Lang, Jun
2015-03-01
In this paper, we propose a novel color image encryption method by using Color Blend (CB) and Chaos Permutation (CP) operations in the reality-preserving multiple-parameter fractional Fourier transform (RPMPFRFT) domain. The original color image is first exchanged and mixed randomly from the standard red-green-blue (RGB) color space to R‧G‧B‧ color space by rotating the color cube with a random angle matrix. Then RPMPFRFT is employed for changing the pixel values of color image, three components of the scrambled RGB color space are converted by RPMPFRFT with three different transform pairs, respectively. Comparing to the complex output transform, the RPMPFRFT transform ensures that the output is real which can save storage space of image and convenient for transmission in practical applications. To further enhance the security of the encryption system, the output of the former steps is scrambled by juxtaposition of sections of the image in the reality-preserving multiple-parameter fractional Fourier domains and the alignment of sections is determined by two coupled chaotic logistic maps. The parameters in the Color Blend, Chaos Permutation and the RPMPFRFT transform are regarded as the key in the encryption algorithm. The proposed color image encryption can also be applied to encrypt three gray images by transforming the gray images into three RGB color components of a specially constructed color image. Numerical simulations are performed to demonstrate that the proposed algorithm is feasible, secure, sensitive to keys and robust to noise attack and data loss.
Applying Quaternion Fourier Transforms for Enhancing Color Images
Directory of Open Access Journals (Sweden)
M.I. Khalil
2012-03-01
Full Text Available The Fourier transforms play a critical role in a broad range of image processing applications, including enhancement, analysis, restoration, and compression. Until recently, it was common to use the conventional methods to deal with colored images. These methods are based on RGB decomposition of the colored image by separating it into three separate scalar images and computing the Fourier transforms of these images separately. The computing of the Hypercomplex 2D Fourier transform of a color image as a whole unit has only recently been realized. This paper is concerned with frequency domain noise reduction of color images using quaternion Fourier transforms. The approach is based on obtaining quaternion Fourier transform of the color image and applying the Gaussian filter to it in the frequency domain. The filtered image is then obtained by calculating the inverse quaternion Fourier transforms.
Feldkhun, Daniel (Inventor); Wagner, Kelvin H. (Inventor)
2013-01-01
Methods and systems are disclosed of sensing an object. A first radiation is spatially modulated to generate a structured second radiation. The object is illuminated with the structured second radiation such that the object produces a third radiation in response. Apart from any spatially dependent delay, a time variation of the third radiation is spatially independent. With a single-element detector, a portion of the third radiation is detected from locations on the object simultaneously. At least one characteristic of a sinusoidal spatial Fourier-transform component of the object is estimated from a time-varying signal from the detected portion of the third radiation.
Subharmonic Fourier domain mode locking.
Eigenwillig, Christoph M; Wieser, Wolfgang; Biedermann, Benjamin R; Huber, Robert
2009-03-15
We demonstrate a subharmonically Fourier domain mode-locked wavelength-swept laser source with a substantially reduced cavity fiber length. In contrast to a standard Fourier domain mode-locked configuration, light is recirculated repetitively in the delay line with the optical bandpass filter used as switch. The laser has a fundamental optical round trip frequency of 285 kHz and can be operated at integer fractions thereof (subharmonics). Sweep ranges up to 95 nm full width centred at 1317 nm are achieved at the 1/5th subharmonic. A maximum sensitivity of 116 dB and an axial resolution of 12 microm in air are measured at an average sweep power of 12 mW. A sensitivity roll-off of 11 dB over 4 mm and 25 dB over 10 mm is observed and optical coherence tomography imaging is demonstrated. Besides the advantage of a reduced fiber length, subharmonic Fourier domain mode locking (shFDML) enables simple scaling of the sweep speed by extracting light from the delay part of the resonator. A sweep rate of 570 kHz is achieved. Characteristic features of shFDML operation, such as power leakage during fly-back and cw breakthrough, are investigated.
Oversampling analysis in fractional Fourier domain
Institute of Scientific and Technical Information of China (English)
ZHANG Feng; TAO Ran; WANG Yue
2009-01-01
Oversampling is widely used in practical applications of digital signal processing. As the fractional Fourier transform has been developed and applied in signal processing fields, it is necessary to consider the oversampling theorem in the fractional Fourier domain. In this paper, the oversampling theorem in the fractional Fourier domain is analyzed. The fractional Fourier spectral relation between the original oversampled sequence and its subsequences is derived first, and then the expression for exact reconstruction of the missing samples in terms of the subsequences is obtained. Moreover, by taking a chirp signal as an example, it is shown that, reconstruction of the missing samples in the oversampled signal Is suitable in the fractional Fourier domain for the signal whose time-frequency distribution has the minimum support in the fractional Fourier domain.
Fourier phase in Fourier-domain optical coherence tomography.
Uttam, Shikhar; Liu, Yang
2015-12-01
Phase of an electromagnetic wave propagating through a sample-of-interest is well understood in the context of quantitative phase imaging in transmission-mode microscopy. In the past decade, Fourier-domain optical coherence tomography has been used to extend quantitative phase imaging to the reflection-mode. Unlike transmission-mode electromagnetic phase, however, the origin and characteristics of reflection-mode Fourier phase are poorly understood, especially in samples with a slowly varying refractive index. In this paper, the general theory of Fourier phase from first principles is presented, and it is shown that Fourier phase is a joint estimate of subresolution offset and mean spatial frequency of the coherence-gated sample refractive index. It is also shown that both spectral-domain phase microscopy and depth-resolved spatial-domain low-coherence quantitative phase microscopy are special cases of this general theory. Analytical expressions are provided for both, and simulations are presented to explain and support the theoretical results. These results are further used to show how Fourier phase allows the estimation of an axial mean spatial frequency profile of the sample, along with depth-resolved characterization of localized optical density change and sample heterogeneity. Finally, a Fourier phase-based explanation of Doppler optical coherence tomography is also provided.
Masked object registration in the Fourier domain.
Padfield, Dirk
2012-05-01
Registration is one of the most common tasks of image analysis and computer vision applications. The requirements of most registration algorithms include large capture range and fast computation so that the algorithms are robust to different scenarios and can be computed in a reasonable amount of time. For these purposes, registration in the Fourier domain using normalized cross-correlation is well suited and has been extensively studied in the literature. Another common requirement is masking, which is necessary for applications where certain regions of the image that would adversely affect the registration result should be ignored. To address these requirements, we have derived a mathematical model that describes an exact form for embedding the masking step fully into the Fourier domain so that all steps of translation registration can be computed efficiently using Fast Fourier Transforms. We provide algorithms and implementation details that demonstrate the correctness of our derivations. We also demonstrate how this masked FFT registration approach can be applied to improve the Fourier-Mellin algorithm that calculates translation, rotation, and scale in the Fourier domain. We demonstrate the computational efficiency, advantages, and correctness of our algorithm on a number of images from real-world applications. Our framework enables fast, global, parameter-free registration of images with masked regions.
Fourier transforms in the complex domain
Wiener, N
1934-01-01
With the aid of Fourier-Mellin transforms as a tool in analysis, the authors were able to attack such diverse analytic questions as those of quasi-analytic functions, Mercer's theorem on summability, Milne's integral equation of radiative equilibrium, the theorems of MÃ¼nz and SzÃ¡sz concerning the closure of sets of powers of an argument, Titchmarsh's theory of entire functions of semi-exponential type with real negative zeros, trigonometric interpolation and developments in polynomials of the form \\sum^N_1A_ne^{i\\lambda_nx}, lacunary series, generalized harmonic analysis in the complex domain,
Resonant Doppler imaging with Fourier domain optical coherence tomography
Leitgeb, Rainer A.; Szklumowska, Anna; Pircher, Michael; Gotzinger, Erich; Fercher, Adolf F.
2005-04-01
Fourier Domain Optical Coherene Tomography (FD OCT) is a high speed imaging modality with increased sensitivity as compared to standard time domain (TD) OCT. The higher sensitivity is especially important, if strongly scattering tissue such as blood is investigated. Recently it could be shown that retinal blood flow can be assessed in-vivo by high speed FD OCT. However the detection bandwidth of color Doppler (CD) FDOCT is strongly limited due to blurring of the detected interference fringes during exposure. This leads to a loss of sensitivity for detection of fast changes in tissue. Using a moving mirror as a reference one can effectively increase the detection bandwidth for CD FDOCT and perform perfusion sectioning. The modality is called resonant CD FDOCT imaging. The principle of the method is presented and experimentally verified.
Digital Backpropagation in the Nonlinear Fourier Domain
Wahls, Sander; Prilepsky, Jaroslaw E; Poor, H Vincent; Turitsyn, Sergei K
2015-01-01
Nonlinear and dispersive transmission impairments in coherent fiber-optic communication systems are often compensated by reverting the nonlinear Schr\\"odinger equation, which describes the evolution of the signal in the link, numerically. This technique is known as digital backpropagation. Typical digital backpropagation algorithms are based on split-step Fourier methods in which the signal has to be discretized in time and space. The need to discretize in both time and space however makes the real-time implementation of digital backpropagation a challenging problem. In this paper, a new fast algorithm for digital backpropagation based on nonlinear Fourier transforms is presented. Aiming at a proof of concept, the main emphasis will be put on fibers with normal dispersion in order to avoid the issue of solitonic components in the signal. However, it is demonstrated that the algorithm also works for anomalous dispersion if the signal power is low enough. Since the spatial evolution of a signal governed by the ...
Double random fractional Fourier domain encoding for optical security
Unnikrishnan, G.; Singh, Kehar
2000-11-01
We propose a new optical encryption technique using the fractional Fourier transform. In this method, the data are encrypted to a stationary white noise by two statistically independent random phase masks in fractional Fourier domains. To decrypt the data correctly, one needs to specify the fractional domains in which the input plane, encryption plane, and output planes exist, in addition to the key used for encryption. The use of an anamorphic fractional Fourier transform for the encryption of 2D data is also discussed. We suggest an optical implementation of the proposed idea. Results of a numerical simulation to analyze the performance of the proposed method are presented.
Screening retinal transplants with Fourier-domain OCT
Rao, Bin
2009-02-01
Transplant technologies have been studied for the recovery of vision loss from retinitis pigmentosa (RP) and age-related macular degeneration (AMD). In several rodent retinal degeneration models and in patients, retinal progenitor cells transplanted as layers to the subretinal space have been shown to restore or preserve vision. The methods for evaluation of transplants are expensive considering the large amount of animals. Alternatively, time-domain Stratus OCT was previously shown to be able to image the morphological structure of transplants to some extent, but could not clearly identify laminated transplants. The efficacy of screening retinal transplants with Fourier-domain OCT was studied on 37 S334ter line 3 rats with retinal degeneration 6-67 days after transplant surgery. The transplants were morphologically categorized as no transplant, detachment, rosettes, small laminated area and larger laminated area with both Fourier-domain OCT and histology. The efficacy of Fourier-domain OCT in screening retinal transplants was evaluated by comparing the categorization results with OCT and histology. Additionally, 4 rats were randomly selected for multiple OCT examinations (1, 5, 9, 14 and 21days post surgery) in order to determine the earliest image time of OCT examination since the transplanted tissue may need some time to show its tendency of growing. Finally, we demonstrated the efficacy of Fourier-domain OCT in screening retinal transplants in early stages and determined the earliest imaging time for OCT. Fourier-domain OCT makes itself valuable in saving resource spent on animals with unsuccessful transplants.
A dual Fourier-wavelet domain authentication-identification watermark.
Ahmed, Farid
2007-04-16
A dual Fourier-Wavelet domain watermarking technique for authentication and identity verification is proposed. Discrete wavelet transform (DWT) domain spread spectrum is used for embedding identity (such as registration number, transaction ID etc.) information. While a blind detector detects an ID, it is important to validate with other ancillary data. To satisfy that requirement, we embed a robust signature and hide it in a mid-band wavelet subband using Fourier domain bit-embedding algorithm. Results are furnished to show the compression tolerance of the method.
Fourier domain OCT imaging of American cockroach nervous system
Wyszkowska, Joanna; Gorczynska, Iwona; Ruminski, Daniel; Karnowski, Karol; Kowalczyk, Andrzej; Stankiewicz, Maria; Wojtkowski, Maciej
2012-01-01
In this pilot study we demonstrate results of structural Fourier domain OCT imaging of the nervous system of Periplaneta americana L. (American cockroach). The purpose of this research is to develop an OCT apparatus enabling structural imaging of insect neural system. Secondary purpose of the presented research is to develop methods of the sample preparation and handling during the OCT imaging experiments. We have performed imaging in the abdominal nerve cord excised from the American cockroach. For this purpose we have developed a Fourier domain / spectral OCT system operating at 820 nm wavelength range.
Multi-modal Color Medical Image Fusion Using Quaternion Discrete Fourier Transform
Nawaz, Qamar; Xiao, Bin; Hamid, Isma; Jiao, Du
2016-12-01
Multimodal image fusion is a process of combining multiple images, generated by identical or diverse imaging modalities, to get precise inside information about the same body organ. In recent years, various multimodal image fusion algorithms have been proposed to fuse medical image. However, most of them focus on fusing grayscale images. This paper proposes a novel algorithm for the fusion of multimodal color medical images. The proposed algorithm divides source images into blocks, converts each RGB block into quaternion representation and transforms them from special domain to frequency domain by applying quaternion discrete Fourier transform. The fused coefficients are obtained by calculating and comparing contrast values of corresponding coefficients in transformed blocks. The resultant fused image is reconstructed by merging all the blocks after applying inverse quaternion discrete Fourier transform on each block. Experimental evaluation demonstrates that the proposed algorithm qualitatively outperforms many existing state-of-the-art multimodal image fusion algorithms.
Rajput, Sudheesh K.; Nishchal, Naveen K.
2017-04-01
We propose a novel security scheme based on the double random phase fractional domain encoding (DRPE) and modified Gerchberg-Saxton (G-S) phase retrieval algorithm for securing two images simultaneously. Any one of the images to be encrypted is converted into a phase-only image using modified G-S algorithm and this function is used as a key for encrypting another image. The original images are retrieved employing the concept of known-plaintext attack and following the DRPE decryption steps with all correct keys. The proposed scheme is also used for encryption of two color images with the help of convolution theorem and phase-truncated fractional Fourier transform. With some modification, the scheme is extended for simultaneous encryption of gray-scale and color images. As a proof-of-concept, simulation results have been presented for securing two gray-scale images, two color images, and simultaneous gray-scale and color images.
Fourier domain asymmetric cryptosystem for privacy protected multimodal biometric security
Choudhury, Debesh
2016-04-01
We propose a Fourier domain asymmetric cryptosystem for multimodal biometric security. One modality of biometrics (such as face) is used as the plaintext, which is encrypted by another modality of biometrics (such as fingerprint). A private key is synthesized from the encrypted biometric signature by complex spatial Fourier processing. The encrypted biometric signature is further encrypted by other biometric modalities, and the corresponding private keys are synthesized. The resulting biometric signature is privacy protected since the encryption keys are provided by the human, and hence those are private keys. Moreover, the decryption keys are synthesized using those private encryption keys. The encrypted signatures are decrypted using the synthesized private keys and inverse complex spatial Fourier processing. Computer simulations demonstrate the feasibility of the technique proposed.
Image recovery from double amplitudes in fractional Fourier domain
Institute of Scientific and Technical Information of China (English)
Liao Tian-He; Gao Qiong
2006-01-01
The classical Gerchberg-Saxton algorithm is introduced into the image recovery in fractional Fourier domain after adaptation. When this algorithm is applied directly, its performance is good for smoothed image, but bad for unsmoothed image. Based on the diversity of fractional Fourier transform on its orders, this paper suggests a novel iterative algorithm, which extracts the information of the original image from amplitudes of its fractional Fourier transform at two orders. This new algorithm consists of two independent Gerchberg-Saxton procedures and an averaging operation in each circle. Numerical simulations are carried out to show its validity for both smoothed and unsmoothed images with most pairs of orders in the interval [0,1] .
Fractional Fourier domain analysis of decimation and interpolation
Institute of Scientific and Technical Information of China (English)
MENG XiangYi; TAO Ran; WANG Yue
2007-01-01
The sampling rate conversion is always used in order to decrease computational amount and storage load in a system. The fractional Fourier transform (FRFT) is a powerful tool for the analysis of nonstationary signals, especially, chirp-like signal.Thus, it has become an active area in the signal processing community, with many applications of radar, communication, electronic warfare, and information security.Therefore, it is necessary for us to generalize the theorem for Fourier domain analysis of decimation and interpolation. Firstly, this paper defines the digital frequency in the fractional Fourier domain (FRFD) through the sampling theorems with FRFT. Secondly, FRFD analysis of decimation and interpolation is proposed in this paper with digital frequency in FRFD followed by the studies of interpolation filter and decimation filter in FRFD. Using these results, FRFD analysis of the sampling rate conversion by a rational factor is illustrated. The noble identities of decimation and interpolation in FRFD are then deduced using previous results and the fractional convolution theorem. The proposed theorems in this study are the bases for the generalizations of the multirate signal processing in FRFD, which can advance the filter banks theorems in FRFD. Finally, the theorems introduced in this paper are validated by simulations.
Fourier domain multispectral multiple scattering low coherence interferometry.
Matthews, Thomas E; Giacomelli, Michael G; Brown, William J; Wax, Adam
2013-12-01
We have implemented multispectral multiple scattering low coherence interferometry (ms2/LCI) with Fourier domain data collection. The ms2/LCI system is designed to localize features with spectroscopic contrast with millimeter resolution up to 1 cm deep in scattering samples by using photons that have undergone multiple low-angle (forward) scattering events. Fourier domain detection both increases the data acquisition speed of the system and gives access to rich spectroscopic information, compared to the previous single channel, time-domain implementation. Separate delivery and detection angular apertures reduce collection of the diffuse background signal in order to isolate localized spectral features from deeper in scattering samples than would be possible with traditional spectroscopic optical coherence tomography. Light from a supercontinuum source is used to acquire absorption spectra of chromophores in the visible range within a tissue-like scattering phantom. An intensity modulation and digital lock-in detection scheme is implemented to mitigate relative intensity and spectral noise inherent in supercontinuum sources. The technical parameters of the system and comparative analysis are presented.
Fourier-domain multichannel autofocus for synthetic aperture radar.
Liu, Kuang-Hung; Munson, David C
2011-12-01
Synthetic aperture radar (SAR) imaging suffers from image focus degradation in the presence of phase errors in the received signal due to unknown platform motion or signal propagation delays. We present a new autofocus algorithm, termed Fourier-domain multichannel autofocus (FMCA), that is derived under a linear algebraic framework, allowing the SAR image to be focused in a noniterative fashion. Motivated by the mutichannel autofocus (MCA) approach, the proposed autofocus algorithm invokes the assumption of a low-return region, which generally is provided within the antenna sidelobes. Unlike MCA, FMCA works with the collected polar Fourier data directly and is capable of accommodating wide-angle monostatic SAR and bistatic SAR scenarios. Most previous SAR autofocus algorithms rely on the prior assumption that radar's range of look angles is small so that the phase errors can be modeled as varying along only one dimension in the collected Fourier data. And, in some cases, implicit assumptions are made regarding the SAR scene. Performance of such autofocus algorithms degrades if the assumptions are not satisfied. The proposed algorithm has the advantage that it does not require prior assumptions about the range of look angles, nor characteristics of the scene.
Fourier Phase Domain Steganography: Phase Bin Encoding Via Interpolation
Rivas, Edward
2007-04-01
In recent years there has been an increased interest in audio steganography and watermarking. This is due primarily to two reasons. First, an acute need to improve our national security capabilities in light of terrorist and criminal activity has driven new ideas and experimentation. Secondly, the explosive proliferation of digital media has forced the music industry to rethink how they will protect their intellectual property. Various techniques have been implemented but the phase domain remains a fertile ground for improvement due to the relative robustness to many types of distortion and immunity to the Human Auditory System. A new method for embedding data in the phase domain of the Discrete Fourier Transform of an audio signal is proposed. Focus is given to robustness and low perceptibility, while maintaining a relatively high capacity rate of up to 172 bits/s.
Fractional Fourier domain analysis of cyclic multirate signal processing
Institute of Scientific and Technical Information of China (English)
2008-01-01
The cyclic filter banks, which are used widely in the image subband coding, refer to signal processing on the finite field. This study investigates the fractional Fourier domain (FRFD) analysis of cyclic multirate systems based on the fractional circular convolution and chirp period. The proposed theorems include the fractional Fourier domain analysis of cyclic decimation and cyclic interpolation, the noble identities of cyclic decimation and cyclic interpolation in the FRFD, the polyphase represen-tation of cyclic signal in the FRFD, and the perfect reconstruction condition for the cyclic filter banks in the FRFD. Furthermore, this paper proposes the design methods for perfect reconstruction cyclic filter bank and cyclic filter bank with chirp modulation in the FRFD. The proposed theorems extend the multirate signal processing in the FRFD, which also advance the applications of the theorems of filter bank in the FRFD on the finite signal field, such as digital image processing. At last, the proposed design methods for the cyclic filter banks in the FRFD are validated by simulations.
