic orthokeratology. Wavefront refraction in the central 80 degrees of the visual field was calculated using three different quality metrics criteria: Paraxial curvature matching, minimum root mean square error (minRMS), and the Through Focus Visual Strehl of the Modulation Transfer Function (VSMTF), for 3- and 6-mm pupil diameters. The three metrics predicted significantly different values for foveal and peripheral refractions. Compared with the Paraxial criteria, the other two metrics predicted more myopic refractions on- and off-axis. Interestingly, the VSMTF predicts only a marginal myopic shift in the axial refraction as the pupil changes from 3 to 6 mm. For peripheral refraction, minRMS and VSMTF metric criteria predicted a higher exposure to peripheral defocus as the pupil increases from 3 to 6 mm. The results suggest that the supposed effect of myopic control produced by ortho-k treatments might be dependent on pupil size. Although the foveal refractive error does not seem to change appreciably with the increase in pupil diameter (VSMTF criteria), the high levels of positive spherical aberration will lead to a degradation of lower spatial frequencies, that is more significant under low illumination levels.
Wavefront sensors and algorithms for adaptive optical systems
Lukin, V. P.; Botygina, N. N.; Emaleev, O. N.; Konyaev, P. A.
2010-07-01
The results of recent works related to techniques and algorithms for wave-front (WF) measurement using Shack-Hartmann sensors show their high efficiency in solution of very different problems of applied optics. The goal of this paper was to develop a sensitive Shack-Hartmann sensor with high precision WF measurement capability on the base of modern technology of optical elements making and new efficient methods and computational algorithms of WF reconstruction. The Shack-Hartmann sensors sensitive to small WF aberrations are used for adaptive optical systems, compensating the wave distortions caused by atmospheric turbulence. A high precision Shack-Hartmann WF sensor has been developed on the basis of a low-aperture off-axis diffraction lens array. The device is capable of measuring WF slopes at array sub-apertures of size 640×640 μm with an error not exceeding 4.80 arcsec (0.15 pixel), which corresponds to the standard deviation equal to 0.017λ at the reconstructed WF with wavelength λ . Also the modification of this sensor for adaptive system of solar telescope using extended scenes as tracking objects, such as sunspot, pores, solar granulation and limb, is presented. The software package developed for the proposed WF sensors includes three algorithms of local WF slopes estimation (modified centroids, normalized cross-correlation and fast Fourierdemodulation), as well as three methods of WF reconstruction (modal Zernike polynomials expansion, deformable mirror response functions expansion and phase unwrapping), that can be selected during operation with accordance to the application.
Aligning a more than 100 degrees of freedom wavefront sensor
Marafatto, Luca; Bergomi, Maria; Brunelli, Alessandro; Dima, Marco; Farinato, Jacopo; Farisato, Giancarlo; Lessio, Luigi; Magrin, Demetrio; Ragazzoni, Roberto; Viotto, Valentina; Bertram, Thomas; Bizenberger, Peter; Brangier, Matthieu; Briegel, Florian; Conrad, Albert; De Bonis, Fulvio; Herbst, Tom; Hofferbert, Ralph; Kittmann, Frank; Kürster, Martin; Meschke, Daniel; Mohr, Lars; Rohloff, Ralf-Rainer
2012-07-01
LINC-NIRVANA is the Fizeau beam combiner for the LBT, with the aim to retrieve the sensitivity of a 12m telescope and the spatial resolution of a 22.8m one. Despite being only one of the four wavefront sensors of a layer-oriented MCAO system, the GWS, which is retrieving the deformation introduced by the lower atmosphere, known to be the main aberration source, reveals a noticeable internal opto-mechanical complexity. The presence of 12 small devices used to select up to the same number of NGSs, with 3 optical components each, moving in a wide annular 2'-6' arcmin Field of View and sending the light to a common pupil re-imager, and the need to obtain and keep a very good super-imposition of the pupil images on the CCD camera, led to an overall alignment procedure in which more than a hundred of degrees of freedom have to be contemporary adjusted. The rotation of the entire WFS to compensate for the sky movement, moreover, introduces a further difficulty both in the alignment and in ensuring the required pupil superposition stability. A detailed description of the alignment procedure is presented here, together with the lessons learned managing the complexity of such a WFS, which led to considerations regarding future instruments, like a possible review of numerical versus optical co-add approach, above all if close to zero read-out noise detectors will be soon available. Nevertheless, the GWS AIV has been carried out and the system will be soon mounted at LBT to perform what is called the Pathfinder experiment, which consists in ground-layer correction, taking advantage of the Adaptive Secondary deformable Mirror.
The shape of the radio wavefront of extensive air showers as measured with LOFAR
Corstanje, A; Nelles, A; Buitink, S; Enriquez, J E; Falcke, H; Frieswijk, W; Hörandel, J R; Krause, M; Rachen, J P; Scholten, O; ter Veen, S; Thoudam, S; Trinh, G; Akker, M van den; Alexov, A; Anderson, J; Avruch, I M; Bell, M E; Bentum, M J; Bernardi, G; Best, P; Bonafede, A; Breitling, F; Broderick, J; Butcher, H R; Ciardi, B; de Gasperin, F; de Geus, E; de Vos, M; Duscha, S; Eislöffel, J; Engels, D; Fallows, R A; Ferrari, C; Garrett, M A; Griessmeier, J; Gunst, A W; Hamaker, J P; Hoeft, M; Horneffer, A; Iacobelli, M; Juette, E; Karastergiou, A; Kohler, J; Kondratiev, V I; Kuniyoshi, M; Kuper, G; Maat, P; Mann, G; McFadden, R; McKay-Bukowski, D; Mevius, M; Munk, H; Norden, M J; Orru, E; Paas, H; Pandey-Pommier, M; Pandey, V N; Pizzo, R; Polatidis, A G; Reich, W; Röttgering, H; Scaife, A M M; Schwarz, D; Smirnov, O; Stewart, A; Swinbank, J; Tagger, M; Tang, Y; Tasse, C; Toribio, C; Vermeulen, R; Vocks, C; van Weeren, R J; Wijnholds, S J; Wucknitz, O; Yatawatta, S; Zarka, P
2014-01-01
Extensive air showers, induced by high energy cosmic rays impinging on the Earth's atmosphere, produce radio emission that is measured with the LOFAR radio telescope. As the emission comes from a finite distance of a few kilometers, the incident wavefront is non-planar. A spherical or conical shape of the wavefront has been proposed, but measurements of individual air showers have been inconclusive so far. For a selected high-quality sample of 161 measured extensive air showers, we have reconstructed the wavefront by measuring pulse arrival times to sub-nanosecond accuracy in 200 to 350 individual antennas. For each measured air shower, we have fitted a conical, spherical, and hyperboloid shape to the arrival times. The fit quality and a likelihood analysis show that a hyperboloid is the best parametrization. Using a non-planar wavefront shape gives an improved angular resolution, when reconstructing the shower arrival direction. Furthermore, a dependence of the wavefront shape on the shower geometry can be s...
Wavefront control of high power laser beams for the National Ignition Facility (NIF)
Energy Technology Data Exchange (ETDEWEB)
Bliss, E; Feldman, M; Grey, A; Koch, J; Lund, L; Sacks, R; Smith, D; Stolz, C; Van Atta, L; Winters, S; Woods, B; Zacharias, R
1999-09-22
The use of lasers as the driver for inertial confinement fusion and weapons physics experiments is based on their ability to produce high-energy short pulses in a beam with low divergence. Indeed, the focus ability of high quality laser beams far exceeds alternate technologies and is a major factor in the rationale for building high power lasers for such applications. The National Ignition Facility (NIF) is a large, 192-beam, high-power laser facility under construction at the Lawrence Livermore National Laboratory for fusion and weapons physics experiments. Its uncorrected minimum focal spot size is limited by laser system aberrations. The NIF includes a Wavefront Control System to correct these aberrations to yield a focal spot small enough for its applications. Sources of aberrations to be corrected include prompt pump-induced distortions in the laser amplifiers, previous-shot thermal distortions, beam off-axis effects, and gravity, mounting, and coating-induced optic distortions. Aberrations from gas density variations and optic manufacturing figure errors are also partially corrected. This paper provides an overview of the NIF Wavefront Control System and describes the target spot size performance improvement it affords. It describes provisions made to accommodate the NIF's high fluence (laser beam and flashlamp), large wavefront correction range, wavefront temporal bandwidth, temperature and humidity variations, cleanliness requirements, and exception handling requirements (e.g. wavefront out-of-limits conditions).
End-To-End performance test of the LINC-NIRVANA Wavefront-Sensor system.
Berwein, Juergen; Bertram, Thomas; Conrad, Al; Briegel, Florian; Kittmann, Frank; Zhang, Xiangyu; Mohr, Lars
2011-09-01
LINC-NIRVANA is an imaging Fizeau interferometer, for use in near infrared wavelengths, being built for the Large Binocular Telescope. Multi-conjugate adaptive optics (MCAO) increases the sky coverage and the field of view over which diffraction limited images can be obtained. For its MCAO implementation, Linc-Nirvana utilizes four total wavefront sensors; each of the two beams is corrected by both a ground-layer wavefront sensor (GWS) and a high-layer wavefront sensor (HWS). The GWS controls the adaptive secondary deformable mirror (DM), which is based on an DSP slope computing unit. Whereas the HWS controls an internal DM via computations provided by an off-the-shelf multi-core Linux system. Using wavefront sensor data collected from a prior lab experiment, we have shown via simulation that the Linux based system is sufficient to operate at 1kHz, with jitter well below the needs of the final system. Based on that setup we tested the end-to-end performance and latency through all parts of the system which includes the camera, the wavefront controller, and the deformable mirror. We will present our loop control structure and the results of those performance tests.