Deep subwavelength nanometric image reconstruction using Fourier domain optical normalization
Institute of Scientific and Technical Information of China (English)
Jing Qin; Richard M Silver; Bryan M Barnes; Hui Zhou; Ronald G Dixson; Mark-Alexander Henn
2016-01-01
Quantitative optical measurements of deep subwavelength,three-dimensional (3D),nanometric structures with sensitivity to sub-nanometer details address a ubiquitous measurement challenge.A Fourier domain normalization approach is used in the Fourier optical imaging code to simulate the full 3D scattered light field of nominally 15 nm-sized structures,accurately replicating the light field as a function of the focus position.Using the full 3D light field,nanometer scale details such as a 2 nm thin conformal oxide and nanometer topography are rigorously fitted for features less than one-thirtiethof the wavelength in size.The densely packed structures are positioned nearly an order of magnitude closer than the conventional Rayleigh resolution limit and can be measured with sub-nanometer parametric uncertainties.This approach enables a practical measurement sensitivity to size variations of only a few atoms in size using a high-throughput optical configuration with broad application in measuring nanometric structures and nanoelectronic devices.
Wang, Xiaogang; Zhao, Daomu
2013-09-01
A nonlinear color and grayscale images cryptosystem based on phase-truncated fractional Fourier transform and optical superposition principle is proposed. In order to realize simultaneous encryption of color and grayscale images, each grayscale image is first converted into two phase masks by using an optical coherent superposition, one of which is treated as a part of input information that will be fractional Fourier transformed while the other in the form of a chaotic random phase mask (CRPM) is used as a decryption key. For the purpose of optical performance, all the processes are performed through three channels, i.e., red, green, and blue. Different from most asymmetric encryption methods, the decryption process is designed to be linear for the sake of effective decryption. The encryption level of a double random phase encryption based on phase-truncated Fourier transform is enhanced by extending it into fractional Fourier domain and the load of the keys management and transmission is lightened by using CRPMs. The security of the proposed cryptosystem is discussed and computer simulation results are presented to verify the validity of the proposed method.
Color vision in the comb frequency domain.
Bonnardel, Valérie; Varela, Francisco J
2003-01-01
In 1982, Horace Barlow considered the question of human trichromacy in the context of information theory: according to the Sampling Theorem, three types of receptors covering the visible spectrum (400-700 nm) might be sufficient to reconstruct the color signal. Although Barlow was led to reject the direct application of the Sampling Theorem to explain color dimensionality, the theoretical framework offers a fresh point of view for analyzing the color system in conjunction with the physical characteristics of natural color signals. This review aims to illustrate that if the strict mathematical reconstruction (as implied by the Sampling Theorem) is replaced by a pragmatic approximation of color signals, then trichromacy, with its subsequent opponent-color process, could be regarded as an optimization of color constancy abilities in the spectral environment of primates. Higher dimension systems (tetrachromacy) found in other species can also serve the purpose of color constancy optimization in environments where color signals exhibit a finer spectral structure.
Domain coloring of complex functions: an implementation-oriented introduction.
Poelke, Konstantin; Polthier, Konrad
2012-01-01
This article gives a short overview of domain coloring for complex functions that have four-dimensional function graphs and therefore can't be visualized traditionally. The authors discuss several color schemes, focus on various aspects of complex functions, and provide Java-like pseudocode examples explaining the crucial ideas of the coloring algorithms to allow for easy reproduction.
Sharma, Kamalesh Kumar; Joshi, Shiv Dutt
2007-10-01
We present a generalized convolution theorem in the fractional Fourier domains that preserves the convolution theorem of the conventional Fourier transform. The Papoulis-like generalized sampling expansions in the fractional Fourier domains using this generalized convolution theorem are also derived and it is shown that the classical generalized Papoulis sampling expansion is a special case of it. Its application in the context of the image superresolution is also discussed.
Foliage Plant Retrieval using Polar Fourier Transform, Color Moments and Vein Features
Kadir, Abdul; Susanto, Adhi; Santosa, Paulus Insap
2011-01-01
This paper proposed a method that combines Polar Fourier Transform, color moments, and vein features to retrieve leaf images based on a leaf image. The method is very useful to help people in recognizing foliage plants. Foliage plants are plants that have various colors and unique patterns in the leaf. Therefore, the colors and its patterns are information that should be counted on in the processing of plant identification. To compare the performance of retrieving system to other result, the experiments used Flavia dataset, which is very popular in recognizing plants. The result shows that the method gave better performance than PNN, SVM, and Fourier Transform. The method was also tested using foliage plants with various colors. The accuracy was 90.80% for 50 kinds of plants.
Filterbank implementation for multi-channel sampling in fractional Fourier domain
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Reconstruction of a continuous time signal from its periodic nonuniform samples and multi-channel samples is fundamental for multi-channel parallel A/D and MIMO systems. In this paper,with a filterbank interpretation of sampling schemes,the efficient interpolation and reconstruction methods for periodic nonuniform sampling and multi-channel sampling in the fractional Fourier domain are presented. Firstly,the interpolation and sampling identities in the fractional Fourier domain are derived by the properties of the fractional Fourier transform. Then,the particularly efficient filterbank implementations for the periodic nonuniform sampling and the multi-channel sampling in the fractional Fourier domain are introduced. At last,the relationship between the multi-channel sampling and the filterbank in the fractional Fourier domain is investigated,which shows that any perfect reconstruction filterbank can lead to new sampling and reconstruction strategies.
Filterbank implementation for multi-channel sampling in fractional Fourier domain
Institute of Scientific and Technical Information of China (English)
ZHANG Feng; TAO Ran; WANG Yue
2009-01-01
Reconstruction of a continuous time signal from its periodic nonuniform samples and multi-channel samples is fundamental for multi-channel parallel A/D and MIMO systems. In this paper, with a filter-bank interpretation of sampling schemes, the efficient interpolation and reconstruction methods for periodic nonuniform sampling and multi-channel sampling in the fractional Fourier domain are pre-sented. Firstly, the interpolation and sampling identities in the fractional Fourier domain are derived by the properties of the fractional Fourier transform. Then, the particularly efficient filterbank implementa-tions for the periodic nonuniform sampling and the multi-channel sampling in the fractional Fourier domain are introduced. At last, the relationship between the multi-channel sampling and the filterbank in the fractional Fourier domain is investigated, which shows that any perfect reconstruction filterbank can lead to new sampling and reconstruction strategies.
MULTIVARIATE FOURIER SERIES OVER A CLASS OF NON TENSOR-PRODUCT PARTITION DOMAINS
Institute of Scientific and Technical Information of China (English)
Jiachang Sun
2003-01-01
This paper finds a way to extend the well-known Fourier methods, to so-called n+1directions partition domains in n-dimension. In particular, in 2-D and 3-D cases, westudy Fourier methods over 3-direction parallel hexagon partitions and 4-direction parallelparallelogram dodecahedron partitions, respectively. It has pointed that, the most conceptsand results of Fourier methods on tensor-product case, such as periodicity, orthogonality ofFourier basis system, partial sum of Fourier series and its approximation behavior, can bemoved on the new non tensor-product partition case.
Recognition of object domain by color distribution
Mugitani, Takako; Mifune, Mitsuru; Nagata, Shigeki
1988-01-01
For the image processing of an object in its natural image, it is necessary to extract in advance the object to be processed from its image. To accomplish this the outer shape of an object is extracted through human instructions, which requires a great deal of time and patience. A method involving the setting of a model of color distribution on the surface of an object is described. This method automatically provides color recognition, a piece of knowledge that represents the properties of an object, from its natural image. A method for recognizing and extracting the object in the image according to the color recognized is also described.
Institute of Scientific and Technical Information of China (English)
Ding Lu; Weimin Jin
2011-01-01
A novel fully phase color image encryption/decryption scheme based on joint fractional Fourier transform correlator (JFRTC) and phase retrieval algorithm (PRA) is proposed. The security of the system is enhanced by the fractional order as a new added key. This method takes full advantage of the parallel processing features of the optical system and could optically realize single-channel color image encryption.The system and operation procedures are simplified. The simulation results of a color image indicate that the new method provides efficient solutions with a strong sense of security.%@@ A novel fully phase color image encryption/decryption scheme based on joint fractional Fourier transform correlator (JFRTC) and phase retrieval algorithm (PRA) is proposed. The security of the system is enhanced by the fractional order as a new added key. This method takes full advantage of the parallel processing features of the optical system and could optically realize single-channel color image encryption. The system and operation procedures are simplified. The simulation results of a color image indicate that the new method provides efficient solutions with a strong sense of security.
Regularized Laplace-Fourier-Domain Full Waveform Inversion Using a Weighted l 2 Objective Function
Jun, Hyunggu; Kwon, Jungmin; Shin, Changsoo; Zhou, Hongbo; Cogan, Mike
2016-09-01
Full waveform inversion (FWI) can be applied to obtain an accurate velocity model that contains important geophysical and geological information. FWI suffers from the local minimum problem when the starting model is not sufficiently close to the true model. Therefore, an accurate macroscale velocity model is essential for successful FWI, and Laplace-Fourier-domain FWI is appropriate for obtaining such a velocity model. However, conventional Laplace-Fourier-domain FWI remains an ill-posed and ill-conditioned problem, meaning that small errors in the data can result in large differences in the inverted model. This approach also suffers from certain limitations related to the logarithmic objective function. To overcome the limitations of conventional Laplace-Fourier-domain FWI, we introduce a weighted l 2 objective function, instead of the logarithmic objective function, as the data-domain objective function, and we also introduce two different model-domain regularizations: first-order Tikhonov regularization and prior model regularization. The weighting matrix for the data-domain objective function is constructed to suitably enhance the far-offset information. Tikhonov regularization smoothes the gradient, and prior model regularization allows reliable prior information to be taken into account. Two hyperparameters are obtained through trial and error and used to control the trade-off and achieve an appropriate balance between the data-domain and model-domain gradients. The application of the proposed regularizations facilitates finding a unique solution via FWI, and the weighted l 2 objective function ensures a more reasonable residual, thereby improving the stability of the gradient calculation. Numerical tests performed using the Marmousi synthetic dataset show that the use of the weighted l 2 objective function and the model-domain regularizations significantly improves the Laplace-Fourier-domain FWI. Because the Laplace-Fourier-domain FWI is improved, the
Regularized Laplace-Fourier-Domain Full Waveform Inversion Using a Weighted l 2 Objective Function
Jun, Hyunggu; Kwon, Jungmin; Shin, Changsoo; Zhou, Hongbo; Cogan, Mike
2017-03-01
Full waveform inversion (FWI) can be applied to obtain an accurate velocity model that contains important geophysical and geological information. FWI suffers from the local minimum problem when the starting model is not sufficiently close to the true model. Therefore, an accurate macroscale velocity model is essential for successful FWI, and Laplace-Fourier-domain FWI is appropriate for obtaining such a velocity model. However, conventional Laplace-Fourier-domain FWI remains an ill-posed and ill-conditioned problem, meaning that small errors in the data can result in large differences in the inverted model. This approach also suffers from certain limitations related to the logarithmic objective function. To overcome the limitations of conventional Laplace-Fourier-domain FWI, we introduce a weighted l 2 objective function, instead of the logarithmic objective function, as the data-domain objective function, and we also introduce two different model-domain regularizations: first-order Tikhonov regularization and prior model regularization. The weighting matrix for the data-domain objective function is constructed to suitably enhance the far-offset information. Tikhonov regularization smoothes the gradient, and prior model regularization allows reliable prior information to be taken into account. Two hyperparameters are obtained through trial and error and used to control the trade-off and achieve an appropriate balance between the data-domain and model-domain gradients. The application of the proposed regularizations facilitates finding a unique solution via FWI, and the weighted l 2 objective function ensures a more reasonable residual, thereby improving the stability of the gradient calculation. Numerical tests performed using the Marmousi synthetic dataset show that the use of the weighted l 2 objective function and the model-domain regularizations significantly improves the Laplace-Fourier-domain FWI. Because the Laplace-Fourier-domain FWI is improved, the
Time-Domain Optical Fourier Transformation for OTDM-DWDM and DWDM-OTDM Conversion
DEFF Research Database (Denmark)
Mulvad, Hans Christian Hansen; Palushani, Evarist; Galili, Michael
2011-01-01
Applications of time-domain optical Fourier transformation (OFT) in ultra-high-speed optical time-division multiplexed systems (OTDM) are reviewed, with emphasis on the recent demonstrations of OFT-based conversion between the OTDM and DWDM formats.......Applications of time-domain optical Fourier transformation (OFT) in ultra-high-speed optical time-division multiplexed systems (OTDM) are reviewed, with emphasis on the recent demonstrations of OFT-based conversion between the OTDM and DWDM formats....
Tan, Ru-Chao; Lei, Tong; Zhao, Qing-Min; Gong, Li-Hua; Zhou, Zhi-Hong
2016-12-01
To improve the slow processing speed of the classical image encryption algorithms and enhance the security of the private color images, a new quantum color image encryption algorithm based on a hyper-chaotic system is proposed, in which the sequences generated by the Chen's hyper-chaotic system are scrambled and diffused with three components of the original color image. Sequentially, the quantum Fourier transform is exploited to fulfill the encryption. Numerical simulations show that the presented quantum color image encryption algorithm possesses large key space to resist illegal attacks, sensitive dependence on initial keys, uniform distribution of gray values for the encrypted image and weak correlation between two adjacent pixels in the cipher-image.
Parametric spectral correlations of disordered systems in the Fourier domain
Guarneri, I; Zakrzewski, J A; Molinari, L; Casati, G; Guarneri, I; Zyczkowski, K; Zakrzewski, J; Molinari, L; Casati, G
1995-01-01
A Fourier analysis of parametric level dynamics for random matrices periodically depending on a phase is developed. We demonstrate both theoretically and numerically that under very general conditions the correlation C(\\varphi ) of level velocities is singular at \\varphi =0 for any symmetry class; the singularity is revealed by algebraic tails in Fourier transforms, and is milder, the stronger the level repulsion in the chosen ensemble. The singularity is strictly connected with the divergence of the 2nd moments of level derivatives of appropriate order, and its type is specified to leading terms for Gaussian, stationary ensembles of GOE, GUE, GSE types, and for the Gaussian ensemble of Periodic Banded Random Matrices, in which a breaking of symmetry occurs. In the latter case, we examine the behaviour of correlations in the diffusive regime and in the localized one as well, finding a singularity like that of pure GUE cases. In all the considered ensembles we study the statistics of the Fourier coefficients o...
Color pattern recognition based on the joint fractional Fourier transform correlator
Institute of Scientific and Technical Information of China (English)
Weimin Jin; Yupei Zhang
2007-01-01
A new system of multi-channel single-output joint fractional Fourier transform correlator (JFRTC) for color pattern recognition is proposed based on the conventional system of multi-channel single-output joint transform correlator (JTC). The theoretical analysis and optical experiments are performed. With this method, one can obtain three correlation peaks at the output plane which show a pair of desired cross-correlation peaks and one auto-correlation peak. In comparison, the conventional system leads to more correlation peaks playing a noise role in color pattern recognition.
MULTIVARIATE FOURIER TRANSFORM METHODS OVER SIMPLEX AND SUPER-SIMPLEX DOMAINS
Institute of Scientific and Technical Information of China (English)
Jiachang Sun
2006-01-01
In this paper we propose the well-known Fourier method on some non-tensor product domains in Rd, including simplex and so-called super-simplex which consists of (d + 1)! simplices. As two examples, in 2-D and 3-D case a super-simplex is shown as a paralle lhexagon and a parallel quadrilateral dodecahedron, respectively. We have extended most of concepts and results of the traditional Fourier methods on multivariate cases, such as Fourier basis system, Fourier series, discrete Fourier transform (DFT) and its fast algorithm(FFT) on the super-simplex, as well as generalized sine and cosine transforms (DST, DCT) and related fast algorithms over a simplex. The relationship between the basic orthogonal system and eigen-functions of a Laplacian-like operator over these domains is explored.
Secured color image watermarking technique in DWT-DCT domain
Gunjal, Baisa L
2011-01-01
The multilayer secured DWT-DCT and YIQ color space based image watermarking technique with robustness and better correlation is presented here. The security levels are increased by using multiple pn sequences, Arnold scrambling, DWT domain, DCT domain and color space conversions. Peak signal to noise ratio and Normalized correlations are used as measurement metrics. The 512x512 sized color images with different histograms are used for testing and watermark of size 64x64 is embedded in HL region of DWT and 4x4 DCT is used. 'Haar' wavelet is used for decomposition and direct flexing factor is used. We got PSNR value is 63.9988 for flexing factor k=1 for Lena image and the maximum NC 0.9781 for flexing factor k=4 in Q color space. The comparative performance in Y, I and Q color space is presented. The technique is robust for different attacks like scaling, compression, rotation etc.
Fingerprint Ridge Frequency Estimation in the Fourier Domain
Directory of Open Access Journals (Sweden)
PATRICIU, V.-V.
2014-11-01
Full Text Available Ridge frequency is an important parameter in fingerprint image processing and feature extraction. However, ridge frequency estimation is a difficult task in noisy fingerprint images. A simple and accurate method for the computation of fingerprint ridge frequency using the Fourier spectrum is proposed. The results of the experiments conducted on a collection of fingerprints as well as a quantitative method for performance evaluation based on a Gabor filter-bank are presented. The proposed method is robust with respect to noise and reliable frequency images are obtained.
Robust color image hiding method in DCT domain
Institute of Scientific and Technical Information of China (English)
LI Qing-zhong; YU Chen; CHU Dong-sheng
2006-01-01
This paper presents a robust color image hiding method based on YCbCr color system in discrete cosine transform (DCT) domain,which can hide a secret color image behind a public color cover image and is compatible with the international image compression standard of JPEG.To overcome the grave distortion problem in the restored secret image,this paper proposes a new embedding scheme consisting of reasonable partition of a pixel value and sign embedding.Moreover,based on human visual system (HVS) and fuzzy theory,this paper also presents a fuzzy classification method for DCT sub-blocks to realize the adaptive selection of embedding strength.The experimental results show that the maximum distortion error in pixel value for the extracted secret image is ±1.And the color cover image can provide good quality after embedding large amount of data.
DWDM-TO-OTDM Conversion by Time-Domain Optical Fourier Transformation
DEFF Research Database (Denmark)
Mulvad, Hans Christian Hansen; Hu, Hao; Galili, Michael
2011-01-01
We propose DWDM-OTDM conversion by time-domain optical Fourier transformation. Error-free conversion of a 16×10 Gbit/s 50 GHz-spacing DWDM data signal to a 160 Gbit/s OTDM signal with a 2.1 dB average penalty is demonstrated.......We propose DWDM-OTDM conversion by time-domain optical Fourier transformation. Error-free conversion of a 16×10 Gbit/s 50 GHz-spacing DWDM data signal to a 160 Gbit/s OTDM signal with a 2.1 dB average penalty is demonstrated....
DEFF Research Database (Denmark)
Hu, Hao; Kong, Deming; Palushani, Evarist
2013-01-01
We demonstrate transmission of a 1.28-Tbaud Nyquist-OTDM signal over a record distance of 100 km with detection by time-domain optical Fourier transformation followed by FEC decoding, resulting in error-free performance for all tributaries.......We demonstrate transmission of a 1.28-Tbaud Nyquist-OTDM signal over a record distance of 100 km with detection by time-domain optical Fourier transformation followed by FEC decoding, resulting in error-free performance for all tributaries....
Fractional Fourier transform for partially coherent beam in spatial-frequency domain
Institute of Scientific and Technical Information of China (English)
Cai Yang-Jian; Lin Qiang
2004-01-01
By using Fourier transform and the tensor analysis method, the fractional Fourier transform (FRT) in the spatialfrequency domain for partially coherent beams is derived. Based on the FRT in the spatial-frequency domain, an analytical transform formula is derived for a partially coherent twisted anisotropic Gaussian-Schell model (GSM) beam passing through the FRT system. The connections between the FRT formula and the generalized diffraction integral formulae for partially coherent beams through an aligned optical system and a misaligned optical system in the spatialfrequency domain are discussed, separately. By using the derived formula, the intensity distribution of partially coherent twisted anisotropic GSM beams in the FRT plane are studied in detail. The formula derived provide a convenient tool for analysing and calculating the FRTs of the partially coherent beams in spatial-frequency domain.
Fourier Domain Decoding Algorithm of Non-Binary LDPC codes for Parallel Implementation
Kasai, Kenta
2010-01-01
For decoding non-binary low-density parity check (LDPC) codes, logarithm-domain sum-product (Log-SP) algorithms were proposed for reducing quantization effects of SP algorithm in conjunction with FFT. Since FFT is not applicable in the logarithm domain, the computations required at check nodes in the Log-SP algorithms are computationally intensive. What is worth, check nodes usually have higher degree than variable nodes. As a result, most of the time for decoding is used for check node computations, which leads to a bottleneck effect. In this paper, we propose a Log-SP algorithm in the Fourier domain. With this algorithm, the role of variable nodes and check nodes are switched. The intensive computations are spread over lower-degree variable nodes, which can be efficiently calculated in parallel. Furthermore, we develop a fast calculation method for the estimated bits and syndromes in the Fourier domain.
Open-geometry Fourier modal method: modeling nanophotonic structures in infinite domains
DEFF Research Database (Denmark)
Häyrynen, Teppo; de Lasson, Jakob Rosenkrantz; Gregersen, Niels
2016-01-01
We present an open-geometry Fourier modal method based on a new combination of open boundary conditions and an efficient k-space discretization. The open boundary of the computational domain is obtained using basis functions that expand the whole space, and the integrals subsequently appearing due...
Chan, Kenny K H; Tang, Shuo
2011-12-19
Gridding based non-uniform fast Fourier transform (NUFFT) has recently been shown as an efficient method of processing non-linearly sampled data from Fourier-domain optical coherence tomography (FD-OCT). This method requires selecting design parameters, such as kernel function type, oversampling ratio and kernel width, to balance between computational complexity and accuracy. The Kaiser-Bessel (KB) and Gaussian kernels have been used independently on the NUFFT algorithm for FD-OCT. This paper compares the reconstruction error and speed for the optimization of these design parameters and justifies particular kernel choice for FD-OCT applications. It is found that for on-the-fly computation of the kernel function, the simpler Gaussian function offers a better accuracy-speed tradeoff. The KB kernel, however, is a better choice in the pre-computed kernel mode of NUFFT, in which the processing speed is no longer dependent on the kernel function type. Finally, the algorithm is used to reconstruct in-vivo images of a human finger at a camera limited 50k A-line/s.
Choi, WooJhon; Baumann, Bernhard; Swanson, Eric A.; Fujimoto, James G.
2012-01-01
We present a numerical approach to extract the dispersion mismatch in ultrahigh-resolution Fourier domain optical coherence tomography (OCT) imaging of the retina. The method draws upon an analogy with a Shack-Hartmann wavefront sensor. By exploiting mathematical similarities between the expressions for aberration in optical imaging and dispersion mismatch in spectral / Fourier domain OCT, Shack-Hartmann principles can be extended from the two-dimensional paraxial wavevector space (or the x-y plane in the spatial domain) to the one-dimensional wavenumber space (or the z-axis in the spatial domain). For OCT imaging of the retina, different retinal layers, such as the retinal nerve fiber layer (RNFL), the photoreceptor inner and outer segment junction (IS/OS), or all the retinal layers near the retinal pigment epithelium (RPE) can be used as point source beacons in the axial direction, analogous to point source beacons used in conventional two-dimensional Shack-Hartman wavefront sensors for aberration characterization. Subtleties regarding speckle phenomena in optical imaging, which affect the Shack-Hartmann wavefront sensor used in adaptive optics, also occur analogously in this application. Using this approach and carefully suppressing speckle, the dispersion mismatch in spectral / Fourier domain OCT retinal imaging can be successfully extracted numerically and used for numerical dispersion compensation to generate sharper, ultrahigh-resolution OCT images. PMID:23187353
Galagusz, Ryan; Nave, Jean-Christophe
2015-01-01
We present a high order, Fourier penalty method for the Maxwell's equations in the vicinity of perfect electric conductor boundary conditions. The approach relies on extending the irregular non-periodic domain of the equations to a regular periodic domain by removing the exact boundary conditions and introducing an analytic forcing term in the extended domain. The forcing, or penalty term is chosen to systematically enforce the boundary conditions to high order in the penalty parameter, which then allows for higher order numerical methods. We present an efficient numerical method for constructing the penalty term, and discretize the resulting equations using a Fourier spectral method. We demonstrate convergence orders of up to 3.5 for the one dimensional Maxwell's equations, and show that the numerical method does not suffer from dispersion (or pollution) errors. We also illustrate the approach in two dimensions and demonstrate convergence orders of 2.5 for transverse magnetic modes and 1.5 for the transverse...
DEFF Research Database (Denmark)
Clausen, Anders; Guan, Pengyu; Mulvad, Hans Christian Hansen
2014-01-01
All-optical time-domain Optical Fourier Transformation utilised for signal processing of ultra-high-speed OTDM signals and OFDM signals will be presented.......All-optical time-domain Optical Fourier Transformation utilised for signal processing of ultra-high-speed OTDM signals and OFDM signals will be presented....
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A new method of resolving overlapped peak, Fourier self-deconvolution (FSD) using approximation CN obtained from frequency domain wavelet transform of F(ω) yielded by Fourier transform of overlapped peak signals f(t) as the linear function, was presented in this paper.Compared with classical FSD, the new method exhibits excellent resolution for different overlapped peak signals such as HPLC signals, and have some characteristics such as an extensive applicability for any overlapped peak shape signals and a simple operation because of no selection procedure of the linear function. Its excellent resolution for those different overlapped peak signals is mainly because F(ω) obtained from Fourier transform of f(t) and CN obtained from wavelet transform of F(ω) have the similar linearity and peak width. The effect of those fake peaks can be eliminated by the algorithm proposed by authors. This method has good potential in the process of different overlapped peak signals.
Optical image encryption based on compressive sensing and chaos in the fractional Fourier domain
Liu, Xingbin; Mei, Wenbo; Du, Huiqian
2014-11-01
We propose a novel image encryption algorithm based on compressive sensing (CS) and chaos in the fractional Fourier domain. The original image is dimensionality reduction measured using CS. The measured values are then encrypted using chaotic-based double-random-phase encoding technique in the fractional Fourier transform domain. The measurement matrix and the random-phase masks used in the encryption process are formed from pseudo-random sequences generated by the chaotic map. In this proposed algorithm, the final result is compressed and encrypted. The proposed cryptosystem decreases the volume of data to be transmitted and simplifies the keys for distribution simultaneously. Numerical experiments verify the validity and security of the proposed algorithm.
A Novel Medical Image Watermarking in Three-dimensional Fourier Compressed Domain
Directory of Open Access Journals (Sweden)
Baoru Han
2015-09-01
Full Text Available Digital watermarking is a research hotspot in the field of image security, which is protected digital image copyright. In order to ensure medical image information security, a novel medical image digital watermarking algorithm in three-dimensional Fourier compressed domain is proposed. The novel medical image digital watermarking algorithm takes advantage of three-dimensional Fourier compressed domain characteristics, Legendre chaotic neural network encryption features and robust characteristics of differences hashing, which is a robust zero-watermarking algorithm. On one hand, the original watermarking image is encrypted in order to enhance security. It makes use of Legendre chaotic neural network implementation. On the other hand, the construction of zero-watermarking adopts differences hashing in three-dimensional Fourier compressed domain. The novel watermarking algorithm does not need to select a region of interest, can solve the problem of medical image content affected. The specific implementation of the algorithm and the experimental results are given in the paper. The simulation results testify that the novel algorithm possesses a desirable robustness to common attack and geometric attack.
Joint multi-mode dispersion extraction in Fourier and space time domains
Bose, Sandip; Valero, Henri-Pierre
2013-01-01
In this paper we present a novel broadband approach for the extraction of dispersion curves of multiple time frequency overlapped dispersive modes such as in borehole acoustic data. The new approach works jointly in the Fourier and space time domains and, in contrast to existing space time approaches that mainly work for time frequency separated signals, efficiently handles multiple signals with significant time frequency overlap. The proposed method begins by exploiting the slowness (phase and group) and time location estimates based on frequency-wavenumber (f-k) domain sparsity penalized broadband dispersion extraction method as presented in \\cite{AeronTSP2011}. In this context we first present a Cramer Rao Bound (CRB) analysis for slowness estimation in the (f-k) domain and show that for the f-k domain broadband processing, group slowness estimates have more variance than the phase slowness estimates and time location estimates. In order to improve the group slowness estimates we exploit the time compactne...
Rafiq Abuturab, Muhammad
2016-06-01
A new multiple color-image authentication system based on HSI (Hue-Saturation-Intensity) color space and QR decomposition in gyrator domains is proposed. In this scheme, original color images are converted from RGB (Red-Green-Blue) color spaces to HSI color spaces, divided into their H, S, and I components, and then obtained corresponding phase-encoded components. All the phase-encoded H, S, and I components are individually multiplied, and then modulated by random phase functions. The modulated H, S, and I components are convoluted into a single gray image with asymmetric cryptosystem. The resulting image is segregated into Q and R parts by QR decomposition. Finally, they are independently gyrator transformed to get their encoded parts. The encoded Q and R parts should be gathered without missing anyone for decryption. The angles of gyrator transform afford sensitive keys. The protocol based on QR decomposition of encoded matrix and getting back decoded matrix after multiplying matrices Q and R, enhances the security level. The random phase keys, individual phase keys, and asymmetric phase keys provide high robustness to the cryptosystem. Numerical simulation results demonstrate that this scheme is the superior than the existing techniques.
Zhang, Dong; Zhang, Xiaolei; Yuan, Jianzheng; Ke, Rui; Yang, Yan; Hu, Ying
2016-01-01
The Laplace-Fourier domain full waveform inversion can simultaneously restore both the long and intermediate short-wavelength information of velocity models because of its unique characteristics of complex frequencies. This approach solves the problem of conventional frequency-domain waveform inversion in which the inversion result is excessively dependent on the initial model due to the lack of low frequency information in seismic data. Nevertheless, the Laplace-Fourier domain waveform inversion requires substantial computational resources and long computation time because the inversion must be implemented on different combinations of multiple damping constants and multiple frequencies, namely, the complex frequencies, which are much more numerous than the Fourier frequencies. However, if the entire target model is computed on every complex frequency for the Laplace-Fourier domain inversion (as in the conventional frequency domain inversion), excessively redundant computation will occur. In the Laplace-Fourier domain waveform inversion, the maximum depth penetrated by the seismic wave decreases greatly due to the application of exponential damping to the seismic record, especially with use of a larger damping constant. Thus, the depth of the area effectively inverted on a complex frequency tends to be much less than the model depth. In this paper, we propose a method for quantitative estimation of the effective inversion depth in the Laplace-Fourier domain inversion based on the principle of seismic wave propagation and mathematical analysis. According to the estimated effective inversion depth, we can invert and update only the model area above the effective depth for every complex frequency without loss of accuracy in the final inversion result. Thus, redundant computation is eliminated, and the efficiency of the Laplace-Fourier domain waveform inversion can be improved. The proposed method was tested in numerical experiments. The experimental results show that
Multiple-image encryption based on phase mask multiplexing in fractional Fourier transform domain.
Liansheng, Sui; Meiting, Xin; Ailing, Tian
2013-06-01
A multiple-image encryption scheme is proposed based on the phase retrieval process and phase mask multiplexing in the fractional Fourier transform domain. First, each original gray-scale image is encoded into a phase only function by using the proposed phase retrieval process. Second, all the obtained phase functions are modulated into an interim, which is encrypted into the final ciphertext by using the fractional Fourier transform. From a plaintext image, a group of phase masks is generated in the encryption process. The corresponding decrypted image can be recovered from the ciphertext only with the correct phase mask group in the decryption process. Simulation results show that the proposed phase retrieval process has high convergence speed, and the encryption algorithm can avoid cross-talk; in addition, its encrypted capacity is considerably enhanced.
Zhong, Zhi; Qin, Haitao; Liu, Lei; Zhang, Yabin; Shan, Mingguang
2017-03-20
A novel approach for silhouette-free image encryption based on interference is proposed using discrete multiple-parameter fractional Fourier transform (DMPFrFT), which generalizes from fractional Fourier transform. An original image is firstly applied by chaotic pixel scrambling (CPS) and then encoded into the real part of a complex signal. Using interference principle, the complex signal generates three phase-only masks in DMPFrFT domain. The silhouette of the original image cannot be extracted using one or two of the three phase-only masks. The parameters of both CPS and DMPFrFT can also serve as encryption keys to extend the key space, which further enhance the level of cryptosystem security. Numerical simulations are demonstrated to show the feasibility and validity of this approach.
Singh, Hukum
2016-05-01
An optical color image encryption in the Fractional Wavelet Transform (FWT) domain is carried out. The original images are segregated into three colors components: R (red), G (green) and B (blue). After that the components are encrypted separately using double random phase encoding (DRPE) in the FWT domain. Random phase masks (RPMs) are used in the input as well as in Fourier plane. The images to be encrypted are transformed with the discrete wavelet transform (DWT), the resulting coefficients from the DWT are multiplied each one by masks different form RPM. Masks are independent each other and the results are applied an inverse discrete Wavelet Transform (IDWT), obtaining the encrypted images. The input images are recovered from their corresponding encrypted images by using the correct parameters of the FWT, and its digital implementation has been performed using MATLAB 7.6.0 (R2008a). The mother wavelet family and fractional orders associated with the FWT are extra keys that access difficulty an attacker; thereby the scheme is more secure as compared to conventional techniques. The sensitivity of proposed scheme is verified with encryption parameters, occlusions, and noise attacks.
Combining double random phase encoding for color image watermarking in quaternion gyrator domain
Shao, Zhuhong; Duan, Yuping; Coatrieux, Gouenou; Wu, Jiasong; Meng, Jinyu; Shu, Huazhong
2015-05-01
Quaternion representation of color image has attracted great attention due to its capability to treat holistically the three color channels. In a more general way, it has successfully been used in multi-channel signal processing applications over the past few decades. In this study, a joint encryption/watermarking system with more security based on double random phase encoding (DRPE) in quaternion gyrator transform domain is addressed. In the proposed scheme, an RGB-scale watermark image together with a grayscale watermark image or not is encoded into a quaternion matrix and encrypted through the DRPE, the encrypted data is then fused into the middle coefficients of the quaternion gyrator-transformed host image. In the process of extracting watermarks, it is impossible to retrieve them without authorized keys. Compared with the three channels independently processing approach implemented in fractional Fourier domain, the proposed algorithm achieves lower complexity by reason of avoiding repetitive operations. Experimental results have demonstrated the feasibility of the proposed algorithm and its superior performance in terms of noise robustness.
Directory of Open Access Journals (Sweden)
Qiuming Cheng
2007-06-01
Full Text Available The patterns shown on two-dimensional images (fields used in geosciences reflect the end products of geo-processes that occurred on the surface and in the subsurface of the Earth. Anisotropy of these types of patterns can provide information useful for interpretation of geo-processes and identification of features in the mapped area. Quantification of the anisotropy property is therefore essential for image processing and interpretation. This paper introduces several techniques newly developed on the basis of multifractal modeling in space, Fourier frequency, and eigen domains, respectively. A singularity analysis method implemented in the space domain can be used to quantify the intensity and anisotropy of local singularities. The second method, called S-A, characterizes the generalized scale invariance property of a field in the Fourier frequency domain. The third method characterizes the field using a power-law model on the basis of eigenvalues and eigenvectors of the field. The applications of these methods are demonstrated with a case study of Environment Scan Electric Microscope (ESEM microimages for identification of sphalerite (ZnS ore minerals from the Jinding Pb/Zn/Ag mineral deposit in Shangjiang District, Yunnan Province, China.
Convergence Properties of Generalized Fourier Series on a Parallel Hexagon Domain
Institute of Scientific and Technical Information of China (English)
WANG SHU-YUN; LIANG XUE-ZHANG; FU YAO; SUN XUE-NAN
2009-01-01
A new Rogosinski-type kernel function is constructed using kernel function of partial sums Sn(f; t) of generalized Fourier series on a parallel hexagon domain Ω associating with three-direction partition. We prove that an operator Wn(f; t) with the new kernel function converges uniformly to any continuous function f(t) ∈ C*(Ω) (the space of all continuous functions with period Ω) on Ω. Moreover, the convergence order of the operator is presented for the smooth approached function.
Fourier domain mode-locked swept source at 1050 nm based on a tapered amplifier
DEFF Research Database (Denmark)
Marschall, Sebastian; Klein, Thomas; Wieser, Wolfgang;
2010-01-01
While swept source optical coherence tomography (OCT) in the 1050 nm range is promising for retinal imaging, there are certain challenges. Conventional semiconductor gain media have limited output power, and the performance of high-speed Fourier domain mode-locked (FDML) lasers suffers from...... achieved stable FDML operation, exploiting the full bandwidth of the tapered amplifier despite high dispersion. The light source operates at a repetition rate of 116 kHz with an effective average output power in excess of 30 mW. With a total sweep range of 70 nm, we achieved an axial resolution of 15 μm...
Olivier, Scot S.; Werner, John S.; Zawadzki, Robert J.; Laut, Sophie P.; Jones, Steven M.
2010-09-07
This invention permits retinal images to be acquired at high speed and with unprecedented resolution in three dimensions (4.times.4.times.6 .mu.m). The instrument achieves high lateral resolution by using adaptive optics to correct optical aberrations of the human eye in real time. High axial resolution and high speed are made possible by the use of Fourier-domain optical coherence tomography. Using this system, we have demonstrated the ability to image microscopic blood vessels and the cone photoreceptor mosaic.
Watanabe, Yuuki; Itagaki, Toshiki
2009-01-01
Fourier domain optical coherence tomography (FD-OCT) requires resampling of spectrally resolved depth information from wavelength to wave number, and the subsequent application of the inverse Fourier transform. The display rates of OCT images are much slower than the image acquisition rates due to processing speed limitations on most computers. We demonstrate a real-time display of processed OCT images using a linear-in-wave-number (linear-k) spectrometer and a graphics processing unit (GPU). We use the linear-k spectrometer with the combination of a diffractive grating with 1200 lines/mm and a F2 equilateral prism in the 840-nm spectral region to avoid calculating the resampling process. The calculations of the fast Fourier transform (FFT) are accelerated by the GPU with many stream processors, which realizes highly parallel processing. A display rate of 27.9 frames/sec for processed images (2048 FFT size x 1000 lateral A-scans) is achieved in our OCT system using a line scan CCD camera operated at 27.9 kHz.
Analysis of collagen fiber domain organization by Fourier second harmonic generation microscopy
Ghazaryan, Ara; Tsai, Halley F.; Hayrapetyan, Gor; Chen, Wei-Liang; Chen, Yang-Fang; Jeong, Myung Yung; Kim, Chang-Seok; Chen, Shean-Jen; Dong, Chen-Yuan
2013-03-01
We present an automated and systematic two-dimensional discrete Fourier transform (2D-FFT) approach to analyze collagen fiber organization through the use of second harmonic generation (SHG) microscopy. Average orientations of individual domains and Ising-like order parameters introduced to characterize the correlation between orientations of adjacent domains may be used to quantitatively characterize fibrous tissues. Our approach was applied to analyze tissues including rat tail tendon, mouse skin, bovine corneas, and human corneas. We also show that collagen fiber organization in normal and keratokonus human corneas may be distinguished. The current approach may be used for the quantitative differentiation of SHG collagen fiber morphology in different tissues and may be applied for diagnostic purposes.
A method for estimating spatial resolution of real image in the Fourier domain
Mizutani, Ryuta; Takekoshi, Susumu; Inomoto, Chie; Nakamura, Naoya; Itokawa, Masanari; Arai, Makoto; Oshima, Kenichi; Takeuchi, Akihisa; Uesugi, Kentaro; Terada, Yasuko; Suzuki, Yoshio
2016-01-01
Spatial resolution is a fundamental parameter in structural sciences. In crystallography, the resolution is determined from the detection limit of high-angle diffraction in reciprocal space. In electron microscopy, correlation in the Fourier domain is used for estimating the resolution. In this paper, we report a method for estimating the spatial resolution of real images from a logarithmic intensity plot in the Fourier domain. The logarithmic intensity plots of test images indicated that the full width at half maximum of a Gaussian point-spread function can be estimated from the images. The spatial resolution of imaging X-ray microtomography using Fresnel zone-plate optics was also estimated with this method. A cross section of a test object visualized with the imaging microtomography indicated that square-wave patterns up to 120-nm pitch were resolved. The logarithmic intensity plot was calculated from a tomographic cross section of brain tissue. The full width at half maximum of the point spread function e...
Study of Anterior Chamber Aqueous Tube Shunt by Fourier-Domain Optical Coherence Tomography
Directory of Open Access Journals (Sweden)
Chunhui Jiang
2012-01-01
Full Text Available Purpose. This cross-sectional, observational study used Fourier-domain optical coherence tomography (OCT to examine the position, patency, and the interior entrance site of anterior chamber (AC aqueous tube shunts. Methods. The OCT, slitlamp biomicroscopy, and gonioscopy findings of 23 eyes of 18 patients with AC shunts were collected and compared. Results. OCT images demonstrated the shunt position and patency in all 23 eyes, and the details of the AC entrance in 16 eyes. The position of the tube varied, with the majority (14/23 on the surface of the iris. The exact position of the AC entrance relative to Schwalbe’s line (SL could be determined in 9 eyes (posterior to SL in 7 eyes, anterior in 2 eyes. At the AC entrance, growth of fibrous scar tissue was present between the tube and the corneal endothelium in all 16 eyes in which the entrance could be clearly visualized. It’s a new finding that could not be visualized by slitlamp examination or lower resolution OCT. Conclusion. Compared to slitlamp examination, Fourier-domain OCT of AC tube shunts provided more detailed anatomic information regarding the insertion level relative to SL, scar tissue between the tube and the corneal endothelium, and patency of the tube opening.
Subtle Solar Retinopathy Detected by Fourier-domain Optical Coherence Tomography
Directory of Open Access Journals (Sweden)
Ya-Hsin Kung
2010-07-01
Full Text Available Solar retinopathy is a retinal injury caused by direct or indirect sun-gazing and solar eclipse observation without protection. Subtle changes in the retinal damage might not be evident on fundus photography and fluorescein angiography. A 40-year-old veteran suffered from paracentral scotoma in his left eye shortly after unprotected solar eclipse observation about 1 month earlier. His visual acuity was 6/5 in the right eye and 6/6 in the left. Anterior segments were normal bilaterally. Dilated fundus examination, fluorescein angiography, and central visual field testing did not reveal any abnormal findings. Fourier-domain optical coherence tomography was used for evaluation, and a focal defect in the inner and outer segments of the photoreceptor layer band was noted in the paracentral region of the fovea in the left eye, with central foveal thickness of 198 μm. Solar retinopathy is preventable with adequate eye protection. Education should be reinforced to the public. In mildly affected individuals with subtle retinal damage, Fourier-domain optical coherence tomography could be a useful imaging tool to detect the disease.