First laboratory results with the LINC-NIRVANA high layer wavefront sensor
Zhang, Xianyu; Gaessler, Wolfgang; Conrad, Albert R.; Bertram, Thomas; Arcidiacono, Carmelo; Herbst, Thomas M.; Kuerster, Martin; Bizenberger, Peter; Meschke, Daniel; Rix, Hans-Walter; Rao, Changhui; Mohr, Lars; Briegel, Florian; Kittmann, Frank; Berwein, Juergen; Trowitzsch, Jan; Schreiber, Laura; Ragazzoni, Roberto; Diolaiti, Emiliano
2011-08-01
In the field of adaptive optics, multi-conjugate adaptive optics (MCAO) can greatly increase the size of the corrected field of view (FoV) and also extend sky coverage. By applying layer oriented MCAO (LO-MCAO) [4], together with multiple guide stars (up to 20) and pyramid wavefront sensors [7], LINC-NIRVANA (L-N for short) [1] will provide two AO-corrected beams to a Fizeau interferometer to achieve 10 milliarcsecond angular resolution on the Large Binocular Telescope. This paper presents first laboratory results of the AO performance achieved with the high layer wavefront sensor (HWS). This sensor, together with its associated deformable mirror (a Xinetics-349), is being operated in one of the L-N laboratories. AO reference stars, spread across a 2 arc-minute FoV and with aberrations resulting from turbulence introduced at specific layers in the atmosphere, are simulated in this lab environment. This is achieved with the Multi-Atmosphere Phase screen and Stars (MAPS) [2] unit. From the wavefront data, the approximate residual wavefront error after correction has been calculated for different turbulent layer altitudes and wind speeds. Using a somewhat undersampled CCD, the FWHM of stars in the nearly 2 arc-minute FoV has also been measured. These test results demonstrate that the high layer wavefront sensor of LINC-NIRVANA will be able to achieve uniform AO correction across a large FoV.
Estimating the point spread function of an imaging system using wavefront measurement
Mao, Hongjun; Liang, Yonghui; Huang, Zongfu; Liu, Jin; Jiang, Pengzhi
2016-10-01
An imaging system is constructed by atmosphere turbulence and ground-based telescope when the latter is used to observe a space object. The wavefront measurement produced by adaptive optics system can be used to estimate the point spread function (PSF) of the imaging system since it contains the wavefront aberration information of the light from the object. But the detector noise of the wavefront sensor (WFS) will inevitably bring estimation error. Based on the statistical theory, a method is presented to improve the PSF estimation accuracy by eliminating the noise error from the wavefront measurement. The numerical simulation shows that the estimation error of this method could be lower than 10%. It also indicates that the higher the signal-noise ratio (SNR) of the WFS is, the more frames of the wavefront measurements are used, and the bigger the Fried constant is, the more accurate the estimation will be. The work in this paper can be applied to performance evaluation of imaging system, deconvolution of AO images, as well as photometric analysis of space object.
Study on the modification of measured wavefront aberration data for customized visual correction
Liu, Ming; Zhang, Yong; Zhang, Zhidong; Quan, Wei; An, Li
2008-12-01
Wavefront aberration of human eye is an important foundation for customized vision correction. In most current aberrometers, near infrared light is used to measure ocular wavefront aberration, whereas for customized visual correction, wavefront aberration data in visible range are required. With the measured wavefront aberration, corneal topography and eye's axial lengths data, individual eye models for twenty normal human eyes are constructed with the optical design software ZEMAX. Changing the incidence light wavelength and the refractive indexes of eye models, the values of defocus, astigmatism, higher-order aberrations in the measuring wavelength (833nm) and at the most sensitive wavelength of human eye (555nm) are obtained. Average focus shift between 833nm and 555nm is found to be about 0.94D, and different slightly for different individuals; the differences of astigmatism and higher-order aberrations between 833nm and 555nm are quite slight. For customized visual correction, the measured defocus value should be modified, whereas the measured astigmatism and higher-order aberrations could be used directly for the current correction precision. Individual eye model is a useful tool for accurate transformation of the measured wavefront aberration data into the data for visible spectrum.
Representation of wavefronts in free-form transmission pupils with Complex Zernike Polynomials
Navarro, Rafael; Rivera, Ricardo; Aporta, Justiniano
2011-01-01
Purpose To propose and evaluate Complex Zernike polynomials (CZPs) to represent general wavefronts with non uniform intensity (amplitude) in free-from transmission pupils. Methods They consist of three stages: (1) theoretical formulation; (2) numerical implementation; and (3) two studies of the fidelity of the reconstruction obtained as a function of the number of Zernike modes used (36 or 91). In the first study, we generated complex wavefronts merging wave aberration data from a group of 11 eyes, with a generic Gaussian model of the Stiles-Crawford effective pupil transmission. In the second study we simulated the wavefront passing through different pupil stop shapes (annular, semicircular, elliptical and triangular). Results The reconstructions of the wave aberration (phase of the generalized pupil function) were always good, the reconstruction RMS error was of the order of 10−4 wave lengths, no matter the number of modes used. However, the reconstruction of the amplitude (effective transmission) was highly dependent of the number of modes used. In particular, a high number of modes is necessary to reconstruct sharp edges, due to their high frequency content. Conclusions CZPs provide a complete orthogonal basis able to represent generalized pupil functions (or complex wavefronts). This provides a unified general framework in contrast to the previous variety of ad oc solutions. Our results suggest that complex wavefronts require a higher number of CZP, but they seem especially well-suited for inhomogeneous beams, pupil apodization, etc.
X-ray wavefront characterization using a rotating shearing interferometer technique.
Wang, Hongchang; Sawhney, Kawal; Berujon, Sébastien; Ziegler, Eric; Rutishauser, Simon; David, Christian
2011-08-15
A fast and accurate method to characterize the X-ray wavefront by rotating one of the two gratings of an X-ray shearing interferometer is described and investigated step by step. Such a shearing interferometer consists of a phase grating mounted on a rotation stage, and an absorption grating used as a transmission mask. The mathematical relations for X-ray Moiré fringe analysis when using this device are derived and discussed in the context of the previous literature assumptions. X-ray beam wavefronts without and after X-ray reflective optical elements have been characterized at beamline B16 at Diamond Light Source (DLS) using the presented X-ray rotating shearing interferometer (RSI) technique. It has been demonstrated that this improved method allows accurate calculation of the wavefront radius of curvature and the wavefront distortion, even when one has no previous information on the grating projection pattern period, magnification ratio and the initial grating orientation. As the RSI technique does not require any a priori knowledge of the beam features, it is suitable for routine characterization of wavefronts of a wide range of radii of curvature.
Optimization design of an adaptive CFRC reflector for high order wave-front error control
Lan, Lan; Fang, Houfei; Wu, Ke; Jiang, Shuidong; Zhou, Yang
2017-04-01
The trend in future space high precision reflectors is going towards large aperture, lightweight and actively controlled deformable antennas. An adaptive shape control system for a Carbon Fiber Reinforced Composite (CFRC) reflector is conducted by Piezoelectric Ceramic Transducer (PZT) actuators. This adaptive shape control system has been shown to effectively mitigate common low order wave-front error, but it is inevitably plagued by high order wave-front error control. In order to improve the controllability of the adaptive CFRC reflector control system for high order wave-front error, the design of adaptive CFRC reflector requires optimizing further. According to numerical and experimental results, the print-through error induced by manufacturing and PZT actuators actuation is a type of predominant high order wave-front error. This paper describes a design which some secondary rib elements are embedded within the triangular cells of the primary ribs. These small secondary ribs are designed to support the reflector surface's weak region. Controllability of this new adaptive CFRC reflector control system with small secondary ribs is evaluated by generalized Zernike functions. This new design scheme can reduce high order residual error and suppress the high order wave-front error such as print-through error. Finally, design parameters of the adaptive CFRC reflector control system with small secondary ribs, such as primary rib height, secondary rib height, cut-out height of primary rib, are optimized.
X-ray wavefront characterization using a rotating shearing interferometer technique
Wang, Hongchang; Sawhney, Kawal; Berujon, Sébastien; Ziegler, Eric; Rutishauser, Simon; David, Christian
2011-08-01
A fast and accurate method to characterize the X-ray wavefront by rotating one of the two gratings of an X-ray shearing interferometer is described and investigated step by step. Such a shearing interferometer consists of a phase grating mounted on a rotation stage, and an absorption grating used as a transmission mask. The mathematical relations for X-ray Moiré fringe analysis when using this device are derived and discussed in the context of the previous literature assumptions. X-ray beam wavefronts without and after X-ray reflective optical elements have been characterized at beamline B16 at Diamond Light Source (DLS) using the presented X-ray rotating shearing interferometer (RSI) technique. It has been demonstrated that this improved method allows accurate calculation of the wavefront radius of curvature and the wavefront distortion, even when one has no previous information on the grating projection pattern period, magnification ratio and the initial grating orientation. As the RSI technique does not require any a priori knowledge of the beam features, it is suitable for routine characterization of wavefronts of a wide range of radii of curvature.
Wavefront alignment research of segmented mirror synthetic aperture optical (SAO) system
Deng, Jian; An, Xiaoqiang; Tian, Hao
2010-05-01
Wavefront control technology and imaging experiment are introduced for a segmented mirror SAO system with deformable sub-mirrors. This system is a RC style with 300mm aperture, 4.5 F#, +/-0.4°FOV, 0.45~0.75μm wave band, and diffraction-limit design MTF. The primary mirror is composed by three sub-mirrors, with parabolic shape, and each deformable sub-mirror has 19 actuators to control and keep the surface shape, and 5 actuators to align sub-mirrors location in 5 degree of freedom. Interferometer is used to feed back and control exit wavefront error, and base on measurement and finite element analysis, location and quanitity of actuators are optimized, making the surface shape and misadjustment errors interact and compensate each other, and the synthetic system exit pupil wavefront error is controlled. The integrated exit pupil wavefront errors are gotten by ZYGO interferometer, and central FOV is 0.077λRMS, and edge FOV is 0.093λRMS. At the end, an imaging experiment is executed, and good results are obtained, which proves, the deformable sub-mirrors have the ability to meliorate alignment and the latter can retroact the former, and this relationship iterate make system exit pupil wavefront error convergence and improve segmented mirror SAO system imaging ability.