Bessaih, Hakima
2015-04-01
The evolution Stokes equation in a domain containing periodically distributed obstacles subject to Fourier boundary condition on the boundaries is considered. We assume that the dynamic is driven by a stochastic perturbation on the interior of the domain and another stochastic perturbation on the boundaries of the obstacles. We represent the solid obstacles by holes in the fluid domain. The macroscopic (homogenized) equation is derived as another stochastic partial differential equation, defined in the whole non perforated domain. Here, the initial stochastic perturbation on the boundary becomes part of the homogenized equation as another stochastic force. We use the twoscale convergence method after extending the solution with 0 in the holes to pass to the limit. By Itô stochastic calculus, we get uniform estimates on the solution in appropriate spaces. In order to pass to the limit on the boundary integrals, we rewrite them in terms of integrals in the whole domain. In particular, for the stochastic integral on the boundary, we combine the previous idea of rewriting it on the whole domain with the assumption that the Brownian motion is of trace class. Due to the particular boundary condition dealt with, we get that the solution of the stochastic homogenized equation is not divergence free. However, it is coupled with the cell problem that has a divergence free solution. This paper represents an extension of the results of Duan and Wang (Comm. Math. Phys. 275:1508-1527, 2007), where a reaction diffusion equation with a dynamical boundary condition with a noise source term on both the interior of the domain and on the boundary was studied, and through a tightness argument and a pointwise two scale convergence method the homogenized equation was derived. © American Institute of Mathematical Sciences.
UND: unite-and-divide method in Fourier and Radon domains for line segment detection.
Shi, Daming; Gao, Junbin; Rahmdel, Payam S; Antolovich, Michael; Clark, Tony
2013-06-01
In this paper, we extend our previously proposed line detection method to line segmentation using a so-called unite-and-divide (UND) approach. The methodology includes two phases, namely the union of spectra in the frequency domain, and the division of the sinogram in Radon space. In the union phase, given an image, its sinogram is obtained by parallel 2D multilayer Fourier transforms, Cartesian-to-polar mapping and 1D inverse Fourier transform. In the division phase, the edges of butterfly wings in the neighborhood of every sinogram peak are firstly specified, with each neighborhood area corresponding to a window in image space. By applying the separated sinogram of each such windowed image, we can extract the line segments. The division Phase identifies the edges of butterfly wings in the neighborhood of every sinogram peak such that each neighborhood area corresponds to a window in image space. Line segments are extracted by applying the separated sinogram of each windowed image. Our experiments are conducted on benchmark images and the results reveal that the UND method yields higher accuracy, has lower computational cost and is more robust to noise, compared to existing state-of-the-art methods.
Institute of Scientific and Technical Information of China (English)
Wang Chuandan; Zhang Zhongpei; Li Shaoqian
2007-01-01
The method of FRactional Fourier Transform (FRFT) is introduced to Transform Domain Communication System (TDCS) for signal transforming in the paper after theoretical analysis. The method yields optimal Basis Function (BF) by FRFT with optimal transform angle. The TDCS using the proposed method has wider usable spectrum, stronger robustness and better ability of anti non-stationary jamming than using usual methods, such as Fourier Transform (FT), Auto Regressive (AR), Wavelet Transform (WT), etc. The main simulation results are as follows. First, the Bit Error Rate (BER) Pb is close to theoretical bound of no jamming no matter in single tone or in linear chirp interference. Second, the interference-to-signal ratio J/E is at least 12dB more than that of Direct Spread Spectrum System (DSSS) under the same BER if the spectrum hopping-to-signal ratio is 1:20 in chirp plus hopping interfering. Third, the Eb/No (when estimation difference is 90% between transmitter and receiver) is about 3.5dB or about 0.5dB (when estimation difference is 10% between transmitter and receiver) more than that of theoretical result when no estimation difference under Pb = 10-2.
Van der Jeught, Sam; Bradu, Adrian; Podoleanu, Adrian Gh
2010-01-01
Fourier domain optical coherence tomography (FD-OCT) requires either a linear-in-wavenumber spectrometer or a computationally heavy software algorithm to recalibrate the acquired optical signal from wavelength to wavenumber. The first method is sensitive to the position of the prism in the spectrometer, while the second method drastically slows down the system speed when it is implemented on a serially oriented central processing unit. We implement the full resampling process on a commercial graphics processing unit (GPU), distributing the necessary calculations to many stream processors that operate in parallel. A comparison between several recalibration methods is made in terms of performance and image quality. The GPU is also used to accelerate the fast Fourier transform (FFT) and to remove the background noise, thereby achieving full GPU-based signal processing without the need for extra resampling hardware. A display rate of 25 framessec is achieved for processed images (1,024 x 1,024 pixels) using a line-scan charge-coupled device (CCD) camera operating at 25.6 kHz.
Modeling and analysis of polarization effects in Fourier domain mode-locked lasers.
Jirauschek, Christian; Huber, Robert
2015-05-15
We develop a theoretical model for Fourier domain mode-locked (FDML) lasers in a non-polarization-maintaining configuration, which is the most widely used type of FDML source. This theoretical approach is applied to analyze a widely wavelength-swept FDML setup, as used for picosecond pulse generation by temporal compression of the sweeps. We demonstrate that good agreement between simulation and experiment can only be obtained by including polarization effects due to fiber bending birefringence, polarization mode dispersion, and cross-phase modulation into the theoretical model. Notably, the polarization dynamics are shown to have a beneficial effect on the instantaneous linewidth, resulting in improved coherence and thus compressibility of the wavelength-swept FDML output.
Fourier domain image fusion for differential X-ray phase-contrast breast imaging.
Coello, Eduardo; Sperl, Jonathan I; Bequé, Dirk; Benz, Tobias; Scherer, Kai; Herzen, Julia; Sztrókay-Gaul, Anikó; Hellerhoff, Karin; Pfeiffer, Franz; Cozzini, Cristina; Grandl, Susanne
2017-04-01
X-Ray Phase-Contrast (XPC) imaging is a novel technology with a great potential for applications in clinical practice, with breast imaging being of special interest. This work introduces an intuitive methodology to combine and visualize relevant diagnostic features, present in the X-ray attenuation, phase shift and scattering information retrieved in XPC imaging, using a Fourier domain fusion algorithm. The method allows to present complementary information from the three acquired signals in one single image, minimizing the noise component and maintaining visual similarity to a conventional X-ray image, but with noticeable enhancement in diagnostic features, details and resolution. Radiologists experienced in mammography applied the image fusion method to XPC measurements of mastectomy samples and evaluated the feature content of each input and the fused image. This assessment validated that the combination of all the relevant diagnostic features, contained in the XPC images, was present in the fused image as well.
Dispersion management for controlling image plane in Fourier-domain spectrally encoded endoscopy.
Merman, Michal; Yelin, Dvir
2011-02-28
Spectrally encoded endoscopy (SEE) uses single optical fiber and miniature diffractive optics to allow imaging through a miniature probe. Utilizing Fourier-domain interferometry, SEE was shown capable of video-rate three-dimensional imaging, albeit at limited depth of field due to the limited spectral resolution of the detection spectrometer. We show that by using dispersion management at the reference arm of the interferometer, the tilt and curvature of the field of view could be adjusted without modifying the endoscopic probe itself. By controlling the group velocity dispersion, this technique is demonstrated useful for imaging specimen regions which reside outside the system's depth of field. This approach could be used to improve usability, functionality and image quality of SEE without affecting probe size and flexibility.
Two-dimensional phase unwrapping in Doppler Fourier domain optical coherence tomography.
Wang, Yimin; Huang, David; Su, Ya; Yao, X Steve
2016-11-14
For phase-related imaging modalities using interferometric techniques, it is important to develop effective method to recover phase information that is mathematically wrapped. In this paper, we propose and demonstrate a two-dimensional (2D) method to achieve effective phase unwrapping in Doppler Fourier-domain (FD) optical coherence tomography (OCT), and recover the discontinuous phase distribution in retinal blood flow successfully for the first time in Doppler OCT studies. The proposed method is based on phase gradient approach in the axial dimension, with phase denoising performed through 2D window moving average in the sampled phase image using complex Doppler OCT data. The 2D unwrapping is carried out to correct phase discontinuities in the wrapped Doppler phase map, and the abrupt phase changes can be identified and corrected accurately. The proposed algorithm is computationally efficient and easy to be implemented.
Xia, Shaoyan; Huang, Yong; Peng, Shizhao; Wu, Yanfeng; Tan, Xiaodi
2016-08-01
Phase image in Fourier domain Doppler optical coherence tomography offers additional flow information of investigated samples, which provides valuable evidence towards accurate medical diagnosis. High quality phase images are thus desirable. We propose a noise reduction method for phase images by combining a synthetic noise estimation criteria based on local noise estimator (LNE) and distance median value (DMV) with anisotropic diffusion model. By identifying noise and signal pixels accurately and diffusing them with different coefficients respectively and adaptive iteration steps, we demonstrated the effectiveness of our proposed method in both phantom and mouse artery images. Comparison with other methods such as filtering method (mean, median filtering), wavelet method, probabilistic method and partial differential equation based methods in terms of peak signal-to-noise ratio (PSNR), equivalent number of looks (ENL) and contrast-to-noise ratio (CNR) showed the advantages of our method in reserving image energy and removing noise.
Calibration of Fourier domain short coherence interferometer for absolute distance measurements.
Montonen, R; Kassamakov, I; Hæggström, E; Österberg, K
2015-05-20
We calibrated and determined the measurement uncertainty of a custom-made Fourier domain short coherence interferometer operated in laboratory conditions. We compared the optical thickness of two thickness standards and three coverslips determined with our interferometer to the geometric thickness determined by SEM. Using this calibration data, we derived a calibration function with a 95% confidence level system uncertainty of (5.9×10(-3)r+2.3) μm, where r is the optical distance in μm, across the 240 μm optical measurement range. The confidence limit includes contributions from uncertainties in the optical thickness, geometric thickness, and refractive index measurements as well as uncertainties arising from cosine errors and thermal expansion. The results show feasibility for noncontacting absolute distance characterization with micrometer-level accuracy. This instrument is intended for verifying the alignment of the discs of an accelerating structure in the possible future compact linear collider.
Broadband Fourier domain mode-locked laser for optical coherence tomography at 1060 nm
DEFF Research Database (Denmark)
Marschall, Sebastian; Klein, Thomas; Wieser, Wolfgang
2012-01-01
, enable acquisition of densely sampled three-dimensional datasets covering a wide field of view. However, semiconductor optical amplifiers (SOAs)-the typical laser gain media for swept sources-for the 1060nm band could until recently only provide relatively low output power and bandwidth. We have......Optical coherence tomography (OCT) in the 1060nm range is interesting for in vivo imaging of the human posterior eye segment (retina, choroid, sclera) due to low absorption in water and deep penetration into the tissue. Rapidly tunable light sources, such as Fourier domain mode-locked (FDML) lasers...... implemented an FDML laser using a new SOA featuring broad gain bandwidth and high output power. The output spectrum coincides with the wavelength range of minimal water absorption, making the light source ideal for OCT imaging of the posterior eye segment. With a moderate SOA current (270 mA) we achieve up...
Fernández-Vigo, J I; Fernández-Vigo, C; Martínez de la Casa, J M; Sáenz-Francés, F; Santos-Bueso, E; García Feijóo, J; Fernández-Vigo, J A
2016-02-01
To study the structures of the iridocorneal angle using anterior segment optical coherence tomography (OCT) defining their tomographic characteristics and quantifying their identification frequency. A cross-sectional study was performed on 267 right eyes of 267 consecutive healthy patients. Fourier domain OCT RTVue (Optovue Inc, CA, EE. UU.) was used to examine the iridocorneal angle in the nasal and temporal sectors. The structures evaluated were: Sclerocorneal limbus, sclerocorneal transition, Schwalbe's line, trabecular meshwork, Schlemm's canal, scleral spur, and angular recess. Within and between agreements to identify structures were calculated using Cohen's kappa coefficient. The mean age was 41.3 ± 14.3 years (range 20-80), with 57% being women. The sclerocorneal limbus, sclerocorneal transition, and Schwalbe's line were identified by 98.7, 97 and 93.4% of the images, respectively, with the trabecular meshwork and Schlemm's canal being identified in 91% of cases. The scleral spur could be identified in 85.4%, and the angular recess in 74.5%. There was no difference in the identification between the temporal and nasal sectors. Within and between agreement was k=0.92 and k=0.88, respectively, in the identification of the structures of the total images studied. Fourier domain OCT is a reliable technique for the identification of the structures of the iridocorneal angle, among which can be highlighted are, the trabecular meshwork, Schlemm's canal, scleral spur, and Schwalbe's line. Copyright © 2015 Sociedad Española de Oftalmología. Published by Elsevier España, S.L.U. All rights reserved.
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
This letter deals with the frequency domain Blind Source Separation of Convolutive Mixtures(CMBSS).From the frequency representation of the"overlap and save",a Weighted General Discrete Fourier Transform (WGDFT) is derived to replace the traditional Discrete Fourier Transform (DFT).The mixing matrix on each frequency bin could be estimated more precisely from WGDFT coefficients than from DFT coefficients,which improves separation performance.Simulation results verify the validity of WGDFT for frequency domain blind source separation of convolutive mixtures.
Yuan, Lin; Ran, Qiwen; Zhao, Tieyu
2017-02-01
In this paper an image authentication scheme is proposed based on double-image encryption and partial phase decryption in nonseparable Fractional Fourier transform domain. Two original images are combined and transformed into the nonseparable fractional Fourier domain. Only part of the phase information of the encrypted result is kept for decryption while the rest part of phase and all the amplitude information are discarded. The two recovered images are hardly recognized by visual inspection but can be authenticated by the nonlinear correlation algorithm. The numerical simulations demonstrate the viability and validity of the proposed image authentication scheme.
The Wavenumber Algorithm: Fast Fourier-Domain Imaging Using Full Matrix Capture
Hunter, A. J.; Drinkwater, B. W.; Wilcox, P. D.
2009-03-01
We develop a Fourier-domain approach to full matrix imaging based on the wavenumber algorithm used in synthetic aperture radar and sonar. The extension to the wavenumber algorithm for full matrix capture is described and the performance of the new algorithm is compared to the total focusing method (TFM), which we use as a representative benchmark for the time-domain algorithms. The wavenumber algorithm provides a mathematically rigorous solution to the inverse problem for the assumed forward wave propagation model, whereas the TFM employs heuristic delay-and-sum beamforming. Consequently, the wavenumber algorithm has an improved point-spread function and provides better imagery. However, the major advantage of the wavenumber algorithm is its superior computational performance. For large arrays and images, the wavenumber algorithm is several orders of magnitude faster than the TFM. On the other hand, the key advantage of the TFM is its flexibility. The wavenumber algorithm requires a regularly sampled linear array, while the TFM can handle arbitrary imaging geometries. The TFM and the wavenumber algorithm are compared using simulated and experimental data.
Artifacts Induced by Selective Blanking of Time-Domain Data in Fourier Transform Mass Spectrometry
Xian, Feng; Valeja, Santosh G.; Beu, Steve C.; Hendrickson, Christopher L.; Marshall, Alan G.
2013-11-01
Fourier transform mass spectrometry (FTMS) of the isolated isotopic distribution for a highly charged biomolecule produces time-domain signal containing large amplitude signal "beats" separated by extended periods of much lower signal magnitude. Signal-to-noise ratio for data sampled between beats is low because of destructive interference of the signals induced by members of the isotopic distribution. Selective blanking of the data between beats has been used to increase spectral signal-to-noise ratio. However, blanking also eliminates signal components and, thus, can potentially distort the resulting FT spectrum. Here, we simulate the time-domain signal from a truncated isotopic distribution for a single charge state of an antibody. Comparison of the FT spectra produced with or without blanking and with or without added noise clearly show that blanking does not improve mass accuracy and introduces spurious peaks at both ends of the isotopic distribution (thereby making it more difficult to identify posttranslational modifications and/or adducts). Although the artifacts are reduced by use of multiple Gaussian (rather than square wave) windowing, blanking appears to offer no advantages for identifying true peaks or for mass measurement.
Li, Jian; Bloch, Pavel; Xu, Jing; Sarunic, Marinko V; Shannon, Lesley
2011-05-01
Fourier domain optical coherence tomography (FD-OCT) provides faster line rates, better resolution, and higher sensitivity for noninvasive, in vivo biomedical imaging compared to traditional time domain OCT (TD-OCT). However, because the signal processing for FD-OCT is computationally intensive, real-time FD-OCT applications demand powerful computing platforms to deliver acceptable performance. Graphics processing units (GPUs) have been used as coprocessors to accelerate FD-OCT by leveraging their relatively simple programming model to exploit thread-level parallelism. Unfortunately, GPUs do not "share" memory with their host processors, requiring additional data transfers between the GPU and CPU. In this paper, we implement a complete FD-OCT accelerator on a consumer grade GPU/CPU platform. Our data acquisition system uses spectrometer-based detection and a dual-arm interferometer topology with numerical dispersion compensation for retinal imaging. We demonstrate that the maximum line rate is dictated by the memory transfer time and not the processing time due to the GPU platform's memory model. Finally, we discuss how the performance trends of GPU-based accelerators compare to the expected future requirements of FD-OCT data rates.
DEFF Research Database (Denmark)
Mulvad, Hans Christian Hansen; Guan, P.; Kasai, K.
2010-01-01
We demonstrate pre-scaled 40 GHz clock recovery from 640 Gbit/s optical time-division-multiplexed data using LiNbO$_3$ modulators, based on time-domain optical Fourier transformation and optical filtering. The clock recovery is used in a 640 Gbit/s error-free transmission over 300 km....
DEFF Research Database (Denmark)
Hu, Hao; Kong, Deming; Palushani, Evarist;
2013-01-01
320 Gb/s Nyquist-OTDM is generated by rectangular filtering with a bandwidth of 320 GHz and received by polarization-insensitive time-domain optical Fourier transformation (TD-OFT) followed by passive filtering. After the time-to-frequency mapping in the TD-OFT, the Nyquist-OTDM is converted...
Iizuka, Masayuki; Kariya, Makoto; Uehara, Shinobu; Nakashima, Yoshio; Takamatsu, Mamoru
2003-05-01
A blue white He-Cd laser composed of three R/G/B component beams in place of He-Ne laser is directly applied to fabricate the optical Fourier transform hologram (OFTH) using the red sensitive silver halide material (SO-253 film) for holography. As a result, the red beams play an important role as the coherent beams in the fabrication of OFTH. A green solid state laser is applied to fabricate the OFTH using the same film for holography. The visual appearance of reconstruted color images caused by He-Cd laser is discussed in contrast to that of an ordinary OFTH which can be made using the He-Ne laser and solid state laser. The visual color effect using the He-Cd laser is checked from the viewpoint of the relative real size and its place in the OFTH, and the visual depth sensation of overlapped ghost images called cross-talk in the Fresnel hologram. The purpose using a commercially available software such as HSL color model is to carry out the intuitive modification of overlapped and deteriorated color images in the digital reconstruction of OFTH and Fresnel hologram.
Application of Fourier Domain OCT Imaging Technology to the Anterior Segment of the Human Eye
Wojtkowski, Maciej; Marcos, Susana; Ortiz, Sergio; Grulkowski, Ireneusz
The anterior segment is the front part of the human eye, which forms the optical system and hence directly impacts vision. Traumatic or pathological changes in the anterior segment may lead to vision loss and, in some cases, even blindness. Since the eighteenth century, optical instrumentation for measuring and imaging the anterior segment of the human eye has been developing along with modern ophthalmology. The application of OCT to the anterior segment imaging is particularly of interest, since this could potentially provide substantial complementary information regarding the large-scale architecture of the cornea and the crystalline lens, or on small portions of tissue imaged with high spatial resolutions comparable to regular microscopy. Especially an introduction of Fourier domain detection in OCT has opened new frontiers in OCT ophthalmic applications. The resultant substantial speed improvement enables rapid image acquisition, helping to reduce artifacts due to patient motion. Thus, it is currently possible to perform high-speed, in vivo, three-dimensional volumetric imaging over large scales within a reasonable time limit and without reducing system sensitivity. This chapter describes the state-of the art OCT technology dedicated to anterior segment imaging and indicates all important parameters which are required for optimization of the performance of OCT instrument.
Directory of Open Access Journals (Sweden)
Ricardo J. Cumba
2012-01-01
Full Text Available Purpose. To evaluate intraobserver and interobserver agreement in locating the scleral spur landmark (SSL and anterior chamber angle measurements obtained using Fourier Domain Anterior Segment Optical Coherence Tomography (ASOCT images. Methods. Two independent, masked observers (SR and AZC identified SSLs on ASOCT images from 31 eyes with open and nonopen angles. A third independent reader, NPB, adjudicated SSL placement if identifications differed by more than 80 μm. Nine months later, SR reidentified SSLs. Intraobserver and interobserver agreement in SSL placement, trabecular-iris space area (TISA750, and angle opening distance (AOD750 were calculated. Results. In 84% of quadrants, SR’s SSL placements during 2 sessions were within 80 μm in both the X- and Y-axes, and in 77% of quadrants, SR and AZC were within 80 μm in both axes. In adjudicated images, 90% of all quadrants were within 80 μm, 88% in nonopen-angle eyes, and 92% in open-angle eyes. The intraobserver and interobserver correlation coefficients (with and without adjudication were above 0.9 for TISA750 and AOD750 for all quadrants. Conclusions. Reproducible identification of the SSL from images obtained with FD-ASOCT is possible. The ability to identify the SSL allows reproducible measurement of the anterior chamber angle using TISA750 and AOD750.
Directory of Open Access Journals (Sweden)
Mohammed Rigi
2016-01-01
Full Text Available Purpose. To evaluate interobserver, intervisit, and interinstrument agreements for gonioscopy and Fourier domain anterior segment optical coherence tomography (FD ASOCT for classifying open and narrow angle eyes. Methods. Eighty-six eyes with open or narrow anterior chamber angles were included. The superior angle was classified open or narrow by 2 of 5 glaucoma specialists using gonioscopy and imaged by FD ASOCT in the dark. The superior angle of each FD ASOCT image was graded as open or narrow by 2 masked readers. The same procedures were repeated within 6 months. Kappas for interobserver and intervisit agreements for each instrument and interinstrument agreements were calculated. Results. The mean age was 50.9 (±18.4 years. Interobserver agreements were moderate to good for both gonioscopy (0.57 and 0.69 and FD ASOCT (0.58 and 0.75. Intervisit agreements were moderate to excellent for both gonioscopy (0.53 to 0.86 and FD ASOCT (0.57 and 0.85. Interinstrument agreements were fair to good (0.34 to 0.63, with FD ASOCT classifying more angles as narrow than gonioscopy. Conclusions. Both gonioscopy and FD ASOCT examiners were internally consistent with similar interobserver and intervisit agreements for angle classification. Agreement between instruments was fair to good, with FD ASOCT classifying more angles as narrow than gonioscopy.
3D homogeneity study in PMMA layers using a Fourier domain OCT system
Briones-R., Manuel de J.; Torre-Ibarra, Manuel H. De La; Tavera, Cesar G.; Luna H., Juan M.; Mendoza-Santoyo, Fernando
2016-11-01
Micro-metallic particles embedded in polymers are now widely used in several industrial applications in order to modify the mechanical properties of the bulk. A uniform distribution of these particles inside the polymers is highly desired for instance, when a biological backscattering is simulated or a bio-framework is designed. A 3D Fourier domain optical coherence tomography system to detect the polymer's internal homogeneity is proposed. This optical system has a 2D camera sensor array that records a fringe pattern used to reconstruct with a single shot the tomographic image of the sample. The system gathers the full 3D tomographic and optical phase information during a controlled deformation by means of a motion linear stage. This stage avoids the use of expensive tilting stages, which in addition are commonly controlled by piezo drivers. As proof of principle, a series of different deformations were proposed to detect the uniform or non-uniform internal deposition of copper micro particles. The results are presented as images coming from the 3D tomographic micro reconstruction of the samples, and the 3D optical phase information that identifies the in-homogeneity regions within the Poly methyl methacrylate (PMMA) volume.
Picosecond pulses from wavelength-swept continuous-wave Fourier domain mode-locked lasers.
Eigenwillig, Christoph M; Wieser, Wolfgang; Todor, Sebastian; Biedermann, Benjamin R; Klein, Thomas; Jirauschek, Christian; Huber, Robert
2013-01-01
Ultrafast lasers have a crucial function in many fields of science; however, up to now, high-energy pulses directly from compact, efficient and low-power semiconductor lasers are not available. Therefore, we introduce a new approach based on temporal compression of the continuous-wave, wavelength-swept output of Fourier domain mode-locked lasers, where a narrowband optical filter is tuned synchronously to the round-trip time of light in a kilometre-long laser cavity. So far, these rapidly swept lasers enabled orders-of-magnitude speed increase in optical coherence tomography. Here we report on the generation of ~60-70 ps pulses at 390 kHz repetition rate. As energy is stored optically in the long-fibre delay line and not as population inversion in the laser-gain medium, high-energy pulses can now be generated directly from a low-power, compact semiconductor-based oscillator. Our theory predicts subpicosecond pulses with this new technique in the future.
Fourier domain mode-locked swept source at 1050 nm based on a tapered amplifier.
Marschall, Sebastian; Klein, Thomas; Wieser, Wolfgang; Biedermann, Benjamin R; Hsu, Kevin; Hansen, Kim P; Sumpf, Bernd; Hasler, Karl-Heinz; Erbert, Götz; Jensen, Ole B; Pedersen, Christian; Huber, Robert; Andersen, Peter E
2010-07-19
While swept source optical coherence tomography (OCT) in the 1050 nm range is promising for retinal imaging, there are certain challenges. Conventional semiconductor gain media have limited output power, and the performance of high-speed Fourier domain mode-locked (FDML) lasers suffers from chromatic dispersion in standard optical fiber. We developed a novel light source with a tapered amplifier as gain medium, and investigated the FDML performance comparing two fiber delay lines with different dispersion properties. We introduced an additional gain element into the resonator, and thereby achieved stable FDML operation, exploiting the full bandwidth of the tapered amplifier despite high dispersion. The light source operates at a repetition rate of 116 kHz with an effective average output power in excess of 30 mW. With a total sweep range of 70 nm, we achieved an axial resolution of 15 microm in air (approximately 11 microm in tissue) in OCT measurements. As our work shows, tapered amplifiers are suitable gain media for swept sources at 1050 nm with increased output power, while high gain counteracts dispersion effects in an FDML laser.
Least-squares fitting of time-domain signals for Fourier transform mass spectrometry.
Aushev, Tagir; Kozhinov, Anton N; Tsybin, Yury O
2014-07-01
To advance Fourier transform mass spectrometry (FTMS)-based molecular structure analysis, corresponding development of the FTMS signal processing methods and instrumentation is required. Here, we demonstrate utility of a least-squares fitting (LSF) method for analysis of FTMS time-domain (transient) signals. We evaluate the LSF method in the analysis of single- and multiple-component experimental and simulated ion cyclotron resonance (ICR) and Orbitrap FTMS transient signals. Overall, the LSF method allows one to estimate the analytical limits of the conventional instrumentation and signal processing methods in FTMS. Particularly, LSF provides accurate information on initial phases of sinusoidal components in a given transient. For instance, the phase distribution obtained for a statistical set of experimental transients reveals the effect of the first data-point problem in FT-ICR MS. Additionally, LSF might be useful to improve the implementation of the absorption-mode FT spectral representation for FTMS applications. Finally, LSF can find utility in characterization and development of filter-diagonalization method (FDM) MS.
Baumann, Bernhard; Choi, WooJhon; Potsaid, Benjamin; Huang, David; Duker, Jay S; Fujimoto, James G
2012-04-23
Polarization sensitive optical coherence tomography (PS-OCT) is a functional imaging method that provides additional contrast using the light polarizing properties of a sample. This manuscript describes PS-OCT based on ultrahigh speed swept source / Fourier domain OCT operating at 1050 nm at 100 kHz axial scan rates using single mode fiber optics and a multiplexing approach. Unlike previously reported PS-OCT multiplexing schemes, the method uses a passive polarization delay unit and does not require active polarization modulating devices. This advance decreases system cost and avoids complex synchronization requirements. The polarization delay unit was implemented in the sample beam path in order to simultaneously illuminate the sample with two different polarization states. The orthogonal polarization components for the depth-multiplexed signals from the two input states were detected using dual balanced detection. PS-OCT images were computed using Jones calculus. 3D PS-OCT imaging was performed in the human and rat retina. In addition to standard OCT images, PS-OCT images were generated using contrast form birefringence and depolarization. Enhanced tissue discrimination as well as quantitative measurements of sample properties was demonstrated using the additional contrast and information contained in the PS-OCT images.
Quantization-Based Digital Audio Watermarking in Discrete Fourier Transform Domain
Directory of Open Access Journals (Sweden)
Senbin Yang
2010-04-01
Full Text Available To explore the principle and performances of Quantization Index Modulation (QIM watermarking algorithm, the realization schemes of this algorithm in Discrete Fourier Transform (DFT domain are classified into three types according to the differences of quantizer parameters, and then the illustrative diagrams of these schemes are given, so the properties of transparency, robustness and capacity of each scheme are concluded. The scheme with best distortion-robustness trade-off is found on that basis. The more efficient embedding and extracting formulas of this scheme are given, and the performances are researched by theoretical analysis rather than computer simulation. The conclusions show that the transparency is in proportion to the square of quantization step and small DFT coefficient leads to poor transparency. The robustness to Additive White Gaussian Noise (AWGN only relates to the quantization step and the algorithm is susceptible to amplitude scale and resampling attacks. The possible capacity is Fo/2 bits per second, which can satisfy various watermarking applications. To improve the robustness, an adaptive quantization algorithm based on masking properties of the Human Auditory System (HAS is proposed at the end of this paper, and the algorithm is evaluated in the analog channel environment and its robustness is proved by the results.
Huang, Yong; Tong, Dedi; Zhu, Shan; Wu, Lehao; Ibrahim, Zuhaib; Lee, WP Andrew; Brandacher, Gerald; Kang, Jin U.
2014-03-01
Vascular and microvascular anastomosis are critical components of reconstructive microsurgery, vascular surgery and transplant surgery. Imaging modality that provides immediate, real-time in-depth view and 3D structure and flow information of the surgical site can be a great valuable tool for the surgeon to evaluate surgical outcome following both conventional and innovative anastomosis techniques, thus potentially increase the surgical success rate. Microvascular anastomosis for vessels with outer diameter smaller than 1.0 mm is extremely challenging and effective evaluation of the outcome is very difficult if not impossible using computed tomography (CT) angiograms, magnetic resonance (MR) angiograms and ultrasound Doppler. Optical coherence tomography (OCT) is a non-invasive high-resolution (micron level), high-speed, 3D imaging modality that has been adopted widely in biomedical and clinical applications. Phaseresolved Doppler OCT that explores the phase information of OCT signals has been shown to be capable of characterizing dynamic blood flow clinically. In this work, we explore the capability of Fourier domain Doppler OCT as an evaluation tool to detect commonly encountered post-operative complications that will cause surgical failure and to confirm positive result with surgeon's observation. Both suture and cuff based techniques were evaluated on the femoral artery and vein in the rodent model.
Zhang, Kang
2011-12-01
In this dissertation, real-time Fourier domain optical coherence tomography (FD-OCT) capable of multi-dimensional micrometer-resolution imaging targeted specifically for microsurgical intervention applications was developed and studied. As a part of this work several ultra-high speed real-time FD-OCT imaging and sensing systems were proposed and developed. A real-time 4D (3D+time) OCT system platform using the graphics processing unit (GPU) to accelerate OCT signal processing, the imaging reconstruction, visualization, and volume rendering was developed. Several GPU based algorithms such as non-uniform fast Fourier transform (NUFFT), numerical dispersion compensation, and multi-GPU implementation were developed to improve the impulse response, SNR roll-off and stability of the system. Full-range complex-conjugate-free FD-OCT was also implemented on the GPU architecture to achieve doubled image range and improved SNR. These technologies overcome the imaging reconstruction and visualization bottlenecks widely exist in current ultra-high speed FD-OCT systems and open the way to interventional OCT imaging for applications in guided microsurgery. A hand-held common-path optical coherence tomography (CP-OCT) distance-sensor based microsurgical tool was developed and validated. Through real-time signal processing, edge detection and feed-back control, the tool was shown to be capable of track target surface and compensate motion. The micro-incision test using a phantom was performed using a CP-OCT-sensor integrated hand-held tool, which showed an incision error less than +/-5 microns, comparing to >100 microns error by free-hand incision. The CP-OCT distance sensor has also been utilized to enhance the accuracy and safety of optical nerve stimulation. Finally, several experiments were conducted to validate the system for surgical applications. One of them involved 4D OCT guided micro-manipulation using a phantom. Multiple volume renderings of one 3D data set were
Directory of Open Access Journals (Sweden)
Zeng Gengsheng L
2012-09-01
Full Text Available Abstract Background Compared with static imaging, dynamic emission computed tomographic imaging with compartment modeling can quantify in vivo physiologic processes, providing useful information about molecular disease processes. Dynamic imaging involves estimation of kinetic rate parameters. For multi-compartment models, kinetic parameter estimation can be computationally demanding and problematic with local minima. Methods This paper offers a new perspective to the compartment model fitting problem where Fourier linear system theory is applied to derive closed-form formulas for estimating kinetic parameters for the two-compartment model. The proposed Fourier domain estimation method provides a unique solution, and offers very different noise response as compared to traditional non-linear chi-squared minimization techniques. Results The unique feature of the proposed Fourier domain method is that only low frequency components are used for kinetic parameter estimation, where the DC (i.e., the zero frequency component in the data is treated as the most important information, and high frequency components that tend to be corrupted by statistical noise are discarded. Computer simulations show that the proposed method is robust without having to specify the initial condition. The resultant solution can be fine tuned using the traditional iterative method. Conclusions The proposed Fourier-domain estimation method has closed-form formulas. The proposed Fourier-domain curve-fitting method does not require an initial condition, it minimizes a quadratic objective function and a closed-form solution can be obtained. The noise is easier to control, simply by discarding the high frequency components, and emphasizing the DC component.
Yang, J; Chan, E H W; Wang, X; Feng, X; Guan, B
2015-05-04
An all-optical photonic microwave phase shifter that can realize a continuous 360° phase shift over a wide frequency range is presented. It is based on the new concept of controlling the amplitude and phase of the two RF modulation sidebands via a Fourier-domain optical processor. The operating frequency range of the phase shifter is largely increased compared to the previously reported Fourier-domain optical processor based phase shifter that uses only one RF modulation sideband. This is due to the extension of the lower RF operating frequency by designing the amplitude and phase of one of the RF modulation sidebands while the other sideband is designed to realize the required RF signal phase shift. The two-sideband amplitude-and-phase-control based photonic microwave phase shifter has a simple structure as it only requires a single laser source, a phase modulator, a Fourier-domain optical processor and a single photodetector. Investigation on the bandwidth limitation problem in the conventional Fourier-domain optical processor based phase shifter is presented. Comparisons between the measured phase shifter output RF amplitude and phase responses with theory, which show excellent agreement, are also presented for the first time. Experimental results demonstrate the full -180° to + 180° phase shift with little RF signal amplitude variation of less than 3 dB and with a phase deviation of less than 4° over a 7.5 GHz to 26.5 GHz frequency range, and the phase shifter exhibits a long term stable performance.
OTDM-to-WDM Conversion of Complex Modulation Formats by Time-Domain Optical Fourier Transformation
DEFF Research Database (Denmark)
Palushani, Evarist; Richter, T.; Ludwig, R.
2012-01-01
We demonstrate the utilization of the optical Fourier transform technique for serial-to-parallel conversion of 64×10-GBd OTDM data tributaries with complex modulation formats into 50-GHz DWDM grid without loss of phase and amplitude information.......We demonstrate the utilization of the optical Fourier transform technique for serial-to-parallel conversion of 64×10-GBd OTDM data tributaries with complex modulation formats into 50-GHz DWDM grid without loss of phase and amplitude information....
Directory of Open Access Journals (Sweden)
Yong Huang
Full Text Available To demonstrate the feasibility of a miniature handheld optical coherence tomography (OCT imager for real time intraoperative vascular patency evaluation in the setting of super-microsurgical vessel anastomosis.A novel handheld imager Fourier domain Doppler optical coherence tomography based on a 1.3-µm central wavelength swept source for extravascular imaging was developed. The imager was minimized through the adoption of a 2.4-mm diameter microelectromechanical systems (MEMS scanning mirror, additionally a 12.7-mm diameter lens system was designed and combined with the MEMS mirror to achieve a small form factor that optimize functionality as a handheld extravascular OCT imager. To evaluate in-vivo applicability, super-microsurgical vessel anastomosis was performed in a mouse femoral vessel cut and repair model employing conventional interrupted suture technique as well as a novel non-suture cuff technique. Vascular anastomosis patency after clinically successful repair was evaluated using the novel handheld OCT imager.With an adjustable lateral image field of view up to 1.5 mm by 1.5 mm, high-resolution simultaneous structural and flow imaging of the blood vessels were successfully acquired for BALB/C mouse after orthotopic hind limb transplantation using a non-suture cuff technique and BALB/C mouse after femoral artery anastomosis using a suture technique. We experimentally quantify the axial and lateral resolution of the OCT to be 12.6 µm in air and 17.5 µm respectively. The OCT has a sensitivity of 84 dB and sensitivity roll-off of 5.7 dB/mm over an imaging range of 5 mm. Imaging with a frame rate of 36 Hz for an image size of 1000(lateral×512(axial pixels using a 50,000 A-lines per second swept source was achieved. Quantitative vessel lumen patency, lumen narrowing and thrombosis analysis were performed based on acquired structure and Doppler images.A miniature handheld OCT imager that can be used for intraoperative evaluation of
NOVEL COLOR FILTER ARRAY DEMOSAICING IN FREQUENCY DOMAIN WITH SPATIAL REFINEMENT
Directory of Open Access Journals (Sweden)
R. Niruban
2014-01-01
Full Text Available The main idea behind wavelet based demosaicing with spatial refinement is to reconstruct the full resolution color image from the mosaiced image. In this study, a new effective wavelet based demosaicing algorithm for interpolating the missing color components in Bayer’s Color Filter Array (CFA pattern is proposed. This interpolation technique uses the interchannel correlation among the high frequency subbands to determine the missing pixels in each color channel, followed by a refining step in spatial domain which uses non-iterative technique that enforces color difference rule with fewer computations. As a result, the proposed demosaicing method yields better performance than bilinear, edge based and subband based demosaicing methods.
Gorcea, Mihaela; Hadgraft, Jonathan; Moore, David J; Lane, Majella E
2012-10-01
The current work describes thermotropic and kinetic Fourier transform infrared (FTIR) spectroscopy studies of lipid dynamics and domain formation in normal and ceramide (CER) deficient lipid samples designed as simple models of the stratum corneum (SC). For the first time, this work focuses on the time dependence of lipid reorganization and domain formation in CER deficient models. By utilizing deuterated fatty acid (FA) and simultaneously monitoring the methylene vibrational modes of both CER and FA chains these experiments follow the time evolution of lipid organization in these SC lipid models following an external stress. Kinetic and thermotropic experiments demonstrate differences in both CER and FA chain fluidity and ordered domain formation with decreased levels of CER. In the CER deficient model, the formation of CER orthorhombic domains is retarded compared to the normal model. Furthermore, there is little evidence of hexongally packed (or mixed) FA domains in the CER deficient model compared to the models of normal SC. These data demonstrate that barrier lipid organization, in terms of ceramide domain formation, is altered in the ceramide deficient model. This work highlights the successful development of an experimental methodology to study time dependent changes in lipid biophysics in simple SC model membranes and suggests this approach will prove useful for understanding some of the biophysical changes that underlie impaired physiological barrier function in diseased skin. Copyright © 2011 Elsevier B.V. All rights reserved.
Private anonymous fingerprinting for color images in the wavelet domain
Abdul, W.; Gaborit, P.; Carré, P.
2010-01-01
An online buyer of multimedia content does not want to reveal his identity or his choice of multimedia content whereas the seller or owner of the content does not want the buyer to further distribute the content illegally. To address these issues we present a new private anonymous fingerprinting protocol. It is based on superposed sending for communication security, group signature for anonymity and traceability and single database private information retrieval (PIR) to allow the user to get an element of the database without giving any information about the acquired element. In the presence of a semi-honest model, the protocol is implemented using a blind, wavelet based color image watermarking scheme. The main advantage of the proposed protocol is that both the user identity and the acquired database element are unknown to any third party and in the case of piracy, the pirate can be identified using the group signature scheme. The robustness of the watermarking scheme against Additive White Gaussian Noise is also shown.
Steiner, Patrick; Meier, Christoph; Koch, Volker M
2010-12-20
We demonstrate depth-resolved spectral absorption measurements in the wavelength range from 750 to 850 nm using a broadband light source consisting of three spectrally shifted superluminescent light-emitting diode modules and a low-cost spectrometer-based Fourier-domain optical coherence tomography system. We present the theoretical model and experimental verification of interferences between autocorrelation terms and the signal carrying cross-correlation terms, strongly affecting the absorption measurements. A simple background subtraction, minimizing the artifacts caused by the interferences of autocorrelation and cross-correlation terms, is presented.
High-speed polarization-sensitive OCT at 1060 nm using a Fourier domain mode-locked swept source
DEFF Research Database (Denmark)
Marschall, Sebastian; Torzicky, Teresa; Klein, Thomas;
2012-01-01
, polarization-maintaining or depolarizing areas within the sample. This information can be used to distinguish retinal layers and structures with different polarization properties. High imaging speed is crucial for imaging ocular structures in vivo in order to minimize motion artifacts while acquiring...... sufficiently large datasets. Here, we demonstrate PS-OCT imaging at 350 kHz A-scan rate using a two-channel PS-OCT system in conjunction with a Fourier domain mode-locked laser. The light source spectrum spans up to 100nm around the water absorption minimum at 1060 nm. By modulating the laser pump current, we...
Encryption of color images using MSVD in DCST domain
Kumar, Manoj; Vaish, Ankita
2017-01-01
In this paper, a new image encryption and decryption algorithm based on Multiresolution Singular Value Decomposition (MSVD) and Discrete Cosine Stockwell Transform (DCST) is proposed. An original image is first transformed in DCST domain and then decomposed into four subbands using MSVD, all the four subbands are further decomposed into four subimages according to their indexing and masked by the parameters generated by MSVD. We have used number of bands of DCST, arrangement of MSVD subbands, arrangement of various subimages obtained from MSVD subbands, values and arrangement of a 4×4 matrix generated by MSVD and the arrangement of masked subimages as encryption and decryption keys. To ensure the correct decryption of encrypted image, it is indeed necessary to have correct knowledge of all keys in correct order along with their exact values. If all the keys are correct but a single key is wrong even though it would be almost impossible to guess the original image. The efficiency of proposed algorithm is evaluated by comparing it with some recent published works and it is evident from the experimental results and analysis that the proposed algorithm can transmit the images more securely and efficiently over the network.