Wakunami, K.; Oi, R.; Senoh, T.; Sasaki, H.; Ichihashi, Y.; Yamamoto, K.
2016-06-01
A hologram recording technique, generally called as "wavefront printer", has been proposed by several research groups for static three-dimensional (3D) image printing. Because the pixel number of current spatial light modulators (SLMs) is not enough to reconstruct the entire wavefront in recording process, typically, hologram data is divided into a set of subhologram data and each wavefront is recorded sequentially as a small sub-hologram cell in tiling manner by using X-Y motorized stage. However since previous works of wavefront printer do not optimize the cell size, the reconstructed images were degraded by obtrusive split line due to visible cell size caused by too large cell size for human eyesight, or by diffraction effect due to discontinuity of phase distribution caused by too small cell size. In this paper, we introduce overlapping recording approach of sub-holograms to achieve both conditions: enough smallness of apparent cell size to make cells invisible and enough largeness of recording cell size to suppress diffraction effect by keeping the phase continuity of reconstructed wavefront. By considering observing condition and optimization of the amount of overlapping and cell size, in the experiment, the proposed approach showed higher quality 3D image reconstruction while the conventional approach suffered visible split lines and cells.
Institute of Scientific and Technical Information of China (English)
HUANG Yueqin; ZHANG Jianzhong
2008-01-01
A kind of three-dimensional(3-D) sound ray tracing algorithm in heterogeneous media is studied. This algorithm includes two steps: the first step computes the wavefront traveltimes forward; the second step traces the sound rays backward. In the first step, the computation of wavefront traveltimes at discrete grid points from the sound source, was found on Eikonal equation solutions and carried out by GMM (Group marching method) wavefront marching method based on level set. In the second step, sound ray tracing was proceeded gradually from the receiver to each cell towards the sound source, with wavefront traveltimes computed in the first step. Time values on arbitrary positions in each cuboid cell can be expressed by linear interpolation of wavefront traveltimes at the same cell's grid points. Thus,an algorithm of 3-D sound ray tracing in heterogeneous media is put forward. The simulation results indicate that this method can improve both the accuracy and the efficiency of 3-D sound ray tracing greatly.
The wavefront of the radio signal emitted by cosmic ray air showers
Apel, W D; Bähren, L; Bekk, K; Bertaina, M; Biermann, P L; Blümer, J; Bozdog, H; Brancus, I M; Cantoni, E; Chiavassa, A; Daumiller, K; de Souza, V; Di Pierro, F; Doll, P; Engel, R; Falcke, H; Fuchs, B; Gemmeke, H; Grupen, C; Haungs, A; Heck, D; Hörandel, J R; Horneffer, A; Huber, D; Huege, T; Isar, P G; Kampert, K -H; Kang, D; Krömer, O; Kuijpers, J; Link, K; Luczak, P; Ludwig, M; Mathes, H J; Melissas, M; Morello, C; Oehlschläger, J; Palmieri, N; Pierog, T; Rautenberg, J; Rebel, H; Roth, M; Rühle, C; Saftoiu, A; Schieler, H; Schmidt, A; Schröder, F G; Sima, O; Toma, G; Trinchero, G C; Weindl, A; Wochele, J; Zabierowski, J; Zensus, J A
2014-01-01
Analyzing measurements of the LOPES antenna array together with corresponding CoREAS simulations for more than 300 measured events with energy above $10^{17}$eV and zenith angles smaller than $45^\\circ$, we find that the radio wavefront of cosmic-ray air showers is of hyperbolic shape. At axis distances $\\gtrsim 50$m, the wavefront can be approximated by a simple cone. According to the simulations, the cone angle is clearly correlated with the shower maximum. Thus, we confirm earlier predictions that arrival time measurements can be used to study the longitudinal shower development, but now using a realistic wavefront. Moreover, we show that the hyperbolic wavefront is compatible with our measurement, and we present several experimental indications that the cone angle is indeed sensitive to the shower development. Consequently, the wavefront can be used to statistically study the primary composition of ultra-high energy cosmic rays. At LOPES, the experimentally achieved precision for the shower maximum is lim...
N'Diaye, M.; Vigan, A.; Dohlen, K.; Sauvage, J.-F.; Caillat, A.; Costille, A.; Girard, J. H. V.; Beuzit, J.-L.; Fusco, T.; Blanchard, P.; Le Merrer, J.; Le Mignant, D.; Madec, F.; Moreaux, G.; Mouillet, D.; Puget, P.; Zins, G.
2016-07-01
The high-contrast imaging instruments VLT/SPHERE and GPI have been routinely observing gas giant planets, brown dwarfs, and debris disks around nearby stars since 2013-2014. In these facilities, low-wind effects or differential aberrations between the extreme Adaptive Optics sensing path and the science path represent critical limitations for the observation of exoplanets orbiting their host star with a contrast ratio larger than 106 at small separations. To circumvent this problem, we proposed ZELDA, a Zernike wavefront sensor to measure these quasistatic aberrations at a nanometric level. A prototype was installed on VLT/SPHERE during its integration in Chile. We recently performed measurements on an internal source with ZELDA in the presence of Zernike or Fourier modes introduced with the deformable mirror of the instrument. In this communication, we present the results of our experiment and report on the contrast gain obtained with a first ZELDA-based wavefront correction. We finally discuss the suitability of such a solution for a possible upgrade of VLT/SPHERE and for its use with future E-ELT instruments or space missions with high-contrast capabilities (e.g. WFIRST-AFTA, HDST).
Some stochastic aspects of quantization
Indian Academy of Sciences (India)
Ichiro Ohba
2002-08-01
From the advent of quantum mechanics, various types of stochastic-dynamical approach to quantum mechanics have been tried. We discuss how to utilize Nelson’s stochastic quantum mechanics to analyze the tunneling phenomena, how to derive relativistic ﬁeld equations via the Poisson process and how to describe a quantum dynamics of open systems by the use of quantum state diffusion, or the stochastic Schrödinger equation.
Stochastic Analysis of Cylindrical Shell
Directory of Open Access Journals (Sweden)
Grzywiński Maksym
2014-06-01
Full Text Available The paper deals with some chosen aspects of stochastic structural analysis and its application in the engineering practice. The main aim of the study is to apply the generalized stochastic perturbation techniques based on classical Taylor expansion with a single random variable for solution of stochastic problems in structural mechanics. The study is illustrated by numerical results concerning an industrial thin shell structure modeled as a 3-D structure.
Verification of Stochastic Process Calculi
DEFF Research Database (Denmark)
Skrypnyuk, Nataliya
Stochastic process calculi represent widely accepted formalisms within Computer Science for modelling nondeterministic stochastic systems in a compositional way. Similar to process calculi in general, they are suited for modelling systems in a hierarchical manner, by explicitly specifying...... subsystems as well as their interdependences and communication channels. Stochastic process calculi incorporate both the quantified uncertainty on probabilities or durations of events and nondeterministic choices between several possible continuations of the system behaviour. Modelling of a system is often...
Stochastic Nature in Cellular Processes
Institute of Scientific and Technical Information of China (English)
刘波; 刘圣君; 王祺; 晏世伟; 耿轶钊; SAKATA Fumihiko; GAO Xing-Fa
2011-01-01
The importance of stochasticity in cellular processes is increasingly recognized in both theoretical and experimental studies. General features of stochasticity in gene regulation and expression are briefly reviewed in this article, which include the main experimental phenomena, classification, quantization and regulation of noises. The correlation and transmission of noise in cascade networks are analyzed further and the stochastic simulation methods that can capture effects of intrinsic and extrinsic noise are described.
Mesoscopic Fluctuations in Stochastic Spacetime
Shiokawa, K
2000-01-01
Mesoscopic effects associated with wave propagation in spacetime with metric stochasticity are studied. We show that the scalar and spinor waves in a stochastic spacetime behave similarly to the electrons in a disordered system. Viewing this as the quantum transport problem, mesoscopic fluctuations in such a spacetime are discussed. The conductance and its fluctuations are expressed in terms of a nonlinear sigma model in the closed time path formalism. We show that the conductance fluctuations are universal, independent of the volume of the stochastic region and the amount of stochasticity.
A recurrent stochastic binary network
Institute of Scientific and Technical Information of China (English)
赵杰煜
2001-01-01
Stochastic neural networks are usually built by introducing random fluctuations into the network. A natural method is to use stochastic connections rather than stochastic activation functions. We propose a new model in which each neuron has very simple functionality but all the connections are stochastic. It is shown that the stationary distribution of the network uniquely exists and it is approximately a Boltzmann-Gibbs distribution. The relationship between the model and the Markov random field is discussed. New techniques to implement simulated annealing and Boltzmann learning are proposed. Simulation results on the graph bisection problem and image recognition show that the network is powerful enough to solve real world problems.
Wavefront depinning in semiconductor superlattices due to discrete-mapping failure
Institute of Scientific and Technical Information of China (English)
Wang Jun; Zheng Zhi-Gang
2008-01-01
We investigate the wavefronts depinning in current biased,infinitely long semiconductor superlattice systems by the method of discrete mapping and show that the wavefront depinning corresponds to the discrete mapping failure.For parameter values near the lower critical current in both discrete drift model (DD model) and discrete drift-diffusion model (DDD model),the mapping failure is determined by the important mapping step from the bottom of branch γ to branch α.For the upper critical parameters in DDD model,the key mapping step is from branch γ to the top of the corresponding branch α,and we may need several active wells to describe the wavefronts.
High contrast imaging of exoplanets on ELTs using a super-Nyquist wavefront control scheme
Gerard, Benjamin L
2016-01-01
One of the key science goals for extremely large telescopes (ELTs) is the detailed characterization of already known directly imaged exoplanets. The typical adaptive optics (AO) Nyquist control region for ELTs is ~0.4 arcseconds, placing many already known directly imaged planets outside the DM control region and not allowing any standard wavefront control scheme to remove speckles that would allow higher SNR images/spectra to be acquired. This can be fixed with super-Nyquist wavefront control (SNWFC), using a sine wave phase plate to allow for wavefront control outside the central DM Nyquist region. We demonstrate that SNWFC is feasible through a simple, deterministic, non-coronagraphic, super-Nyquist speckle nulling technique in the adaptive optics laboratory at the National Research Council of Canada. We also present results in simulation of how SNWFC using the self coherent camera (SCC) can be used for high contrast imaging. This technique could be implemented on future high contrast imaging instruments t...