Xu, Daguang; Huang, Yong; Kang, Jin U
2014-06-16
We implemented the graphics processing unit (GPU) accelerated compressive sensing (CS) non-uniform in k-space spectral domain optical coherence tomography (SD OCT). Kaiser-Bessel (KB) function and Gaussian function are used independently as the convolution kernel in the gridding-based non-uniform fast Fourier transform (NUFFT) algorithm with different oversampling ratios and kernel widths. Our implementation is compared with the GPU-accelerated modified non-uniform discrete Fourier transform (MNUDFT) matrix-based CS SD OCT and the GPU-accelerated fast Fourier transform (FFT)-based CS SD OCT. It was found that our implementation has comparable performance to the GPU-accelerated MNUDFT-based CS SD OCT in terms of image quality while providing more than 5 times speed enhancement. When compared to the GPU-accelerated FFT based-CS SD OCT, it shows smaller background noise and less side lobes while eliminating the need for the cumbersome k-space grid filling and the k-linear calibration procedure. Finally, we demonstrated that by using a conventional desktop computer architecture having three GPUs, real-time B-mode imaging can be obtained in excess of 30 fps for the GPU-accelerated NUFFT based CS SD OCT with frame size 2048(axial) × 1,000(lateral).
Klaseboer, Evert; Sepehrirahnama, Shahrokh; Chan, Derek Y C
2017-08-01
The general space-time evolution of the scattering of an incident acoustic plane wave pulse by an arbitrary configuration of targets is treated by employing a recently developed non-singular boundary integral method to solve the Helmholtz equation in the frequency domain from which the space-time solution of the wave equation is obtained using the fast Fourier transform. The non-singular boundary integral solution can enforce the radiation boundary condition at infinity exactly and can account for multiple scattering effects at all spacings between scatterers without adverse effects on the numerical precision. More generally, the absence of singular kernels in the non-singular integral equation confers high numerical stability and precision for smaller numbers of degrees of freedom. The use of fast Fourier transform to obtain the time dependence is not constrained to discrete time steps and is particularly efficient for studying the response to different incident pulses by the same configuration of scatterers. The precision that can be attained using a smaller number of Fourier components is also quantified.
Color theorems, chiral domain topology, and magnetic properties of Fe(x)TaS2.
Horibe, Yoichi; Yang, Junjie; Cho, Yong-Heum; Luo, Xuan; Kim, Sung Baek; Oh, Yoon Seok; Huang, Fei-Ting; Asada, Toshihiro; Tanimura, Makoto; Jeong, Dalyoung; Cheong, Sang-Wook
2014-06-11
Common mathematical theories can have profound applications in understanding real materials. The intrinsic connection between aperiodic orders observed in the Fibonacci sequence, Penrose tiling, and quasicrystals is a well-known example. Another example is the self-similarity in fractals and dendrites. From transmission electron microscopy experiments, we found that FexTaS2 crystals with x = 1/4 and 1/3 exhibit complicated antiphase and chiral domain structures related to ordering of intercalated Fe ions with 2a × 2a and √3a × √3a superstructures, respectively. These complex domain patterns are found to be deeply related with the four color theorem, stating that four colors are sufficient to identify the countries on a planar map with proper coloring and its variations for two-step proper coloring. Furthermore, the domain topology is closely relevant to their magnetic properties. Our discovery unveils the importance of understanding the global topology of domain configurations in functional materials.
Chen, Wen; Chen, Xudong; Sheppard, Colin J R
2012-02-13
We propose a new method using coherent diffractive imaging for optical color-image encryption and synthesis in the Fresnel domain. An optical multiple-random-phase-mask encryption system is applied, and a strategy based on lateral translations of a phase-only mask is employed during image encryption. For the decryption, an iterative phase retrieval algorithm is applied to extract high-quality decrypted color images from diffraction intensity maps (i.e., ciphertexts). In addition, optical color-image synthesis is also investigated based on coherent diffractive imaging. Numerical results are presented to demonstrate feasibility and effectiveness of the proposed method. Compared with conventional interference methods, coherent diffractive imaging approach may open up a new research perspective or can provide an effective alternative for optical color-image encryption and synthesis.
Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain
Chen, Wen; Chen, Xudong
2011-08-01
In recent years, optical color image encryption has attracted much attention in the information security field. Some approaches, such as digital holography, have been proposed to encrypt color images, but the previously proposed methods are developed based on optical symmetric cryptographic strategies. In this paper, we apply an optical asymmetric cryptosystem for the color image encryption instead of conventional symmetric cryptosystems. A phase-truncated strategy is applied in the Fresnel domain, and multiple-wavelength and indexed image methods are further employed. The security of optical asymmetric cryptosystem is also analyzed during the decryption. Numerical results are presented to demonstrate the feasibility and effectiveness of the proposed optical asymmetric cryptosystem for color image encryption.
A NEW TECHNIQUE BASED ON CHAOTIC STEGANOGRAPHY AND ENCRYPTION TEXT IN DCT DOMAIN FOR COLOR IMAGE
Directory of Open Access Journals (Sweden)
MELAD J. SAEED
2013-10-01
Full Text Available Image steganography is the art of hiding information into a cover image. This paper presents a new technique based on chaotic steganography and encryption text in DCT domain for color image, where DCT is used to transform original image (cover image from spatial domain to frequency domain. This technique used chaotic function in two phases; firstly; for encryption secret message, second; for embedding in DCT cover image. With this new technique, good results are obtained through satisfying the important properties of steganography such as: imperceptibility; improved by having mean square error (MSE, peak signal to noise ratio (PSNR and normalized correlation (NC, to phase and capacity; improved by encoding the secret message characters with variable length codes and embedding the secret message in one level of color image only.
Fourier-Domain Analysis of Hydriding Kinetics Using Pneumato-Chemical Impedance Spectroscopy
Directory of Open Access Journals (Sweden)
P. Millet
2007-10-01
Full Text Available Analysis of phase transformation processes observed in hydrogen absorbing materials (pure metals, alloys, or compounds is still a matter of active research. Using pneumato-chemical impedance spectroscopy (PIS, it is now possible to analyze the mechanism of hydriding reactions induced by the gas phase. Experimental impedance diagrams, measured on activated LaNi5 in single- and two-phase domains, are reported in this paper. It is shown that their shape is mostly affected by the slope of the isotherm at the measurement point. By considering the details of the multistep reaction paths involved in the hydriding reaction, model impedance equations have been derived for single- and two-phase domains, and fitted to experimental impedance diagrams. The possibility of separately measuring surface and phase transformation resistances, hydrogen diffusion coefficient, and hydrogen solubility in each composition domain is discussed.
Shao, Zhuhong; Shu, Huazhong; Wu, Jiasong; Dong, Zhifang; Coatrieux, Gouenou; Coatrieux, Jean Louis
2014-03-10
This paper describes a novel algorithm to encrypt double color images into a single undistinguishable image in quaternion gyrator domain. By using an iterative phase retrieval algorithm, the phase masks used for encryption are obtained. Subsequently, the encrypted image is generated via cascaded quaternion gyrator transforms with different rotation angles. The parameters in quaternion gyrator transforms and phases serve as encryption keys. By knowing these keys, the original color images can be fully restituted. Numerical simulations have demonstrated the validity of the proposed encryption system as well as its robustness against loss of data and additive Gaussian noise.
Modestova, Yulia; Koksharov, Mikhail I; Ugarova, Natalia N
2014-09-01
Firefly luciferase is a two-domain enzyme that catalyzes the bioluminescent reaction of firefly luciferin oxidation. Color of the emitted light depends on the structure of the enzyme, yet the exact color-tuning mechanism remains unknown by now, and the role of the C-domain in it is rarely discussed, because a very few color-shifting mutations in the C-domain were described. Recently we reported a strong red-shifting mutation E457K in the C-domain; the bioluminescence spectra of this enzyme were independent of temperature or pH. In the present study we investigated the role of the residue E457 in the enzyme using the Luciola mingrelica luciferase with a thermostabilized N-domain as a parent enzyme for site-directed mutagenesis. We obtained a set of mutants and studied their catalytic properties, thermal stability and bioluminescence spectra. Experimental spectra were represented as a sum of two components (bioluminescence spectra of putative "red" and "green" emitters); λmax of these components were constant for all the mutants, but the ratio of these emitters was defined by temperature and mutations in the C-domain. We suggest that each emitter is stabilized by a specific conformation of the active site; thus, enzymes with two forms of the active site coexist in the reactive media. The rigid structure of the C-domain is crucial for maintaining the conformation corresponding to the "green" emitter. We presume that the emitters are the keto- and enol forms of oxyluciferin.
Bagnaninchi, Pierre O
2010-04-01
To assess non-invasively and in real time the three- dimensional organization of cells within porous matrices by combining Fourier Domain Optical Coherence Tomography (FDOCT) and Impedance Spectroscopy (IS). Broadband interferences resulting from the recombination of in-depth light scattering events within the sample and light from a reference arm are measured as a modulation of the spectrum generated by a superluminescent laser diode (lambdao = 930nm, FWHM 90nm). Fourier transform allows in-depth localization of the scatterers, and the 3D microstructure of the sample is reconstructed by raster scanning. Simultaneously impedance spectroscopy is performed with a dielectric probe connected to an impedance analyzer to gather additional cellular information, and synchronized with FDOCT measurements. A combined IS-FDOCT system allowing an axial resolution of 5 micrometer in tissues and impedance measurements over the range 20MHz-1GHz has been developed. Alginate matrices have been characterized in terms of microstructure and impedance. Matrices seeded with adipose-derived stem cells have been monitored without the use of labeling agent. We have developed a multimodality system that will be instrumental to non-invasively monitor changes in total cell volume fraction and infer cell-specific dielectric properties in 3D structure.
1-D Directional Filter Based Texture Descriptor in Fractional Fourier Domain
Institute of Scientific and Technical Information of China (English)
Kai Tian; Hongzhang Jin; Liying Zheng
2015-01-01
Texture analysis is a fundamental field in computer vision. However, it is also a particularly difficult problem for no universal mathematical model of real world textures. By extending a new application of the fractional Fourier transform ( FrFT) in the field of texture analysis, this paper proposes an FrFT⁃based method for describing textures. Firstly, based on the Radon⁃Wigner transform, 1⁃D directional FrFT filters are designed to two types of texture features, i.e., the coarseness and directionality. Then, the frequencies with maximum and median amplitudes of the FrFT of the input signal are regarded as the output of the 1⁃D directional FrFT filter. Finally, the mean and the standard deviation are used to compose of the feature vector. Compared to the WD⁃based method, three benefits can be achieved with the proposed FrFT⁃based method, i. e., less memory size, lower computational load, and less disturbed by the cross⁃terms. The proposed method has been tested on 16 standard texture images. The experimental results show that the proposed method is superior to the popular Gabor filtering⁃based method.
Robles, Francisco E.; Zhu, Yizheng; Lee, Jin; Sharma, Sheela; Wax, Adam
2011-03-01
We present Fourier domain low coherence interferometry (fLCI) applied to the detection of preneoplastic changes in the colon using the ex-vivo azoxymethane (AOM) rat carcinogenesis model. fLCI measures depth resolved spectral oscillations, also known as local oscillations, resulting from coherent fields induced by the scattering of cell nuclei. The depth resolution of fLCI permits nuclear morphology measurements within thick tissues, making the technique sensitive to the earliest stages of precancerous development. To achieve depth resolved spectroscopic analysis, we use the dual window method, which obtains simultaneously high spectral and depth resolution and yields access to the local oscillations. The results show highly statistically significant differences between the AOM-treated and control group samples. Further, the results suggest that fLCI may be used to detect the field effect of carcinogenesis, in addition to identifying specific areas where more advanced neoplastic development has occurred.
Liu, Qiaoyan; Li, Yuejie; Xu, Qiujing; Zhao, Jincheng; Wang, Liwei; Gao, Yonghe
2013-01-01
This investigation introduces GPU (Graphics Processing Unit)- based CUDA (Compute Unified Device Architecture) technology into signal processing of ophthalmic FD-OCT (Fourier-Domain Optical Coherence Tomography) imaging system, can realize parallel data processing, using CUDA to optimize relevant operations and algorithms, in order to solve the technical bottlenecks that currently affect ophthalmic real-time imaging in OCT system. Laboratory results showed that with GPU as a general parallel computing processor, the speed of imaging data processing using GPU+CPU mode is more than dozens times faster than traditional CPU platform based serial computing and imaging mode when executing the same data processing, which reaches the clinical requirements for two dimensional real-time imaging.
Huang, Yong; Zhang, Kang; Kang, Jin U.; Calogero, Don; James, Robert H.; Ilev, Ilko K.
2011-12-01
We propose a novel common-path Fourier domain optical coherence tomography (CP-FD-OCT) method for noncontact, accurate, and objective in vitro measurement of the dioptric power of intraocular lenses (IOLs) implants. The CP-FD-OCT method principle of operation is based on simple two-dimensional scanning common-path Fourier domain optical coherence tomography. By reconstructing the anterior and posterior IOL surfaces, the radii of the two surfaces, and thus the IOL dioptric power are determined. The CP-FD-OCT design provides high accuracy of IOL surface reconstruction. The axial position detection accuracy is calibrated at 1.22 μm in balanced saline solution used for simulation of in situ conditions. The lateral sampling rate is controlled by the step size of linear scanning systems. IOL samples with labeled dioptric power in the low-power (5D), mid-power (20D and 22D), and high-power (36D) ranges under in situ conditions are tested. We obtained a mean power of 4.95/20.11/22.09/36.25 D with high levels of repeatability estimated by a standard deviation of 0.10/0.18/0.2/0.58 D and a relative error of 2/0.9/0.9/1.6%, based on five measurements for each IOL respectively. The new CP-FD-OCT method provides an independent source of IOL power measurement data as well as information for evaluating other optical properties of IOLs such as refractive index, central thickness, and aberrations.
Automatic online spectral calibration of Fourier-domain OCT for robotic surgery
Liu, Xuan; Balicki, Marcin; Taylor, Russell H.; Kang, Jin U.
2011-03-01
We present a new automatic spectral calibration (ASC) method for spectral Domain optical coherence tomography (SD-OCT). Our ASC method calibrates the spectral mapping of the spectrometer in SD-OCT, and does not require external calibrating light source or a commercial spectral analyzer. The ASC method simultaneously calibrates the physical pixel spacing of the A-scan in static and dynamic environments. Experimental results show that the proposed ASC method can provide satisfactory calibration for SD-OCT to achieve high axial resolution and high ranging accuracy, without increasing hardware complexity.
In vivo sweat film layer thickness measured with Fourier-domain optical coherence tomography
CSIR Research Space (South Africa)
Jonathan, E
2008-01-01
Full Text Available and pore can be located. In addition, other measure- ments of interest, for example, thickness of the SCL, diameter of an open sweat pore or depth position of DEJ can be performed. References [1] Weller AS. Body temperature and its regulation. Physiol... of tissue microstructure is achieved from operating in the optical low-coherence interferometry domain. 1. Introduction Sweat secretion in humans is accepted as a mechanism by which the body cools off [1,2]. Interest in sweat secretion in humans’ dates...
Sub-Nyquist Sampling and Fourier Domain Beamforming in Volumetric Ultrasound Imaging.
Burshtein, Amir; Birk, Michael; Chernyakova, Tanya; Eilam, Alon; Kempinski, Arcady; Eldar, Yonina C
2016-05-01
A key step in ultrasound image formation is digital beamforming of signals sampled by several transducer elements placed upon an array. High-resolution digital beamforming introduces the demand for sampling rates significantly higher than the signals' Nyquist rate, which greatly increases the volume of data that must be transmitted from the system's front end. In 3-D ultrasound imaging, 2-D transducer arrays rather than 1-D arrays are used, and more scan lines are needed. This implies that the amount of sampled data is vastly increased with respect to 2-D imaging. In this work, we show that a considerable reduction in data rate can be achieved by applying the ideas of Xampling and frequency domain beamforming (FDBF), leading to a sub-Nyquist sampling rate, which uses only a portion of the bandwidth of the ultrasound signals to reconstruct the image. We extend previous work on FDBF for 2-D ultrasound imaging to accommodate the geometry imposed by volumetric scanning and a 2-D grid of transducer elements. High image quality from low-rate samples is demonstrated by simulation of a phantom image composed of several small reflectors. Our technique is then applied to raw data of a heart ventricle phantom obtained by a commercial 3-D ultrasound system. We show that by performing 3-D beamforming in the frequency domain, sub-Nyquist sampling and low processing rate are achievable, while maintaining adequate image quality.
DEFF Research Database (Denmark)
Guan, P.; Mulvad, Hans Christian Hansen; Tomiyama, Y.;
2010-01-01
A single-channel 1.28 Tbit/s transmission over 525 km is demonstrated for the first time with a single-polarization DQPSK signal. Ultrafast time-domain optical Fourier transformation is successfully applied to DQPSK signals and results in improved performance and increased system margin.......A single-channel 1.28 Tbit/s transmission over 525 km is demonstrated for the first time with a single-polarization DQPSK signal. Ultrafast time-domain optical Fourier transformation is successfully applied to DQPSK signals and results in improved performance and increased system margin....
Bindi, D.; Spallarossa, D.; Pacor, F.
2017-08-01
In this study, we analyse a regional data set composed by about 9000 waveforms from 231 earthquakes in the magnitude range from 3 to 6 and recorded in central Italy in the time period 2008-2013. We derive a seismological model whose source, attenuation and site parameters are used to explain the ground motion variability associated with a set of ground motion prediction equation (GMPE) calibrated ad hoc for both Fourier and acceleration response spectra. The main results are the following: (1) the between-event residuals δΒe show a clear dependence on the stress drop for frequencies above 2 Hz; (2) the standard deviation τ of δΒe is strongly reduced (up to 80 per cent) by introducing in the functional form the stress drop values estimated from each source spectrum; (3) the standard deviation τ depends on the magnitude scale used to calibrate the GMPE: while the moment magnitude better describes the source variability at low frequency, the local magnitude better capture the source-related ground motion variability at frequencies larger than 2 Hz; (4) for frequencies higher than 10 Hz, the observed increase of τ with frequency correlate well with the attenuation parameter ksource, computed from the high-frequency slope of the source spectra. Regarding the station-to-station residuals δS2S, their frequency dependency is in good agreement with the site amplifications extracted from the S-wave spectra. Finally, while the overall dependences of the ground motion variability on seismological parameters are similar when observed either in the Fourier or in the response spectra domains (e.g. the dependency of the between event on stress drop), differences in the results suggest that the response spectra do not allow to fully capture the ground motion variability, as well as the site amplifications, at high frequencies.
DEFF Research Database (Denmark)
Guan, P.; Mulvad, Hans Christian Hansen; Kasai, K.
2010-01-01
We present a novel scheme for subharmonic clock recovery from an optical time-division-multiplexing signal using time-domain optical Fourier transformation and a narrowband optical filter. High-resolution 640-Gb/s clock recovery is successfully demonstrated with no pattern dependence. The clock...
DEFF Research Database (Denmark)
Mulvad, Hans Christian Hansen; Palushani, Evarist; Hu, Hao
2011-01-01
We demonstrate conversion from 64 × 10 Gbit/s optical timedivision multiplexed (OTDM) data to dense wavelength division multiplexed (DWDM) data with 25 GHz spacing. The conversion is achieved by time-domain optical Fourier transformation (OFT) based on four-wave mixing (FWM) in a 3.6 mm long...
Z. Jamil (Z.); G.J. Tearney (Guillermo); N. Bruining (Nico); K. Sihan (Kenji); G. van Soest (Gijs); J.M.R. Ligthart (Jürgen); R.T. van Domburg (Ron); B.E. Bouma (Brett); E.S. Regar (Eveline)
2013-01-01
textabstractRecently, Fourier domain OCT (FD-OCT) has been introduced for clinical use. This approach allows in vivo, high resolution (15 micron) imaging with very fast data acquisition, however, it requires brief flushing of the lumen during imaging. The reproducibility of such fast data acquisitio
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Manso, M. [Centro de Fisica Atomica, Universidade de Lisboa, Faculdade de Ciencias, Av. Prof. Gama Pinto 2, 1649-003 Lisboa (Portugal); Valadas, S. [Chemistry Department, Evora Chemistry Centre and HERCULES Centre, University of Evora, Rua Romao Ramalho, 59 Evora (Portugal); Pessanha, S.; Guilherme, A. [Centro de Fisica Atomica, Universidade de Lisboa, Faculdade de Ciencias, Av. Prof. Gama Pinto 2, 1649-003 Lisboa (Portugal); Queralt, I. [Laboratory of X-ray Analytical Applications, Institute of Earth Sciences ' Jaume Almera' , CSIC, Sole Sabaris s/n. 08028 Barcelona (Spain); Candeias, A.E. [Chemistry Department, Evora Chemistry Centre and HERCULES Centre, University of Evora, Rua Romao Ramalho, 59 Evora (Portugal); Carvalho, M.L., E-mail: luisa@cii.fc.ul.p [Centro de Fisica Atomica, Universidade de Lisboa, Faculdade de Ciencias, Av. Prof. Gama Pinto 2, 1649-003 Lisboa (Portugal)
2010-04-15
This work comprises the use of energy dispersive X-ray fluorescence (EDXRF), X-ray diffraction (XRD) and Fourier transformed infrared (FTIR) techniques for the study of the composition of twentieth century traditional Japanese color sticks. By using the combination of analytical techniques it was possible to obtain information on inorganic and organic pigments, binders and fillers present in the sticks. The colorant materials identified in the sticks were zinc and titanium white, chrome yellow, yellow and red ochre, vermillion, alizarin, indigo, Prussian and synthetic ultramarine blue. The results also showed that calcite and barite were used as inorganic mineral fillers while Arabic gum was the medium used. EDXRF offered great potential for such investigations since it allowed the identification of the elements present in the sample preserving its integrity. However, this information alone was not enough to clearly identify some of the materials in study and therefore it was necessary to use XRD and FTIR techniques.
Montonen, Risto; Hæggström, Edward; Österberg, Kenneth
2016-01-01
The internal shape and alignment of accelerator discs is crucial for efficient collider operation at the future compact linear collider (CLIC). We applied a calibrated custom-made Fourier-domain short coherence interferometer to measure the height of 40 and 60μm60 μm ultraprecisely turned steps (surface roughness Ra≤25nmRa≤25 nm, flatness ≤2μm≤2 μm) on an oxygen-free electronic copper disc. The step heights were quantified to be (39.6±2.6)μm(39.6±2.6) μm and (59.0±2.3)μm(59.0±2.3) μm. The uncertainties are quoted at 95% confidence level and include contributions from calibration, refractive index of air, cosine error, surface roughness, and thermal expansion in comparison to standard temperature of 20°C. The results were verified by measuring the same steps using a commercial white light interferometer Veeco—NT3300. Our instrument can ensure that the accelerator discs of the CLIC are aligned within the tolerance required for efficient collider operation.
Ultrahigh-speed imaging of the rat retina using ultrahigh-resolution spectral/Fourier domain OCT
Liu, Jonathan J.; Potsaid, Benjamin; Chen, Yueli; Gorczynska, Iwona; Srinivasan, Vivek J.; Duker, Jay S.; Fujimoto, James G.
2010-02-01
We performed OCT imaging of the rat retina at 70,000 axial scans per second with ~3 μm axial resolution. Three-dimensional OCT (3D-OCT) data sets of the rat retina were acquired. The high speed and high density data sets enable improved en face visualization by reducing eye motion artifacts and improve Doppler OCT measurements. Minimal motion artifacts were visible and the OCT fundus images offer more precise registration of individual OCT images to retinal fundus features. Projection OCT fundus images show features such as the nerve fiber layer, retinal capillary networks and choroidal vasculature. Doppler OCT images and quantitative measurements show pulsatility in retinal blood vessels. Doppler OCT provides noninvasive in vivo quantitative measurements of retinal blood flow properties and may benefit studies of diseases such as glaucoma and diabetic retinopathy. Ultrahigh speed imaging using ultrahigh resolution spectral / Fourier domain OCT promises to enable novel protocols for measuring small animal retinal structure and retinal blood flow. This non-invasive imaging technology is a promising tool for monitoring disease progression in rat and mouse models to assess ocular disease pathogenesis and response to treatment.
Directory of Open Access Journals (Sweden)
Tong Lin
2015-01-01
Full Text Available Dry eye is highly prevalent and has a significant impact on quality of life. Acupuncture was found to be effective to treat dry eye. However, little was known about the effect of acupuncture on different subtypes of dry eye. The objective of this study was to investigate the applicability of tear meniscus assessment by Fourier-domain optical coherence tomography in the evaluation of acupuncture treatment response in dry eye patients and to explore the effect of acupuncture on different subtypes of dry eye compared with artificial tear treatment. A total of 108 dry eye patients were randomized into acupuncture or artificial tear group. Each group was divided into three subgroups including lipid tear deficiency (LTD, Sjögren syndrome dry eye (SSDE, and non-Sjögren syndrome dry eye (Non-SSDE for data analysis. After 4-week treatment, the low tear meniscus parameters including tear meniscus height (TMH, tear meniscus depth (TMD, and tear meniscus area (TMA in the acupuncture group increased significantly for the LTD and Non-SSDE subgroups compared with both the baseline and the control groups (all P values < 0.05, but not for the SSDE. Acupuncture provided a measurable improvement of the tear meniscus dimensions for the Non-SSDE and LTD patients, but not for the SSDE patients.
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Saban Gonul
2014-12-01
Full Text Available Purpose: To compare the results of central corneal thickness (CCT measurements obtained using optical low-coherence reflectometry (OLCR, Fourier domain optical coherence tomography (FD-OCT, and a Scheimpflug camera (SC, combined with Placido corneal topography. Methods: A total of 25 healthy subjects were enrolled in the present study, and one eye of each subject was included. A detailed ophthalmic examination was performed in all cases following CCT measurements with OLCR, FD-OCT, and SC. The results were compared using an ANOVA test. Bland-Altman analysis was used to demonstrate agreement between methods. Intra-examiner repeatability was assessed by using intraclass correlation coefficients (ICCs. Results: Statistically significant differences were observed between the results of the CCT measurements obtained using the three different devices (p=0.009. Significant correlations were found between OLCR and FD-OCT (r=0.97; p0.98. Conclusion: Although the results of CCT measurements obtained from these three devices were highly correlated with one another and the mean differences between instruments were comparable with the reported diurnal CCT fluctuation, the measurements are not directly interchangeable in clinical practice because of the wide LOA values.
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S. Catalan
2016-01-01
Full Text Available Purpose. To compare the characteristics of asymmetric keratoconic eyes and normal eyes by Fourier domain optical coherence tomography (OCT corneal mapping. Methods. Retrospective corneal and epithelial thickness OCT data for 74 patients were compared in three groups of eyes: keratoconic (n=22 and normal fellow eyes (n=22 in patients with asymmetric keratoconus and normal eyes (n=104 in healthy subjects. Areas under the curve (AUC of receiver operator characteristic (ROC curves for each variable were compared across groups to indicate their discrimination capacity. Results. Three variables were found to differ significantly between fellow eyes and normal eyes (all p<0.05: minimum corneal thickness, thinnest corneal point, and central corneal thickness. These variables combined showed a high discrimination power to differentiate fellow eyes from normal eyes indicated by an AUC of 0.840 (95% CI: 0.762–0.918. Conclusions. Our findings indicate that topographically normal fellow eyes in patients with very asymmetric keratoconus differ from the eyes of healthy individuals in terms of their corneal epithelial and pachymetry maps. This type of information could be useful for an early diagnosis of keratoconus in topographically normal eyes.
Montonen, Risto; Kassamakov, Ivan; Hæggström, Edward; Österberg, Kenneth
2016-01-01
The internal shape and alignment of accelerator discs is crucial for efficient collider operation at the future compact linear collider (CLIC). We applied a calibrated custom-made Fourier-domain short coherence interferometer to measure the height of 40 and 60 μm ultraprecisely turned steps (surface roughness Ra≤25 nm, flatness ≤2 μm) on an oxygen-free electronic copper disc. The step heights were quantified to be (39.6±2.6) μm and (59.0±2.3) μm. The uncertainties are quoted at 95% confidence level and include contributions from calibration, refractive index of air, cosine error, surface roughness, and thermal expansion in comparison to standard temperature of 20°C. The results were verified by measuring the same steps using a commercial white light interferometer Veeco-NT3300. Our instrument can ensure that the accelerator discs of the CLIC are aligned within the tolerance required for efficient collider operation.
Bradu, Adrian; Marques, Manuel J.; Bouchal, Petr; Podoleanu, Adrian Gh.
2013-03-01
The purpose of this study was to show how to favorably mix two e_ects to improve the sensitivity with depth in Fourier domain optical coherence tomography (OCT): Talbot bands (TB) and Gabor-based fusion (GF) technique. TB operation is achieved by directing the two beams, from the object arm and from the reference arm in the OCT interferometer, along parallel separate paths towards the spectrometer. By changing the lateral gap between the two beams in their path towards the spectrometer, the position for the maximum sensitivity versus the optical path difference in the interferometer is adjusted. For five values of the focus position, the gap between the two beams is readjusted to reach maximum sensitivity. Then, similar to the procedure employed in the GF technique, a composite image is formed by edging together the parts of the five images that exhibited maximum brightness. The combined procedure, TB/GF is examined for four different values of the beam diameters of the two beams. Also we demonstrate volumetric FD-OCT images with mirror term attenuation and sensitivity profile shifted towards higher OPD values by applying a Talbot bands configuration.
Rouze, Ned C; Palmeri, Mark L; Nightingale, Kathryn R
2015-08-01
Recent measurements of shear wave propagation in viscoelastic materials have been analyzed by constructing the two-dimensional Fourier transform (2D-FT) of the spatial-temporal shear wave signal and using an analysis procedure derived under the assumption the wave is described as a plane wave, or as the asymptotic form of a wave expanding radially from a cylindrically symmetric source. This study presents an exact, analytic expression for the 2D-FT description of shear wave propagation in viscoelastic materials following asymmetric Gaussian excitations and uses this expression to evaluate the bias in 2D-FT measurements obtained using the plane or cylindrical wave assumptions. A wide range of biases are observed depending on specific values of frequency, aspect ratio R of the source asymmetry, and material properties. These biases can be reduced significantly by weighting the shear wave signal in the spatial domain to correct for the geometric spreading of the shear wavefront using a factor of x(p). The optimal weighting power p is found to be near the theoretical value of 0.5 for the case of a cylindrical source with R = 1, and decreases for asymmetric sources with R > 1.
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Daniel E. Rio
2013-01-01
Full Text Available A linear time-invariant model based on statistical time series analysis in the Fourier domain for single subjects is further developed and applied to functional MRI (fMRI blood-oxygen level-dependent (BOLD multivariate data. This methodology was originally developed to analyze multiple stimulus input evoked response BOLD data. However, to analyze clinical data generated using a repeated measures experimental design, the model has been extended to handle multivariate time series data and demonstrated on control and alcoholic subjects taken from data previously analyzed in the temporal domain. Analysis of BOLD data is typically carried out in the time domain where the data has a high temporal correlation. These analyses generally employ parametric models of the hemodynamic response function (HRF where prewhitening of the data is attempted using autoregressive (AR models for the noise. However, this data can be analyzed in the Fourier domain. Here, assumptions made on the noise structure are less restrictive, and hypothesis tests can be constructed based on voxel-specific nonparametric estimates of the hemodynamic transfer function (HRF in the Fourier domain. This is especially important for experimental designs involving multiple states (either stimulus or drug induced that may alter the form of the response function.
Nan, Nan; Bu, Peng; Guo, Xin; Wang, Xiangzhao
2012-03-01
A three dimensional full-range complex Fourier domain optical coherence tomography (complex FDOCT) system based on sinusoidal phase-modulating method is proposed. With the system, the range of imaging depth is doubled and the sensitivity degradation with the lateral scan distance is avoided. Fourier analysis of B-scan data along lateral scan distance is used for reconstructing the complex spectral interferograms. The B-scan based Fourier method improves the system tolerance of sample movement and makes data processing less time consuming. In vivo volumetric imaging of human skin with the proposed full-range FDOCT system is demonstrated. The mirror image rejection ratio is about 30 dB. The stratum corneum, the epidermis and the upper dermis of skin can be clearly identified in the reconstructed three dimensional FDOCT images.
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Lucas Barasnevicius Quagliato
2014-08-01
Full Text Available Purpose: The goal of this cross-sectional observational study was to quantify the pattern-shift visual evoked potentials (VEP and the thickness as well as the volume of retinal layers using optical coherence tomography (OCT across a cohort of Parkinson's disease (PD patients and age-matched controls. Methods: Forty-three PD patients and 38 controls were enrolled. All participants underwent a detailed neurological and ophthalmologic evaluation. Idiopathic PD cases were included. Cases with glaucoma or increased intra-ocular pressure were excluded. Patients were assessed by VEP and high-resolution Fourier-domain OCT, which quantified the inner and outer thicknesses of the retinal layers. VEP latencies and the thicknesses of the retinal layers were the main outcome measures. Results: The mean age, with standard deviation (SD, of the PD patients and controls were 63.1 (7.5 and 62.4 (7.2 years, respectively. The patients were predominantly in the initial Hoehn-Yahr (HY disease stages (34.8% in stage 1 or 1.5, and 55.8 % in stage 2. The VEP latencies and the thicknesses as well as the volumes of the retinal inner and outer layers of the groups were similar. A negative correlation between the retinal thickness and the age was noted in both groups. The thickness of the retinal nerve fibre layer (RNFL was 102.7 μm in PD patients vs. 104.2 μm in controls. Conclusions: The thicknesses of retinal layers, VEP, and RNFL of PD patients were similar to those of the controls. Despite the use of a representative cohort of PD patients and high-resolution OCT in this study, further studies are required to establish the validity of using OCT and VEP measurements as the anatomic and functional biomarkers for the evaluation of retinal and visual pathways in PD patients.
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Hong-Wei Deng
2014-11-01
Full Text Available AIM: To detect the macular ganglion cell complex thickness in monocular strabismus amblyopia patients, in order to explore the relationship between the degree of amblyopia and retinal ganglion cell complex thickness, and found out whether there is abnormal macular ganglion cell structure in strabismic amblyopia. METHODS: Using a fourier-domain optical coherence tomography(FD-OCTinstrument iVue®(Optovue Inc, Fremont, CA, Macular ganglion cell complex(mGCCthickness was measured and statistical the relation rate with the best vision acuity correction was compared Gman among 26 patients(52 eyesincluded in this study. RESULTS: The mean thickness of the mGCC in macular was investigated into three parts: centrial, inner circle(3mmand outer circle(6mm. The mean thicknesses of mGCC in central, inner and outer circle was 50.74±21.51μm, 101.4±8.51μm, 114.2±9.455μm in the strabismic amblyopia eyes(SAE, and 43.79±11.92μm,92.47±25.01μm, 113.3±12.88μm in the contralateral sound eyes(CSErespectively. There was no statistically significant difference among the eyes(P>0.05. But the best corrected vision acuity had a good correlation rate between mGcc thicknesses, which was better relative for the lower part than the upper part.CONCLUSION:There is a relationship between the amblyopia vision acuity and the mGCC thickness. Although there has not statistically significant difference of the mGCC thickness compared with the SAE and CSE. To measure the macular center mGCC thickness in clinic may understand the degree of amblyopia.
Werkmeister, René M.; Vietauer, Martin; Knopf, Corinna; Fürnsinn, Clemens; Leitgeb, Rainer A.; Reitsamer, Herbert; Gröschl, Martin; Garhöfer, Gerhard; Vilser, Walthard; Schmetterer, Leopold
2014-10-01
A wide variety of ocular diseases are associated with abnormalities in ocular circulation. As such, there is considerable interest in techniques for quantifying retinal blood flow, among which Doppler optical coherence tomography (OCT) may be the most promising. We present an approach to measure retinal blood flow in the rat using a new optical system that combines the measurement of blood flow velocities via Doppler Fourier-domain optical coherence tomography and the measurement of vessel diameters using a fundus camera-based technique. Relying on fundus images for extraction of retinal vessel diameters instead of OCT images improves the reliability of the technique. The system was operated with an 841-nm superluminescent diode and a charge-coupled device camera that could be operated at a line rate of 20 kHz. We show that the system is capable of quantifying the response of 100% oxygen breathing on the retinal blood flow. In six rats, we observed a decrease in retinal vessel diameters of 13.2% and a decrease in retinal blood velocity of 42.6%, leading to a decrease in retinal blood flow of 56.7%. Furthermore, in four rats, the response of retinal blood flow during stimulation with diffuse flicker light was assessed. Retinal vessel diameter and blood velocity increased by 3.4% and 28.1%, respectively, leading to a relative increase in blood flow of 36.2%;. The presented technique shows much promise to quantify early changes in retinal blood flow during provocation with various stimuli in rodent models of ocular diseases in rats.
Chen, Junyi; Huang, Haili; Zhang, Shenghai; Chen, Xueli; Sun, Xinghuai
2013-02-07
To determine the effect of travoprost 0.004% on Schlemm's canal (SC) in healthy human eyes using Fourier-domain optical coherence tomography (FD-OCT). Twelve healthy volunteers were recruited for a double-blind, placebo-controlled, randomized, and paired comparison study. Right eyes of subjects were randomly assigned to receive either travoprost 0.004% or placebo; the contralateral eye received the other treatment. FD-OCT imaging of SC and measurements of IOP were carried out before and at 1, 2, 4, 6, 8, 12, 24, 36, 48, 60, 72, and 84 hours after eye drop instillation. After instillation of travoprost eye drops, IOP gradually reduced, and the SC lumens expanded, while those values remained unchanged in placebo treated eyes. At 8 hours after the travoprost administration, the mean SC area increased 90.30% and 90.20%, respectively, in the nasal and temporal quadrant of the treated eyes as compared with the placebo group. The SC area and IOP showed a similar pattern of changes at most time points examined. In travoprost-treated eyes, a statistically significant correlation between SC area and IOP is observed (r = -0.2817; P = 0.0004). Measurements of the SC area showed sufficient repeatability and reproducibility. SC can be noninvasively imaged and quantitatively assessed in the living healthy human eye by FD-OCT. Travoprost treatment leads to SC lumen expansion accompanied by a drop of IOP in the healthy eye, likely as a result of the enhancement of pressure sensitive trabecular meshwork outflow induced by travoprost.
Watanabe, Yuuki; Maeno, Seiya; Aoshima, Kenji; Hasegawa, Haruyuki; Koseki, Hitoshi
2010-09-01
The real-time display of full-range, 2048?axial pixelx1024?lateral pixel, Fourier-domain optical-coherence tomography (FD-OCT) images is demonstrated. The required speed was achieved by using dual graphic processing units (GPUs) with many stream processors to realize highly parallel processing. We used a zero-filling technique, including a forward Fourier transform, a zero padding to increase the axial data-array size to 8192, an inverse-Fourier transform back to the spectral domain, a linear interpolation from wavelength to wavenumber, a lateral Hilbert transform to obtain the complex spectrum, a Fourier transform to obtain the axial profiles, and a log scaling. The data-transfer time of the frame grabber was 15.73?ms, and the processing time, which includes the data transfer between the GPU memory and the host computer, was 14.75?ms, for a total time shorter than the 36.70?ms frame-interval time using a line-scan CCD camera operated at 27.9?kHz. That is, our OCT system achieved a processed-image display rate of 27.23 frames/s.
A Review of Various Transform Domain Digital Image Fusion for Multifocus Colored Images
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Arun Begill
2015-11-01
Full Text Available Image fusion is the idea to enhance the image content by fusing two or more images obtained from visual sensor network. The main goal of image fusion is to eliminate redundant information and merging more useful information from source images. Various transform domain image fusion methods like DWT, SIDWT and DCT, ACMax DCT etc. are developed in recent years. Every method has its own advantages and disadvantages. ACMax Discrete cosine transform (DCT is very efficient approach for image fusion because of its energy compaction property as well as improve quality of image. Furthermore, this technique has also some disadvantages like color artifacts, noise and degrade the sharpness of edges. In this paper ACMax DCT method is integrated with saturation weighting and Joint Trilateral filter to get the high quality image and compare with traditional methods. The results have shown that ACMax DCT with Saturation weighting and Joint Trilateral filter method has outperformed the state of art techniques.
Abuturab, Muhammad Rafiq
2014-06-01
A new color image security system based on singular value decomposition (SVD) in gyrator transform (GT) domains is proposed. In the encryption process, a color image is decomposed into red, green and blue channels. Each channel is independently modulated by random phase masks and then separately gyrator transformed at different parameters. The three gyrator spectra are joined by multiplication to get one gray ciphertext. The ciphertext is separated into U, S, and V parts by SVD. All the three parts are individually gyrator transformed at different transformation angles. The three encoded information can be assigned to different authorized users for highly secure verification. Only when all the authorized users place the U, S, and V parts in correct multiplication order in the verification system, the correct information can be obtained with all the right keys. In the proposed method, SVD offers one-way asymmetrical decomposition algorithm and it is an optimal matrix decomposition in a least-square sense. The transformation angles of GT provide very sensitive additional keys. The pre-generated keys for red, green and blue channels are served as decryption (private) keys. As all the three encrypted parts are the gray scale ciphertexts with stationary white noise distributions, which have camouflage property to some extent. These advantages enhance the security and robustness. Numerical simulations are presented to support the viability of the proposed verification system.
Su, Yonggang; Tang, Chen; Li, Biyuan; Chen, Xia; Xu, Wenjun; Cai, Yuanxue
2017-01-20
We propose an optical color image encryption system based on the single-lens Fourier transform, the Fresnel transform, and the chaotic random phase masks (CRPMs). The proposed encryption system contains only one optical lens, which makes it more efficient and concise to implement. The introduction of the Fresnel transform makes the first phase mask of the proposed system also act as the main secret key when the input image is a non-negative amplitude-only map. The two CRPMs generated by dual two-dimensional chaotic maps can provide more security to the proposed system. In the proposed system, the key management is more convenient and the transmission volume is reduced greatly. In addition, the secret keys can be updated conveniently in each encryption process to invalidate the chosen plaintext attack and the known plaintext attack. Numerical simulation results have demonstrated the feasibility and security of the proposed encryption system.