On distributed wavefront reconstruction for large-scale adaptive optics systems.
de Visser, Cornelis C; Brunner, Elisabeth; Verhaegen, Michel
2016-05-01
The distributed-spline-based aberration reconstruction (D-SABRE) method is proposed for distributed wavefront reconstruction with applications to large-scale adaptive optics systems. D-SABRE decomposes the wavefront sensor domain into any number of partitions and solves a local wavefront reconstruction problem on each partition using multivariate splines. D-SABRE accuracy is within 1% of a global approach with a speedup that scales quadratically with the number of partitions. The D-SABRE is compared to the distributed cumulative reconstruction (CuRe-D) method in open-loop and closed-loop simulations using the YAO adaptive optics simulation tool. D-SABRE accuracy exceeds CuRe-D for low levels of decomposition, and D-SABRE proved to be more robust to variations in the loop gain.
Effect of the laser wavefront in a laser-plasma accelerator
Beaurepaire, B; Bocoum, M; Böhle, F; Jullien, A; Rousseau, J-P; Lefrou, T; Douillet, D; Iaquaniello, G; Lopez-Martens, R; Lifschitz, A; Faure, J
2015-01-01
A high repetition rate electron source was generated by tightly focusing kHz, few-mJ laser pulses into an underdense plasma. This high intensity laser-plasma interaction led to stable electron beams over several hours but with strikingly complex transverse distributions even for good quality laser focal spots. Analysis of the experimental data, along with results of PIC simulations demonstrate the role of the laser wavefront on the acceleration of electrons. Distortions of the laser wavefront cause spatial inhomogeneities in the out-of-focus laser distribution and consequently, the laser pulse drives an inhomogenous transverse wakefield whose focusing/defocusing properties affect the electron distribution. These findings explain the experimental results and suggest the possibility of controlling the electron spatial distribution in laser-plasma accelerators by tailoring the laser wavefront.
Bayesian inference for a wavefront model of the Neolithisation of Europe
Baggaley, Andrew W; Shukurov, Anvar; Boys, Richard J; Golightly, Andrew
2012-01-01
We consider a wavefront model for the spread of Neolithic culture across Europe, and use Bayesian inference techniques to provide estimates for the parameters within this model, as constrained by radiocarbon data from Southern and Western Europe. Our wavefront model allows for both an isotropic background spread (incorporating the effects of local geography), and a localized anisotropic spread associated with major waterways. We introduce an innovative numerical scheme to track the wavefront, allowing us to simulate the times of the first arrival at any site orders of magnitude more efficiently than traditional PDE approaches. We adopt a Bayesian approach to inference and use Gaussian process emulators to facilitate further increases in efficiency in the inference scheme, thereby making Markov chain Monte Carlo methods practical. We allow for uncertainty in the fit of our model, and also infer a parameter specifying the magnitude of this uncertainty. We obtain a magnitude for the background spread of order 1 ...
Energy Technology Data Exchange (ETDEWEB)
Poyneer, Lisa A; Bauman, Brian J
2015-03-31
Reference-free compensated imaging makes an estimation of the Fourier phase of a series of images of a target. The Fourier magnitude of the series of images is obtained by dividing the power spectral density of the series of images by an estimate of the power spectral density of atmospheric turbulence from a series of scene based wave front sensor (SBWFS) measurements of the target. A high-resolution image of the target is recovered from the Fourier phase and the Fourier magnitude.
Hinnen, K.; Verhaegen, M.; Doelman, N.
2005-01-01
Even though the wavefront distortion introduced by atmospheric turbulence is a dynamic process, its temporal evolution is usually neglected in the adaptive optics (AO) control design. Most AO control systems consider only the spatial correlation in a separate wavefront reconstruction step. By accoun
Hybrid iterative wavefront shaping for high-speed focusing through scattering media
Hemphill, Ashton S.; Wang, Lihong V.
2016-03-01
A major limiting factor of optical imaging in biological applications is the diffusion of light by tissue, preventing focusing at depths greater than ~1 mm in the body. To overcome this issue, phase-based wavefront shaping alters the phase of sections of the incident wavefront to counteract aberrations in phase caused by scattering. This enables focusing through scattering media beyond the optical diffusion limit and increases signal compared to amplitude-based compensation. However, in previous studies, speed of optimization has typically been limited by the use of a liquid crystal spatial light modulator (SLM) for measurement and display. SLMs usually have refresh rates of less than 100 Hz and require much longer than the speckle correlation time of tissue in vivo, usually on the order of milliseconds, to determine the optimal wavefront. Here, we present a phase-based iterative wavefront shaping method based on an onaxis digital micromirror device (DMD) in conjunction with an electro-optic modulator (EOM) for measurement and a fast SLM for display. By combining phase modulation from an EOM with the modal selection of the DMD, we take advantage of DMDs higher refresh rate, approximately 23 kHz, for iterative phase measurement. The slower SLM requires one update for display following the rapid determination of the optimal wavefront via the DMD, allowing for high-speed wavefront shaping. Using this system, we are able to focus through scattering media using 64 modes in under 8 milliseconds, on the order of the speckle correlation time for tissue in vivo.
Institute of Scientific and Technical Information of China (English)
Zhang Li
2009-01-01
This paper investigates the phenomenon of stochastic resonance in a single-mode laser driven by quadratic pump noise and amplitude-modulated signal.A new linear approximation approach is advanced to calculate the signal-to-noise ratio.In the linear approximation only the drift term is linearized,the multiplicative noise term is unchangeable.It is found that there appears not only the standard form of stochastic resonance but also the broad sense of stochastic resonance,especially stochastic multiresonance appears in the curve of signal-to-noise ratio as a function of coupling strength λ between the real and imaginary parts of the pump noise.
Stochastic Physicochemical Dynamics
Tsekov, R.
2001-02-01
Thermodynamic Relaxation in Quantum Systems: A new approach to quantum Markov processes is developed and the corresponding Fokker-Planck equation is derived. The latter is examined to reproduce known results from classical and quantum physics. It was also applied to the phase-space description of a mechanical system thus leading to a new treatment of this problem different from the Wigner presentation. The equilibrium probability density obtained in the mixed coordinate-momentum space is a reasonable extension of the Gibbs canonical distribution. The validity of the Einstein fluctuation-dissipation relation is discussed in respect to the type of relaxation in an isothermal system. The first model, presuming isothermic fluctuations, leads to the Einstein formula. The second model supposes adiabatic fluctuations and yields another relation between the diffusion coefficient and mobility of a Brownian particle. A new approach to relaxations in quantum systems is also proposed that demonstrates applicability only of the adiabatic model for description of the quantum Brownian dynamics. Stochastic Dynamics of Gas Molecules: A stochastic Langevin equation is derived, describing the thermal motion of a molecule immersed in a rested fluid of identical molecules. The fluctuation-dissipation theorem is proved and a number of correlation characteristics of the molecular Brownian motion are obtained. A short review of the classical theory of Brownian motion is presented. A new method is proposed for derivation of the Fokker-Planck equations, describing the probability density evolution, from stochastic differential equations. It is also proven via the central limit theorem that the white noise is only Gaussian. The applicability of stochastic differential equations to thermodynamics is considered and a new form, different from the classical Ito and Stratonovich forms, is introduced. It is shown that the new presentation is more appropriate for the description of thermodynamic
Portfolio Optimization with Stochastic Dividends and Stochastic Volatility
Varga, Katherine Yvonne
2015-01-01
We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…
Portfolio Optimization with Stochastic Dividends and Stochastic Volatility
Varga, Katherine Yvonne
2015-01-01
We consider an optimal investment-consumption portfolio optimization model in which an investor receives stochastic dividends. As a first problem, we allow the drift of stock price to be a bounded function. Next, we consider a stochastic volatility model. In each problem, we use the dynamic programming method to derive the Hamilton-Jacobi-Bellman…
Ali, M Syed; Rani, M Esther
2015-01-01
This paper investigates the problem of robust passivity of uncertain stochastic neural networks with time-varying delays and Markovian jumping parameters. To reflect most of the dynamical behaviors of the system, both parameter uncertainties and stochastic disturbances are considered; stochastic disturbances are given in the form of a Brownian motion. By utilizing the Lyapunov functional method, the Itô differential rule, and matrix analysis techniques, we establish a sufficient criterion such that, for all admissible parameter uncertainties and stochastic disturbances, the stochastic neural network is robustly passive in the sense of expectation. A delay-dependent stability condition is formulated, in which the restriction of the derivative of the time-varying delay should be less than 1 is removed. The derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical software. Illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results.
Koukourakis, Nektarios; Fregin, Bob; König, Jörg; Büttner, Lars; Czarske, Jürgen W
2016-09-19
Imaging-based flow measurement techniques, like particle image velocimetry (PIV), are vulnerable to time-varying distortions like refractive index inhomogeneities or fluctuating phase boundaries. Such distortions strongly increase the velocity error, as the position assignment of the tracer particles and the decrease of image contrast exhibit significant uncertainties. We demonstrate that wavefront shaping based on spatially distributed guide stars has the potential to significantly reduce the measurement uncertainty. Proof of concept experiments show an improvement by more than one order of magnitude. Possible applications for the wavefront shaping PIV range from measurements in jets and film flows to biomedical applications.
Transmitted wavefront error of a volume phase holographic grating at cryogenic temperature.
Lee, David; Taylor, Gordon D; Baillie, Thomas E C; Montgomery, David
2012-06-01
This paper describes the results of transmitted wavefront error (WFE) measurements on a volume phase holographic (VPH) grating operating at a temperature of 120 K. The VPH grating was mounted in a cryogenically compatible optical mount and tested in situ in a cryostat. The nominal root mean square (RMS) wavefront error at room temperature was 19 nm measured over a 50 mm diameter test aperture. The WFE remained at 18 nm RMS when the grating was cooled. This important result demonstrates that excellent WFE performance can be obtained with cooled VPH gratings, as required for use in future cryogenic infrared astronomical spectrometers planned for the European Extremely Large Telescope.
Wave propagation of the traffic flow dynamic model based on wavefront expansion
Institute of Scientific and Technical Information of China (English)
李莉; 施鹏飞
2004-01-01
This paper discusses propagation of perturbations along traffic flow modeled by a modified second-order macroscopic model through the wavefront expansion technique. The coefficients in this expansion satisfy a sequence of transport equations that can be solved analytically. One of these analytic solutions yields information about wavefront shock. Numerical simulations based on a Padé approximation of this expansion were done at the end of this paper and results showed that propagation of perturbations at traffic flow speed conforms to the theoretical analysis results.
High-precision system identification method for a deformable mirror in wavefront control.
Huang, Lei; Ma, Xingkun; Bian, Qi; Li, Tenghao; Zhou, Chenlu; Gong, Mali
2015-05-10
Based on a mathematic model, the relation between the accuracy of the influence matrix and the performance of the wavefront correction is established. Based on the least squares method, a two-step system identification is proposed to improve the accuracy of the influence matrix, where the measurement noise can be suppressed and the nonlinearity of the deformable mirror can be compensated. The validity of the two-step system identification method is tested in the experiment, where improvements in wavefront correction precision as well as closed-loop control efficiency were observed.
X-ray active mirror coupled with a Hartmann wavefront sensor
Energy Technology Data Exchange (ETDEWEB)
Idir, Mourad, E-mail: mourad.idir@synchrotron-soleil.f [Synchrotron SOLEIL, L' orme des Merisiers, BP 48, 91 192 Gif sur Yvette (France); Mercere, Pascal [Synchrotron SOLEIL, L' orme des Merisiers, BP 48, 91 192 Gif sur Yvette (France); Modi, Mohammed H. [X-ray Optics Section, Raja Ramanna Centre for Advanced Technology, Indore (India); Dovillaire, Guillaume; Levecq, Xavier; Bucourt, Samuel [Imagine Optic, 18 rue Charles de Gaulle, Orsay 91400 (France); Escolano, Lionel; Sauvageot, Paul [ISP System, ZI de la Herray BP 10047, Vic en Bigorre (France)
2010-05-01
This paper reports on the design and performances of a test prototype active X-ray mirror (AXM) which has been designed and manufactured in collaboration with the French Small and Medium Enterprise mechanical company ISP System for the national French storage ring SOLEIL. Coupled with this active X-ray mirror and also in collaboration with another French Small and Medium Enterprise (Imagine Optic) a lot of efforts have been done in order to design and fabricate a wavefront X-ray analyzer based on the Hartmann principle (Hartman wavefront sensor, HWS).
2D wave-front shaping in optical superlattices using nonlinear volume holography.
Yang, Bo; Hong, Xu-Hao; Lu, Rong-Er; Yue, Yang-Yang; Zhang, Chao; Qin, Yi-Qiang; Zhu, Yong-Yuan
2016-07-01
Nonlinear volume holography is employed to realize arbitrary wave-front shaping during nonlinear processes with properly designed 2D optical superlattices. The concept of a nonlinear polarization wave in nonlinear volume holography is investigated. The holographic imaging of irregular patterns was performed using 2D LiTaO3 crystals with fundamental wave propagating along the spontaneous polarization direction, and the results agree well with the theoretical predictions. This Letter not only extends the application area of optical superlattices, but also offers an efficient method for wave-front shaping technology.
110 °C range athermalization of wavefront coding infrared imaging systems
Feng, Bin; Shi, Zelin; Chang, Zheng; Liu, Haizheng; Zhao, Yaohong
2017-09-01
110 °C range athermalization is significant but difficult for designing infrared imaging systems. Our wavefront coding athermalized infrared imaging system adopts an optical phase mask with less manufacturing errors and a decoding method based on shrinkage function. The qualitative experiments prove that our wavefront coding athermalized infrared imaging system has three prominent merits: (1) working well over a temperature range of 110 °C; (2) extending the focal depth up to 15.2 times; (3) achieving a decoded image being approximate to its corresponding in-focus infrared image, with a mean structural similarity index (MSSIM) value greater than 0.85.
Directory of Open Access Journals (Sweden)
Shuang Li
2015-06-01
Full Text Available This article concerns the existence of traveling wavefronts for a nonlocal diffusive predator-prey system with functional response of Holling type II. We first establish the existence principle for the system with a general functional response by using a fixed point theorem and upper-lower solution technique. We apply this result to a predator-prey model with Holling type II functional response. We deduce the existence of traveling wavefronts that connect the zero equilibrium and the positive equilibrium.
Geometry and dynamics of fast magnetosonic wavefronts near magnetic null points
Núñez, Manuel
2017-02-01
The behavior of two-dimensional fast magnetosonic waves in the vicinity of isolated points where the magnetic field vanishes is studied analytically. The geometry of rays and wavefronts is described, and the curvature of both is found using conformal mapping techniques. These results are applied to the formation of shock waves, obtaining that shock formation is guaranteed at a finite time for any initial condition of the perturbation when the wavefront is concave and the rays tend to focus, whereas otherwise shocks occur only for a certain range of initial conditions.
Occlusion culling for computer generated hologram based on ray-wavefront conversion.
Wakunami, Koki; Yamashita, Hiroaki; Yamaguchi, Masahiro
2013-09-23
We propose a new method for occlusion culling in the computation of a hologram based on the mutual conversion between light-rays and wavefront. Since the occlusion culling is performed with light-ray information, conventional rendering techniques such as ray-tracing or image-based rendering can be employed. On the other hand, the wavefront is derived for the calculation of light propagation, the hologram of 3-D objects can be obtained in high accuracy. In the numerical experiment, we demonstrate that our approach can reproduce a high-resolution image for deep 3-D scene with correct occlusion effect between plural objects.
Leszczyński, Adam
2015-01-01
We present a method to calibrate wavefront distortion of the spatial light modulator setup by registering far field images of several gaussian beams diffracted off the modulator. The Fourier transform of resulting interference images reveals phase differences between typically 5 movable points on the modulator. Repeating this measurement yields wavefront surface. Next, the amplitude efficiency is calibrated be registering near field image. As a verification we produced a superposition of 7th and 8th Bessel beams with different phase velocities and observed their interference.
Leszczyński, Adam; Wasilewski, Wojciech
2016-04-01
We present a method to calibrate wavefront distortion of the spatial light modulator setup by registering far-field images of several Gaussian beams diffracted off the modulator. The Fourier transform of resulting interference images reveals phase differences among typically five movable points on the modulator. Repeating this measurement yields a wavefront surface. Next, the amplitude efficiency is calibrated for registering the near-field image. For verification, we produced a superposition of seventh and eighth Bessel beams with different phase velocities and observed their interference.
Stochastic ontogenetic growth model
West, B. J.; West, D.
2012-02-01
An ontogenetic growth model (OGM) for a thermodynamically closed system is generalized to satisfy both the first and second law of thermodynamics. The hypothesized stochastic ontogenetic growth model (SOGM) is shown to entail the interspecies allometry relation by explicitly averaging the basal metabolic rate and the total body mass over the steady-state probability density for the total body mass (TBM). This is the first derivation of the interspecies metabolic allometric relation from a dynamical model and the asymptotic steady-state distribution of the TBM is fit to data and shown to be inverse power law.
Deduction as Stochastic Simulation
2013-07-01
Eab Oa b Eab Ob a Iab Aab Iab Aba Iab Eab Iab EbaIab Iab Iab Iba Iab Oa b Iab Ob a Oa bAa b Oa bAb a Oa bEa b Oa bEb a Oa bIa b Oa bIb a Oa bO ab Oa bO...Oa bIa b Oa bIb a Oa bO ab Oa bO ba % C or re ct A. B. stochastic system’s parameters could be tweaked for individual reasoners. For example, the λ
Carpentier, Pierre; Cohen, Guy; De Lara, Michel
2015-01-01
The focus of the present volume is stochastic optimization of dynamical systems in discrete time where - by concentrating on the role of information regarding optimization problems - it discusses the related discretization issues. There is a growing need to tackle uncertainty in applications of optimization. For example the massive introduction of renewable energies in power systems challenges traditional ways to manage them. This book lays out basic and advanced tools to handle and numerically solve such problems and thereby is building a bridge between Stochastic Programming and Stochastic Control. It is intended for graduates readers and scholars in optimization or stochastic control, as well as engineers with a background in applied mathematics.
An Averaging Principle for Stochastic Differential Delay Equations with Fractional Brownian Motion
Directory of Open Access Journals (Sweden)
Yong Xu
2014-01-01
Full Text Available An averaging principle for a class of stochastic differential delay equations (SDDEs driven by fractional Brownian motion (fBm with Hurst parameter in (1/2,1 is considered, where stochastic integration is convolved as the path integrals. The solutions to the original SDDEs can be approximated by solutions to the corresponding averaged SDDEs in the sense of both convergence in mean square and in probability, respectively. Two examples are carried out to illustrate the proposed averaging principle.
Biometric iris image acquisition system with wavefront coding technology
Hsieh, Sheng-Hsun; Yang, Hsi-Wen; Huang, Shao-Hung; Li, Yung-Hui; Tien, Chung-Hao
2013-09-01
Biometric signatures for identity recognition have been practiced for centuries. Basically, the personal attributes used for a biometric identification system can be classified into two areas: one is based on physiological attributes, such as DNA, facial features, retinal vasculature, fingerprint, hand geometry, iris texture and so on; the other scenario is dependent on the individual behavioral attributes, such as signature, keystroke, voice and gait style. Among these features, iris recognition is one of the most attractive approaches due to its nature of randomness, texture stability over a life time, high entropy density and non-invasive acquisition. While the performance of iris recognition on high quality image is well investigated, not too many studies addressed that how iris recognition performs subject to non-ideal image data, especially when the data is acquired in challenging conditions, such as long working distance, dynamical movement of subjects, uncontrolled illumination conditions and so on. There are three main contributions in this paper. Firstly, the optical system parameters, such as magnification and field of view, was optimally designed through the first-order optics. Secondly, the irradiance constraints was derived by optical conservation theorem. Through the relationship between the subject and the detector, we could estimate the limitation of working distance when the camera lens and CCD sensor were known. The working distance is set to 3m in our system with pupil diameter 86mm and CCD irradiance 0.3mW/cm2. Finally, We employed a hybrid scheme combining eye tracking with pan and tilt system, wavefront coding technology, filter optimization and post signal recognition to implement a robust iris recognition system in dynamic operation. The blurred image was restored to ensure recognition accuracy over 3m working distance with 400mm focal length and aperture F/6.3 optics. The simulation result as well as experiment validates the proposed code
Servin, Manuel
2012-01-01
This paper presents a digital interferometric method to demodulate Placido fringe patterns. This method uses a computer-stored conic-wavefront as reference carrier. Even though, Placido mires are widely used in corneal topographers. This is not however a paper on corneal topography and/or its clinical use. This paper focuses on the theoretical aspects to phase-demodulate Placido mires using synchronous interferometric techniques. Placido patterns may also be applied to test optical wavefronts using a Placido-Hartmann opaque plate with periodic annular apertures. This test is sensitive to the radial slope of the measuring wavefront. Another wavefront testing approach may use a Placido-Hartmann-Shack screen with a periodic array of toroidal lenslets. This periodic screen is sensitive to the wavefront's radial-slope at the focal plane of the lenslets. In brief, digital interferometric methods are herein applied for the first time to demodulate conic-carrier Placido images. Finally it should be mentioned that thi...
Baranec, Christoph; Dekany, Richard
2008-10-01
We introduce a Shack-Hartmann wavefront sensor for adaptive optics that enables dynamic control of the spatial sampling of an incoming wavefront using a segmented mirror microelectrical mechanical systems (MEMS) device. Unlike a conventional lenslet array, subapertures are defined by either segments or groups of segments of a mirror array, with the ability to change spatial pupil sampling arbitrarily by redefining the segment grouping. Control over the spatial sampling of the wavefront allows for the minimization of wavefront reconstruction error for different intensities of guide source and different atmospheric conditions, which in turn maximizes an adaptive optics system's delivered Strehl ratio. Requirements for the MEMS devices needed in this Shack-Hartmann wavefront sensor are also presented.
Stochastic Runge-Kutta Software Package for Stochastic Differential Equations
Gevorkyan, M N; Korolkova, A V; Kulyabov, D S; Sevastyanov, L A
2016-01-01
As a result of the application of a technique of multistep processes stochastic models construction the range of models, implemented as a self-consistent differential equations, was obtained. These are partial differential equations (master equation, the Fokker--Planck equation) and stochastic differential equations (Langevin equation). However, analytical methods do not always allow to research these equations adequately. It is proposed to use the combined analytical and numerical approach studying these equations. For this purpose the numerical part is realized within the framework of symbolic computation. It is recommended to apply stochastic Runge--Kutta methods for numerical study of stochastic differential equations in the form of the Langevin. Under this approach, a program complex on the basis of analytical calculations metasystem Sage is developed. For model verification logarithmic walks and Black--Scholes two-dimensional model are used. To illustrate the stochastic "predator--prey" type model is us...
Wavefront Control for Space Telescope Applications Using Adaptive Optics
2007-12-01
science and chemistry . Although many of the principles behind adaptive optics have been understood for quite some time it hasn’t been until recent... SIMULINK and DSPACE by applying a voltage between +/-5 volts. Figure 11 Baker One Inch Fast Steering Mirror 16 E. POSITION SENSING MODULE
Stochasticity in numerical solutions of the nonlinear Schroedinger equation
Shen, Mei-Mei; Nicholson, D. R.
1987-01-01
The cubically nonlinear Schroedinger equation is an important model of nonlinear phenomena in fluids and plasmas. Numerical solutions in a spatially periodic system commonly involve truncation to a finite number of Fourier modes. These solutions are found to be stochastic in the sense that the largest Liapunov exponent is positive. As the number of modes is increased, the size of this exponent appears to converge to zero, in agreement with the recent demonstration of the integrability of the spatially periodic case.
Mixed effects in stochastic differential equation models
DEFF Research Database (Denmark)
Ditlevsen, Susanne; De Gaetano, Andrea
2005-01-01
maximum likelihood; pharmacokinetics; population estimates; random effects; repeated measurements; stochastic processes......maximum likelihood; pharmacokinetics; population estimates; random effects; repeated measurements; stochastic processes...
Optically levitated nanoparticle as a model system for stochastic bistable dynamics
Ricci, F.; Rica, R. A.; Spasenović, M.; Gieseler, J.; Rondin, L.; Novotny, L.; Quidant, R.
2017-05-01
Nano-mechanical resonators have gained an increasing importance in nanotechnology owing to their contributions to both fundamental and applied science. Yet, their small dimensions and mass raises some challenges as their dynamics gets dominated by nonlinearities that degrade their performance, for instance in sensing applications. Here, we report on the precise control of the nonlinear and stochastic bistable dynamics of a levitated nanoparticle in high vacuum. We demonstrate how it can lead to efficient signal amplification schemes, including stochastic resonance. This work contributes to showing the use of levitated nanoparticles as a model system for stochastic bistable dynamics, with applications to a wide variety of fields.
Optimal Filtering Algorithm for Stochastic 2-D FMM Ⅱ with Multiplicative Noise
Institute of Scientific and Technical Information of China (English)
CHU Dongsheng; LIANG Meng; SHI Xin; ZHANG Ling
2004-01-01
A stochastic two-dimensional Fornasini-Marchesini's Model Ⅱ (2-D FMM Ⅱ) with multiplicative noise is given,and a filtering algorithm for this model, which is optimal in the sense of linear minimum-variance, is developed. The stochastic 2-D FMM Ⅱ with multiplicative noise can be reduced to a 1-D model, and the proposed optimal filtering algorithm for the stochastic 2-D FMM Ⅱ with multiplicative noise is obtained by using the state estimation theory of 1-D systems. An example is given to illustrate the validity of this algorithm.
Stochastic Pi-calculus Revisited
DEFF Research Database (Denmark)
Cardelli, Luca; Mardare, Radu Iulian
2013-01-01
We develop a version of stochastic Pi-calculus with a semantics based on measure theory. We dene the behaviour of a process in a rate environment using measures over the measurable space of processes induced by structural congruence. We extend the stochastic bisimulation to include the concept of...
Stochastic ferromagnetism analysis and numerics
Brzezniak, Zdzislaw; Neklyudov, Mikhail; Prohl, Andreas
2013-01-01
This monograph examines magnetization dynamics at elevated temperatures which can be described by the stochastic Landau-Lifshitz-Gilbert equation (SLLG). Comparative computational studies with the stochastic model are included. Constructive tools such as e.g. finite element methods are used to derive the theoretical results, which are then used for computational studies.
Discretization error of Stochastic Integrals
Fukasawa, Masaaki
2010-01-01
Asymptotic error distribution for approximation of a stochastic integral with respect to continuous semimartingale by Riemann sum with general stochastic partition is studied. Effective discretization schemes of which asymptotic conditional mean-squared error attains a lower bound are constructed. Two applications are given; efficient delta hedging strategies with transaction costs and effective discretization schemes for the Euler-Maruyama approximation are constructed.
Stochastic Pi-calculus Revisited
DEFF Research Database (Denmark)
Cardelli, Luca; Mardare, Radu Iulian
2013-01-01
We develop a version of stochastic Pi-calculus with a semantics based on measure theory. We dene the behaviour of a process in a rate environment using measures over the measurable space of processes induced by structural congruence. We extend the stochastic bisimulation to include the concept of...
Stochastic power flow modeling
Energy Technology Data Exchange (ETDEWEB)
1980-06-01
The stochastic nature of customer demand and equipment failure on large interconnected electric power networks has produced a keen interest in the accurate modeling and analysis of the effects of probabilistic behavior on steady state power system operation. The principle avenue of approach has been to obtain a solution to the steady state network flow equations which adhere both to Kirchhoff's Laws and probabilistic laws, using either combinatorial or functional approximation techniques. Clearly the need of the present is to develop sound techniques for producing meaningful data to serve as input. This research has addressed this end and serves to bridge the gap between electric demand modeling, equipment failure analysis, etc., and the area of algorithm development. Therefore, the scope of this work lies squarely on developing an efficient means of producing sensible input information in the form of probability distributions for the many types of solution algorithms that have been developed. Two major areas of development are described in detail: a decomposition of stochastic processes which gives hope of stationarity, ergodicity, and perhaps even normality; and a powerful surrogate probability approach using proportions of time which allows the calculation of joint events from one dimensional probability spaces.
AA, stochastic precooling pickup
1980-01-01
The freshly injected antiprotons were subjected to fast stochastic "precooling". In this picture of a precooling pickup, the injection orbit is to the left, the stack orbit to the far right. After several seconds of precooling with the system's kickers (in momentum and in the vertical plane), the precooled antiprotons were transferred, by means of RF, to the stack tail, where they were subjected to further stochastic cooling in momentum and in both transverse planes, until they ended up, deeply cooled, in the stack core. During precooling, a shutter near the central orbit shielded the pickups from the signals emanating from the stack-core, whilst the stack-core was shielded from the violent action of the precooling kickers by a shutter on these. All shutters were opened briefly during transfer of the precooled antiprotons to the stack tail. Here, the shutter is not yet mounted. Precooling pickups and kickers had the same design, except that the kickers had cooling circuits and the pickups had none. Peering th...
Stochastic Blind Motion Deblurring
Xiao, Lei
2015-05-13
Blind motion deblurring from a single image is a highly under-constrained problem with many degenerate solutions. A good approximation of the intrinsic image can therefore only be obtained with the help of prior information in the form of (often non-convex) regularization terms for both the intrinsic image and the kernel. While the best choice of image priors is still a topic of ongoing investigation, this research is made more complicated by the fact that historically each new prior requires the development of a custom optimization method. In this paper, we develop a stochastic optimization method for blind deconvolution. Since this stochastic solver does not require the explicit computation of the gradient of the objective function and uses only efficient local evaluation of the objective, new priors can be implemented and tested very quickly. We demonstrate that this framework, in combination with different image priors produces results with PSNR values that match or exceed the results obtained by much more complex state-of-the-art blind motion deblurring algorithms.
Schilstra, Maria J; Martin, Stephen R
2009-01-01
Stochastic simulations may be used to describe changes with time of a reaction system in a way that explicitly accounts for the fact that molecules show a significant degree of randomness in their dynamic behavior. The stochastic approach is almost invariably used when small numbers of molecules or molecular assemblies are involved because this randomness leads to significant deviations from the predictions of the conventional deterministic (or continuous) approach to the simulation of biochemical kinetics. Advances in computational methods over the three decades that have elapsed since the publication of Daniel Gillespie's seminal paper in 1977 (J. Phys. Chem. 81, 2340-2361) have allowed researchers to produce highly sophisticated models of complex biological systems. However, these models are frequently highly specific for the particular application and their description often involves mathematical treatments inaccessible to the nonspecialist. For anyone completely new to the field to apply such techniques in their own work might seem at first sight to be a rather intimidating prospect. However, the fundamental principles underlying the approach are in essence rather simple, and the aim of this article is to provide an entry point to the field for a newcomer. It focuses mainly on these general principles, both kinetic and computational, which tend to be not particularly well covered in specialist literature, and shows that interesting information may even be obtained using very simple operations in a conventional spreadsheet.
Variance decomposition in stochastic simulators
Le Maître, O. P.
2015-06-28
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Variance decomposition in stochastic simulators.
Le Maître, O P; Knio, O M; Moraes, A
2015-06-28
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Variance decomposition in stochastic simulators
Le Maître, O. P.; Knio, O. M.; Moraes, A.
2015-06-01
This work aims at the development of a mathematical and computational approach that enables quantification of the inherent sources of stochasticity and of the corresponding sensitivities in stochastic simulations of chemical reaction networks. The approach is based on reformulating the system dynamics as being generated by independent standardized Poisson processes. This reformulation affords a straightforward identification of individual realizations for the stochastic dynamics of each reaction channel, and consequently a quantitative characterization of the inherent sources of stochasticity in the system. By relying on the Sobol-Hoeffding decomposition, the reformulation enables us to perform an orthogonal decomposition of the solution variance. Thus, by judiciously exploiting the inherent stochasticity of the system, one is able to quantify the variance-based sensitivities associated with individual reaction channels, as well as the importance of channel interactions. Implementation of the algorithms is illustrated in light of simulations of simplified systems, including the birth-death, Schlögl, and Michaelis-Menten models.
Brownian motion and stochastic calculus
Karatzas, Ioannis
1998-01-01
This book is designed as a text for graduate courses in stochastic processes. It is written for readers familiar with measure-theoretic probability and discrete-time processes who wish to explore stochastic processes in continuous time. The vehicle chosen for this exposition is Brownian motion, which is presented as the canonical example of both a martingale and a Markov process with continuous paths. In this context, the theory of stochastic integration and stochastic calculus is developed. The power of this calculus is illustrated by results concerning representations of martingales and change of measure on Wiener space, and these in turn permit a presentation of recent advances in financial economics (option pricing and consumption/investment optimization). This book contains a detailed discussion of weak and strong solutions of stochastic differential equations and a study of local time for semimartingales, with special emphasis on the theory of Brownian local time. The text is complemented by a large num...
Computing gap free Pareto front approximations with stochastic search algorithms.
Schütze, Oliver; Laumanns, Marco; Tantar, Emilia; Coello, Carlos A Coello; Talbi, El-Ghazali
2010-01-01
Recently, a convergence proof of stochastic search algorithms toward finite size Pareto set approximations of continuous multi-objective optimization problems has been given. The focus was on obtaining a finite approximation that captures the entire solution set in some suitable sense, which was defined by the concept of epsilon-dominance. Though bounds on the quality of the limit approximation-which are entirely determined by the archiving strategy and the value of epsilon-have been obtained, the strategies do not guarantee to obtain a gap free approximation of the Pareto front. That is, such approximations A can reveal gaps in the sense that points f in the Pareto front can exist such that the distance of f to any image point F(a), a epsilon A, is "large." Since such gap free approximations are desirable in certain applications, and the related archiving strategies can be advantageous when memetic strategies are included in the search process, we are aiming in this work for such methods. We present two novel strategies that accomplish this task in the probabilistic sense and under mild assumptions on the stochastic search algorithm. In addition to the convergence proofs, we give some numerical results to visualize the behavior of the different archiving strategies. Finally, we demonstrate the potential for a possible hybridization of a given stochastic search algorithm with a particular local search strategy-multi-objective continuation methods-by showing that the concept of epsilon-dominance can be integrated into this approach in a suitable way.
Paul, B; Mugnier, L M; Sauvage, J-F; Dohlen, K; Ferrari, M
2013-12-30
The estimation and compensation of quasi-static aberrations is mandatory to reach the ultimate performance of high-contrast imaging systems. COFFEE is a focal plane wave-front sensing method that consists in the extension of phase diversity to high-contrast imaging systems. Based on a Bayesian approach, it estimates the quasi-static aberrations from two focal plane images recorded from the scientific camera itself. In this paper, we present COFFEE's extension which allows an estimation of low and high order aberrations with nanometric precision for any coronagraphic device. The performance is evaluated by realistic simulations, performed in the SPHERE instrument framework. We develop a myopic estimation that allows us to take into account an imperfect knowledge on the used diversity phase. Lastly, we evaluate COFFEE's performance in a compensation process, to optimize the contrast on the detector, and show it allows one to reach the 10(-6) contrast required by SPHERE at a few resolution elements from the star. Notably, we present a non-linear energy minimization method which can be used to reach very high contrast levels (better than 10(7) in a SPHERE-like context).
Stochastic switching in biology: from genotype to phenotype
Bressloff, Paul C.
2017-03-01
There has been a resurgence of interest in non-equilibrium stochastic processes in recent years, driven in part by the observation that the number of molecules (genes, mRNA, proteins) involved in gene expression are often of order 1-1000. This means that deterministic mass-action kinetics tends to break down, and one needs to take into account the discrete, stochastic nature of biochemical reactions. One of the major consequences of molecular noise is the occurrence of stochastic biological switching at both the genotypic and phenotypic levels. For example, individual gene regulatory networks can switch between graded and binary responses, exhibit translational/transcriptional bursting, and support metastability (noise-induced switching between states that are stable in the deterministic limit). If random switching persists at the phenotypic level then this can confer certain advantages to cell populations growing in a changing environment, as exemplified by bacterial persistence in response to antibiotics. Gene expression at the single-cell level can also be regulated by changes in cell density at the population level, a process known as quorum sensing. In contrast to noise-driven phenotypic switching, the switching mechanism in quorum sensing is stimulus-driven and thus noise tends to have a detrimental effect. A common approach to modeling stochastic gene expression is to assume a large but finite system and to approximate the discrete processes by continuous processes using a system-size expansion. However, there is a growing need to have some familiarity with the theory of stochastic processes that goes beyond the standard topics of chemical master equations, the system-size expansion, Langevin equations and the Fokker-Planck equation. Examples include stochastic hybrid systems (piecewise deterministic Markov processes), large deviations and the Wentzel-Kramers-Brillouin (WKB) method, adiabatic reductions, and queuing/renewal theory. The major aim of this
Davies, Ian M.; Truman, Aubrey; Zhao, Huaizhong
2005-04-01
We study the inviscid limit, μ →0, of the stochastic viscous Burgers equation, for the velocity field vμ(x,t), t >0, x εRd, (∂vμ/∂t)+(vμ.∇)vμ=-∇c(x,t)-ε∇k(x,t)Ẇt+(μ2/2)Δvμ, for small ε, with vμ(x,0)≡∇S0(x) for some given S0, Ẇt representing white noise. Here we use the Hopf-Cole transformation, vμ=-μ2∇lnuμ, where uμ satisfies the stochastic heat equation of Stratonovich-type and the Feynmac-Kac Truman-Zhao formula for uμ, where dutμ(x )=[(μ2/2)Δutμ(x)+μ-2c(x,t)utμ(x)]dt+εμ-2k(x,t)utμ(x)∘dWt, with u0μ(x)=T0(x)exp(-S0(x)/μ2), S0 as before and T0 a smooth positive function. In an earlier paper, Davies, Truman, and Zhao [J. Math. Phys. 43, 3293 (2002)], an exact solution of the stochastic viscous Burgers equation was used to show how the formal "blow-up" of the Burgers velocity field occurs on random shockwaves for the vμ =0 solution of Burgers equation coinciding with the caustics of a corresponding Hamiltonian system with classical flow map Φ. Moreover, the uμ =0 solution of the stochastic heat equation has its wavefront determined by the behavior of the Hamilton principal function of the corresponding stochastic mechanics. This led in particular to the level surface of the minimizing Hamilton-Jacobi function developing cusps at points corresponding to points of intersection of the corresponding prelevel surface with the precaustic, "pre" denoting the preimage under Φ determined algebraically. These results were primarily of a geometrical nature. In this paper we consider small ε and derive the shape of the random shockwave for the inviscid limit of the stochastic Burgers velocity field and also give the equation determining the random wavefront for the stochastic heat equation both correct to first order in ε. In the case c (x,t)=1/2xTΩ2x, ∇k(x,t)=-a(t), we obtain the exact random shockwave and prove that its shape is unchanged by the addition of noise, it merely being displaced by a random Brownian vector
High-resolution wavefront shaping with a photonic crystal fiber for multimode fiber imaging
Amitonova, L. V.; Descloux, A.; Petschulat, J.; Frosz, M. H.; Ahmed, G.; Babic, F.; Jiang, X.; Mosk, A. P.; Russell, P. S. J.; Pinkse, P.W.H.
2016-01-01
We demonstrate that a high-numerical-aperture photonic crystal fiber allows lensless focusing at an unparalleled res- olution by complex wavefront shaping. This paves the way toward high-resolution imaging exceeding the capabilities of imaging with multi-core single-mode optical fibers. We analyze t
Koek, W.D.; Zwet, E.J. van
2015-01-01
When using a commonly-used quadri-wave lateral shearing interferometer wavefront sensor (QWLSI WFS) for beam size measurements on a high power CO2 laser, artefacts have been observed in the measured irradiance distribution. The grating in the QWLSI WFS not only generates the diffracted first orders
Spatial-frequency analysis algorithm for in-situ measurement of wavefront
Liu, Qian; Wang, Yang; Ji, Fang; He, Jianguo
2015-05-01
To apply phase-shifting interferometry (PSI) to in-situ measurement, we have proposed an algorithm to detect and suppress phase-shifting error and contrast fluctuation. The phase shift and contrast are analyzed in spatial-frequency domain. The strength of baseband and sideband implies the pattern contrast. The position and phase angle of the sideband indicates the tilt gradients and translational value of phase shift. Thus, the phase shift error and contrast fluctuation could be extracted. A contrast-compensated equation is established to calculate the wavefront phase. The proposed algorithm was applied to the interferograms subjecting to vibration and wavefront phase was calculated. The experimental results show that, under vibration of one micron amplitude and 60Hz frequency, the error of wavefront PV value is less than 0.01wave and the 2σ repeatability is less than 0.01wave. For no hardware is required, the proposed algorithm provides a cost-effective method for wavefront in-situ measurement with PSI.
2011-03-01
during our journey through the rigorous AFIT curriculum . Last, but not least, I would like to thank my wife who sacrificed as much as I did to assure...54 36. Transverse magnification...The optical field of the wavefront is typically represented as a complex number in the plane transverse to propagation with amplitude A and a phase
Characterization of wavefront errors in mouse cranial bone using second-harmonic generation
Tehrani, Kayvan Forouhesh; Kner, Peter; Mortensen, Luke J.
2017-03-01
Optical aberrations significantly affect the resolution and signal-to-noise ratio of deep tissue microscopy. As multiphoton microscopy is applied deeper into tissue, the loss of resolution and signal due to propagation of light in a medium with heterogeneous refractive index becomes more serious. Efforts in imaging through the intact skull of mice cannot typically reach past the bone marrow (˜150 μm of depth) and have limited resolution and penetration depth. Mechanical bone thinning or optical ablation of bone enables deeper imaging, but these methods are highly invasive and may impact tissue biology. Adaptive optics is a promising noninvasive alternative for restoring optical resolution. We characterize the aberrations present in bone using second-harmonic generation imaging of collagen. We simulate light propagation through highly scattering bone and evaluate the effect of aberrations on the point spread function. We then calculate the wavefront and expand it in Zernike orthogonal polynomials to determine the strength of different optical aberrations. We further compare the corrected wavefront and the residual wavefront error, and suggest a correction element with high number of elements or multiconjugate wavefront correction for this highly scattering environment.
Novel method of high-accuracy wavefront-phase and amplitude correction for coronagraphy
Bowers, Charles W.; Woodgate, Bruce E.; Lyon, Richard G.
2003-11-01
Detection of extra-solar, and especially terrestrial-like planets, using coronagraphy requires an extremely high level of wavefront correction. For example, the study of Woodruff et al. (2002) has shown that phase uniformity of order 10-4λ(rms) must be achieved over the critical range of spatial frequencies to produce the ~1010 contrast needed for the Terrestrial Planet Finder (TPF) mission. Correction of wavefront phase errors to this level may be accomplished by using a very high precision deformable mirror (DM). However, not only phase but also amplitude uniformity of the same scale (~10-4) and over the same spatial frequency range must be simultaneously obtained to remove all residual speckle in the image plane. We present a design for producing simultaneous wavefront phase and amplitude uniformity to high levels from an input wavefront of lower quality. The design uses a dual Michelson interferometer arrangement incorporating two DM and a single, fixed mirror (all at pupils) and two beamsplitters: one with unequal (asymmetric) beam splitting and one with symmetric beam splitting. This design allows high precision correction of both phase and amplitude using DM with relatively coarse steps and permits a simple correction algorithm.
Koek, W.D.; Zwet, E.J. van
2015-01-01
When using a commonly-used quadri-wave lateral shearing interferometer wavefront sensor (QWLSI WFS) for beam size measurements on a high power CO2 laser, artefacts have been observed in the measured irradiance distribution. The grating in the QWLSI WFS not only generates the diffracted first orders
Calibrating a high-Esolution wavefront corrector with a static focal-Plane camera
Korkiakoski, V.; Doelman, N.J.; Codona, J.; Kenworthy, M.; Otten, G.; Keller, C.U.
2013-01-01
We present a method to calibrate a high-resolution wavefront (WF)-correcting device with a single, static camera, located in the focal-plane; no moving of any component is needed. The method is based on a localized diversity and differential optical transfer functions to compute both the phase and a
Tool to estimate optical metrics from summary wave-front analysis data in the human eye
Jansonius, Nomdo M.
2013-01-01
Purpose Studies in the field of cataract and refractive surgery often report only summary wave-front analysis data data that are too condensed to allow for a retrospective calculation of metrics relevant to visual perception. The aim of this study was to develop a tool that can be used to estimate t
Two-Sided Pyramid Wavefront Sensor in the Direct Phase Mode
Energy Technology Data Exchange (ETDEWEB)
Phillion, D; Baker, K
2006-04-12
The two-sided pyramid wavefront sensor has been extensively simulated in the direct phase mode using a wave optics code. The two-sided pyramid divides the focal plane so that each half of the core only interferes with the speckles in its half of the focal plane. A relayed image of the pupil plane is formed at the CCD camera for each half. Antipodal speckle pairs are separated so that a pure phase variation causes amplitude variations in the two images. The phase is reconstructed from the difference of the two amplitudes by transforming cosine waves into sine waves using the Hilbert transform. There are also other corrections which have to be applied in Fourier space. The two-sided pyramid wavefront sensor performs extremely well: After two or three iterations, the phase error varies purely in y. The two-sided pyramid pair enables the phase to be completely reconstructed. Its performance has been modeled closed loop with atmospheric turbulence and wind. Both photon noise and read noise were included. The three-sided and four-sided pyramid wavefront sensors have also been studied in direct phase mode. Neither performs nearly as well as does the two-sided pyramid wavefront sensor.
Ferran, C.; Bosch, S.; Carnicer, A.
2012-01-01
A practical activity designed to introduce wavefront coding techniques as a method to extend the depth of field in optical systems is presented. The activity is suitable for advanced undergraduate students since it combines different topics in optical engineering such as optical system design, aberration theory, Fourier optics, and digital image…
The shape of the radio wavefront of extensive air showers as measured with LOFAR
Corstanje, A.; et al., [Unknown; Swinbank, J.
2015-01-01
Extensive air showers, induced by high energy cosmic rays impinging on the Earth’s atmosphere, produce radio emission that is measured with the LOFAR radio telescope. As the emission comes from a finite distance of a few kilometers, the incident wavefront is non-planar. A spherical, conical or hyper
Strauch, Matthias; Konijnenberg, Sander; Shao, Yifeng; Urbach, H. Paul
2017-02-01
Liquid lenses are used to correct for low order wavefront aberrations. Electrowetting liquid lenses can nowadays control defocus and astigmatism effectively, so they start being used for ophthalmology applications. To increase the performance and applicability, we introduce a new driving mechanism to create, detect and correct higher order aberrations using standing waves on the liquid interface. The speed of a liquid lens is in general limited, because the liquid surface cannot follow fast voltage changes, while providing a spherical surface. Surface waves are created instead and with them undesired aberrations. We try to control those surface waves to turn them into an effective wavefront shaping tool. We introduce a model, which treats the liquid lens as a circular vibrating membrane with adjusted boundary conditions. Similar to tunable acoustic gradient (TAG) lenses, the nature of the surface modes are predicted to be Bessel functions. Since Bessel functions are a full set of orthogonal basis functions any surface can be created as a linear combination of different Bessel functions. The model was investigated experimentally in two setups. First the point spread functions were studied and compared to a simulation of the intensity distribution created by Fresnel propagated Bessel surfaces. Second the wavefronts were measured directly using a spatial light modulator. The surface resonance frequencies confirm the predictions made by the model as well as the wavefront measurements. By superposition of known surface modes, it is possible to create new surface shapes, which can be used to simulate and measure the human eye.
Efficient Irregular Wavefront Propagation Algorithms on Hybrid CPU-GPU Machines.
Teodoro, George; Pan, Tony; Kurc, Tahsin; Kong, Jun; Cooper, Lee; Saltz, Joel
2013-04-01
We address the problem of efficient execution of a computation pattern, referred to here as the irregular wavefront propagation pattern (IWPP), on hybrid systems with multiple CPUs and GPUs. The IWPP is common in several image processing operations. In the IWPP, data elements in the wavefront propagate waves to their neighboring elements on a grid if a propagation condition is satisfied. Elements receiving the propagated waves become part of the wavefront. This pattern results in irregular data accesses and computations. We develop and evaluate strategies for efficient computation and propagation of wavefronts using a multi-level queue structure. This queue structure improves the utilization of fast memories in a GPU and reduces synchronization overheads. We also develop a tile-based parallelization strategy to support execution on multiple CPUs and GPUs. We evaluate our approaches on a state-of-the-art GPU accelerated machine (equipped with 3 GPUs and 2 multicore CPUs) using the IWPP implementations of two widely used image processing operations: morphological reconstruction and euclidean distance transform. Our results show significant performance improvements on GPUs. The use of multiple CPUs and GPUs cooperatively attains speedups of 50× and 85× with respect to single core CPU executions for morphological reconstruction and euclidean distance transform, respectively.