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Ramamoorthy, Sripriya [Oregon Hearing Research Center, Oregon Health & Science University, Portland, Oregon (United States); Zhang, Yuan; Jacques, Steven [Department of Biomedical Engineering, Oregon Health & Science University, Portland, Oregon (United States); Petrie, Tracy; Wang, Ruikang [Department of Bioengineering, University of Washington, Seattle, Washington (United States); Nuttall, Alfred L. [Oregon Hearing Research Center, Oregon Health & Science University, Portland, Oregon (United States); Kresge Hearing Research Institute, The University of Michigan, Ann Arbor, Michigan (United States)
2015-12-31
In this study, we have developed a phase-sensitive Fourier-domain optical coherence tomography system to simultaneously measure the in vivo inner ear vibrations in the hook area and second turn of the mouse cochlea. This technical development will enable measurement of intra-cochlear distortion products at ideal locations such as the distortion product generation site and reflection site. This information is necessary to un-mix the complex mixture of intra-cochlear waves comprising the DPOAE and thus leads to the non-invasive identification of the local region of cochlear damage.
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Steffen, Jason H.; /Fermilab; Fabrycky, Daniel C.; /Lick Observ.; Ford, Eric B.; /Florida U.; Carter, Joshua A.; /Harvard-Smithsonian Ctr. Astrophys.; Fressin, Francois; /Harvard-Smithsonian Ctr. Astrophys.; Holman, Matthew J.; /Harvard-Smithsonian Ctr. Astrophys.; Lissauer, Jack J.; /NASA, Ames; Rowe, Jason F.; /SETI Inst., Mtn. View /NASA, Ames; Ragozzine, Darin; /Harvard-Smithsonian Ctr. Astrophys.; Welsh, William F.; /Caltech; Borucki, William J.; /NASA, Ames /UC, Santa Barbara
2012-01-01
We present a method to confirm the planetary nature of objects in systems with multiple transiting exoplanet candidates. This method involves a Fourier-domain analysis of the deviations in the transit times from a constant period that result from dynamical interactions within the system. The combination of observed anticorrelations in the transit times and mass constraints from dynamical stability allow us to claim the discovery of four planetary systems, Kepler-25, Kepler-26, Kepler-27 and Kepler-28, containing eight planets and one additional planet candidate.
Steffen, Jason H; Ford, Eric B; Carter, Joshua A; Desert, Jean-Michel; Fressin, Francois; Holman, Matthew J; Lissauer, Jack J; Moorhead, Althea V; Rowe, Jason F; Ragozzine, Darin; Welsh, William F; Batalha, Natalie M; Borucki, William J; Buchhave, Lars A; Bryson, Steve; Caldwell, Douglas A; Charbonneau, David; Ciardi, David R; Cochran, William D; Endl, Michael; Everett, Mark E; Gautier, Thomas N; Gilliland, Ron L; Girouard, Forrest R; Jenkins, Jon M; Horch, Elliott; Howell, Steve B; Isaacson, Howard; Klaus, Todd C; Koch, David G; Latham, David W; Li, Jie; Lucas, Philip; MacQueen, Phillip J; Marcy, Geoffrey W; McCauliff, Sean; Middour, Christopher K; Morris, Robert L; Mullally, Fergal R; Quinn, Samuel N; Quintana, Elisa V; Shporer, Avi; Still, Martin; Tenenbaum, Peter; Thompson, Susan E; Twicken, Joseph D; Van Cleve, Jeffery
2012-01-01
We present a method to confirm the planetary nature of objects in systems with multiple transiting exoplanet candidates. This method involves a Fourier-Domain analysis of the deviations in the transit times from a constant period that result from dynamical interactions within the system. The combination of observed anti-correlations in the transit times and mass constraints from dynamical stability allow us to claim the discovery of four planetary systems Kepler-25, Kepler-26, Kepler-27, and Kepler-28, containing eight planets and one additional planet candidate.
Ramamoorthy, Sripriya; Zhang, Yuan; Petrie, Tracy; Jacques, Steven; Wang, Ruikang; Nuttall, Alfred L.
2015-12-01
In this study, we have developed a phase-sensitive Fourier-domain optical coherence tomography system to simultaneously measure the in vivo inner ear vibrations in the hook area and second turn of the mouse cochlea. This technical development will enable measurement of intra-cochlear distortion products at ideal locations such as the distortion product generation site and reflection site. This information is necessary to un-mix the complex mixture of intra-cochlear waves comprising the DPOAE and thus leads to the non-invasive identification of the local region of cochlear damage.
A Secure and Semi-Blind Technique of Embedding Color Watermark in RGB Image Using Curvelet Domain
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Ranjeeta
2017-03-01
Full Text Available A semi-blind and secure watermarking technique for the color image using curvelet domain has been proposed. To make the algorithm secure a Bijection mapping function has been used. The watermark also separated into color planes and each color plane into a bit planes. The most significant bit (MSB planes of each color used as the embedding information and remaining bit planes are used as a key at the time of extraction. The MSB planes of each color of watermark image embedded into the curvelet coefficients of the blue color plane of the processed cover image. For embedding the MSB bit planes of watermark image in the cover image each curvelet coefficient of blue planes of the processed cover image has been compared with the value of its 8 connected coefficients (neighbors. The results of the watermarking scheme have been analyzed by different quality assessment metric such as PSNR, Correlation Coefficient (CC and Mean Structure Similarity Index Measure (MSSIM. The experimental results show that the proposed technique gives the good invisibility of watermark, the quality of extracting watermark and robustness against different attacks.
DEFF Research Database (Denmark)
Palushani, Evarist; Mulvad, Hans Christian Hansen; Galili, Michael
2012-01-01
a dispersive medium followed by phase modulation; the latter being achieved by a four-wave mixing process with linearly chirped pump pulses. Both numerical and experimental investigations of the OTDM-to-WDM conversion technique are carried out. Experimental validations are performed on......This paper reports on the utilization of the timedomain optical Fourier transformation (OFT) technique for serial-to-parallel conversion of optical time division multiplexed (OTDM) data tributaries into dense wavelength division multiplexed (DWDM) channels. The OFT is implemented by using...
Real-time all-optical OFDM transmission system based on time-domain optical fourier transformation
DEFF Research Database (Denmark)
Guan, Pengyu; Kong, Deming; Røge, Kasper Meldgaard
2014-01-01
We propose a novel simple all-optical OFDM transmission system based on time-domain OFT using time-lenses. A real-time 160 Gbit/s DPSK OFDM transmission with 16 decorrelated data subcarriers is successfully demonstrated over 100 km.......We propose a novel simple all-optical OFDM transmission system based on time-domain OFT using time-lenses. A real-time 160 Gbit/s DPSK OFDM transmission with 16 decorrelated data subcarriers is successfully demonstrated over 100 km....
Watanabe, Yuuki
2012-05-01
The author presents a graphics processing unit (GPU) programming for real-time Fourier domain optical coherence tomography (FD-OCT) with fixed-pattern noise removal by subtracting mean and median. In general, the fixed-pattern noise can be removed by the averaged spectrum from the many spectra of an actual measurement. However, a mean-spectrum results in artifacts as residual lateral lines caused by a small number of high-reflective points on a sample surface. These artifacts can be eliminated from OCT images by using medians instead of means. However, median calculations that are based on a sorting algorithm can generate a large amount of computation time. With the developed GPU programming, highly reflective surface regions were obtained by calculating the standard deviation of the Fourier transformed data in the lateral direction. The medians and means were then subtracted at the observed regions and other regions, such as backgrounds. When the median calculation was less than 256 positions out of a total 512 depths in an OCT image with 1024 A-lines, the GPU processing rate was faster than that of the line scan camera (46.9 kHz). Therefore, processed OCT images can be displayed in real-time using partial medians.
Puvanathasan, Prabakar; Forbes, Peter; Ren, Zhao; Malchow, Doug; Boyd, Shelley; Bizheva, Kostadinka
2008-11-01
A high-speed (47,000 A-scans/s), ultrahigh axial resolution Fourier domain optical coherence tomography (OCT) system for retinal imaging at approximately 1060 nm, based on a 1024 pixel linear array, 47 kHz readout rate InGaAs camera is presented. When interfaced with a custom superluminescent diode (lambda(c) = 1020 nm, Deltalambda = 108 nm, Pout = 9 mW), the system provides 3.3 microm axial OCT resolution at the surface of biological tissue, approximately 4.5 microm in vivo in rat retina, approximately 5.7 microm in vivo in human retina, and 110 dB sensitivity for 870 microW incident power and 21 mus integration time. Retinal tomograms acquired in vivo from a human volunteer and a rat animal model show clear visualization of all intraretinal layer and increased penetration into the choroid.
Cheng, Kyle H Y; Standish, Beau A; Yang, Victor X D; Cheung, K K Y; Gu, Xijia; Lam, Edmund Y; Wong, K K Y
2010-02-01
We report the first Fourier domain modelocked (FDML) laser constructed using optical parametric amplifier (OPA) in conjunction with an erbium-doped fiber amplifier (EDFA), centered at approximately 1555 nm, to the best of our knowledge. We utilize a one-pump OPA and a C-band EDFA in serial configuration with a tunable Fabry-Perot interferometer to generate a hybrid FDML spectrum. Results demonstrate a substantially better spectral shape, output power and stability than individual configurations, with decreased sensitivity to polarization changes. We believe this technique has the potential to enable several amplifiers to complement individual deficiencies resulting in improved spectral shapes and power generation for imaging applications such as optical coherence tomography (OCT).
Ramamoorthy, Sripriya; Zhang, Yuan; Petrie, Tracy; Fridberger, Anders; Ren, Tianying; Wang, Ruikang; Jacques, Steven L.; Nuttall, Alfred L.
2015-02-01
In this study, we measure the in vivo apical-turn vibrations of the guinea pig organ of Corti in both axial and radial directions using phase-sensitive Fourier domain optical coherence tomography. The apical turn in guinea pig cochlea has best frequencies around 100 - 500 Hz which are relevant for human speech. Prior measurements of vibrations in the guinea pig apex involved opening the otic capsule, which has been questioned on the basis of the resulting changes to cochlear hydrodynamics. Here this limitation is overcome by measuring the vibrations through bone without opening the otic capsule. Furthermore, we have significantly reduced the surgery needed to access the guinea pig apex in the axial direction by introducing a miniature mirror inside the bulla. The method and preliminary data are discussed in this article.
Choudhury, Niloy; Zeng, Yaguang; Fridberger, Anders; Chen, Fangyi; Zha, Dingjun; Nuttall, Alfred L.; Wang, Ruikang K.
2011-03-01
Studying the sound stimulated vibrations of various membranes that form the complex structure of the organ of Corti in the cochlea of the inner ear is essential for understanding how the travelling sound wave of the basilar membrane couples its energy to the organ structures. In this paper we report the feasibility of using phase-sensitive Fourier domain optical coherence tomography (FD-OCT) to image the vibration of various micro-structures of the cochlea at the same time. An excised cochlea of a guinea pig was stimulated using sounds at various frequencies and vibration image was obtained. When measuring the apex area, vibration signal from different turns, which have different best response frequencies are obtained in the same image. The method has the potential to measure the response from a much wider region of the cochlea than any other currently used method. The noise floor for vibration image for the system at 200 Hz was ~0.3nm.
Shin, D. H.; Park, S. H.; Kim, B. Y.; Lee, M. Y.; Baik, H. K.; Seo, J. H.; Kang, J. U.; Song, C. G.
2013-03-01
The objective of this experiment is to evaluate the utility and limitations of optical coherence tomography (OCT) for real-time, high-resolution structural analysis. We monitored the degradation of the rat's articular cartilage inducing osteoarthritis (OA) and the change of the rat's articular cartilage recovery by treatment medication, using our developed common-path Fourier-domain (CP-FD) OCT. Also, we have done a comparative analysis the rat's articular cartilage and OA grade. To observe the progression of OA, we induced OA by injecting the monosodium iodoacetate (MIA) into the right knee joint. After the injection of MIA, we sacrificed the rats at intervals of 3 days and obtained OCT and histological images. OCT and histological images showed the OA progress of similar pattern. These results illustrated the potential for non-invasive diagnosis about the grade of OA using CP-FD OCT.
Directory of Open Access Journals (Sweden)
Ramzan Ullah
2013-01-01
Full Text Available We present terahertz time domain spectra of acrylamide in the frequency range from 0.2 to 2 THz with nearly constant refractive index having an average value of 1.33 and an absorption coefficient. Raman (95–3000 cm−1 and FTIR (450–4000 cm−1 spectra also show good agreement with density functional theory (DFT B3LYP 6-311G++ (3df 3pd calculations except C-H and N-H stretching frequencies even after scaling with scale factor of 0.9679. We use MOLVIB to rescale such frequencies to match experimental values.
Color image zero-watermarking based on SVD and visual cryptography in DWT domain
Liu, Xilin; Chen, Beijing; Coatrieux, Gouenou; Shu, Huazhong
2017-02-01
This paper presents a novel robust color image zero-watermarking scheme based on SVD and visual cryptography. We firstly generate the image feature from the SVD of the image blocks, and then employ the visual secret sharing scheme to construct ownership share from the watermark and the image feature. The low frequency component of one level discrete wavelet transform of the color image is partitioned into blocks. Then we propose to use the feature generated from the first singular value of the blocks to construct the master share. When ownership debate occurs, the ownership share is used to extract the watermark. Experimental results show the better performance of the proposed watermarking system in terms of robustness to various attacks, including noise, filtering, JPEG compression and so on, than other visual cryptography based color image watermarking algorithm.
KaraliÅ«nas, Mindaugas; Venckevičius, Rimvydas; Kašalynas, Irmantas; Puc, Uroš; Abina, Andreja; Jeglič, Anton; Zidanšek, Aleksander; Valušis, Gintaras
2015-08-01
Several pharmaceutical drugs, such as alprazolam, ibuprofen, acetaminophen, activated carbon and others, and caffeine-containing foods were tested using terahertz (THz) time domain spectroscopy in the range from 0.3 to 2 THz. The dry powder of pharmaceutical drugs was mixed with HDPE and pressed into the pellets using hydraulic press. The coffee grounds were also pressed into the pellets after ball-milling and mixing with HDPE. The caffeine containing liquid foods were dried out on the paper strips of various stacking. Experiments allow one to determine characteristic spectral signatures of the investigated substances within THz range caused by active pharmaceutical ingredients, like in the case of caffeine, as well as supporting pharmaceutical ingredients. Spectroscopic THz imaging approach is considered as a possible option to identify packaged pharmaceutical drugs. The caffeine spectral features in the tested caffeine containing foods are difficult to observed due to the low caffeine concentration and complex caffeine chemical surrounding.
Spatial Domain Watermarking Scheme for Colored Images Based on Log-average Luminance
Hussein, Jamal A
2010-01-01
In this paper a new watermarking scheme is presented based on log-average luminance. A colored-image is divided into blocks after converting the RGB colored image to YCbCr color space. A monochrome image of 1024 bytes is used as the watermark. To embed the watermark, 16 blocks of size 8X8 are selected and used to embed the watermark image into the original image. The selected blocks are chosen spirally (beginning form the center of the image) among the blocks that have log-average luminance higher than or equal the log-average luminance of the entire image. Each byte of the monochrome watermark is added by updating a luminance value of a pixel of the image. If the byte of the watermark image represented white color (255) a value is added to the image pixel luminance value, if it is black (0) the is subtracted from the luminance value. To extract the watermark, the selected blocks are chosen as the above, if the difference between the luminance value of the watermarked image pixel and the original image pixe...
Parent-Child Interaction and Lexical Acquisition in two Domains: Color Words and Animal Names
Directory of Open Access Journals (Sweden)
Gleason Jean Berko
2014-11-01
Full Text Available This paper explores young children’s and parents’ use of color words and animal names in two published studies. The aim is to compare the ranges and kinds of these words in parentchild interaction and to consider the implications of these findings for our understanding of early lexical development. Color term data were drawn from the Gleason corpus in CHILDES: 12 boys and 12 girls ranging in age from 25-62 months, and their parents. Results showed that parents used and emphasized only the same 10 most basic colors, with many teaching episodes. Parents’ most frequent terms, red, blue, and green were also children’s most frequent terms and are the ones acquired earliest according to MacArthur Bates lexical norms. In the second study CLAN programs were used to identify animal names in corpora from a variety of families in CHILDES, with 44 children ranging in age from 1;6-6;2. Children and parents produced a remarkable number and range of animal terms, with individual preschoolers naming as many as 96 different, often rare, animals, such as crocodile and pelican. Parents and children thus attend to the same limited set of basic color terms. By contrast, biophilia, our shared human love of the living world is reflected in children’s extensive animal lexicon.
Tolstov, Georgi P
1962-01-01
Richard A. Silverman's series of translations of outstanding Russian textbooks and monographs is well-known to people in the fields of mathematics, physics, and engineering. The present book is another excellent text from this series, a valuable addition to the English-language literature on Fourier series.This edition is organized into nine well-defined chapters: Trigonometric Fourier Series, Orthogonal Systems, Convergence of Trigonometric Fourier Series, Trigonometric Series with Decreasing Coefficients, Operations on Fourier Series, Summation of Trigonometric Fourier Series, Double Fourie
Gregori, Giovanni; Yehoshua, Zohar; Garcia Filho, Carlos Alexandre de Amorim; Sadda, SriniVas R.; Portella Nunes, Renata; Feuer, William J.; Rosenfeld, Philip J.
2014-01-01
Purpose. To investigate the relationship between drusen areas measured with color fundus images (CFIs) and those with spectral-domain optical coherence tomography (SDOCT). Methods. Forty-two eyes from thirty patients with drusen in the absence of geographic atrophy were recruited to a prospective study. Digital color fundus images and SDOCT images were obtained at baseline and at follow-up visits at 3 and 6 months. Registered, matched circles centered on the fovea with diameters of 3 mm and 5 mm were identified on both CFIs and SDOCT images. Spectral-domain OCT drusen measurements were obtained using a commercially available proprietary algorithm. Drusen boundaries on CFIs were traced manually at the Doheny Eye Institute Image Reading Center. Results. Mean square root drusen area (SQDA) measurements for the 3-mm circles on the SDOCT images were 1.451 mm at baseline and 1.464 mm at week 26, whereas the measurements on CFIs were 1.555 mm at baseline and 1.584 mm at week 26. Mean SQDA measurements from CFIs were larger than those from the SDOCT measurements at all time points (P = 0.004 at baseline, P = 0.003 at 26 weeks). Changes in SQDA over 26 weeks measured with SDOCT were not different from those measured with CFIs (mean difference = 0.014 mm, P = 0.5). Conclusions. Spectral-domain OCT drusen area measurements were smaller than the measurements obtained from CFIs. However, there were no differences in the change in drusen area over time between the two imaging modalities. Spectral-domain OCT measurements were considerably more sensitive in assessing drusen area changes. PMID:25335982
Deng, Xiaopeng; Zhao, Daomu
2011-11-01
A single-channel color image encryption is proposed based on the modified Gerchberg-Saxton algorithm (MGSA) and mutual encoding in the Fresnel domain. Similar to the double random phase encoding (DRPE), this encryption scheme also employs a pair of phase-only functions (POFs) as encryption keys. But the two POFs are generated by the use of the MGSA rather than a random function generator. In the encryption process, only one color component is needed to be encrypted when these POFs are mutually served as the second encryption keys. As a result, a more compact and simple color encryption system based on one-time-pad, enabling only one gray cipheretext to be recorded and transmitted when holographic recording is used, is obtained. Moreover, the optical setup is lensless, thus easy to be implemented and the system parameters and wavelength can be served as additional keys to further enhance the security of the system. The feasibility and effectiveness of the proposed method are demonstrated by numerical results. © 2011 Optical Society of America
Institute of Scientific and Technical Information of China (English)
2015-01-01
Sampling is the bridge between analog source signal and digital signal. Based on image signal in the fractional Fourier domain(FRFT), fractional cosine domain(FRCT) with sparse features, this article makes a preliminary comparison of the performance of gray image compression perception in the above two kinds of transform domain. This article uses the method of orthogonal matching pursuit (OMP) to reconstruct the original signal, uses local hada code matrix as measurement matrix, and uses the peak signal-to-noise ratio (PSNR) and mean square error (MSE) as the objective evaluation standard.%模拟信号的数字采样是模拟通向数字信息世界的纽带。本文基于图像信号在分数阶Fourier域(FRFT)、分数阶余弦域(FRCT)域具有稀疏性的特性，对灰度图像压缩感知在以上两种变换域的性能做了初步比较。本文采用正交匹配追踪法(OMP)重构原信号，采用局部哈达码矩阵作为测量矩阵，采用峰值信噪比(PSNR)和均方误差(MSE)作为客观评价标准。
Directory of Open Access Journals (Sweden)
Tromeur-Dervout Damien
2013-12-01
Full Text Available This paper deals with the representation of the trace of iterative Schwarz solutions at the interfaces of domain decomposition to approximate adaptively the interface error operator. This allows to build a cost-effectively accelerating of the convergence of the iterative method by extending to the vectorial case the Aitken’s accelerating convergence technique. The first representation is based on the building of a nonuniform discrete Fourier transform defined on a non-regular grid. We show how to construct a Fourier basis of dimension N+1 on this grid by building numerically a sesquilinear form, its exact accuracy to represent trigonometric polynomials of degree N / 2, and its spectral approximation property that depends on the continuity of the function to approximate. The decay of Fourier-like modes of the approximation of the trace of the iterative solution at the interfaces provides an estimate to adaptively select the modes involved in the acceleration. The drawback of this approach is to be dependent on the continuity of the trace of the iterated solution at the interfaces. The second representation, purely algebraic, uses a singular value decomposition of the trace of the iterative solution at the interfaces to provide a set of orthogonal singular vectors of which the associated singular values provide an estimate to adapt the acceleration. The resulting Aitken-Schwarz methodology is then applied to large scale computing on 3D linear Darcy flow where the permeability follows a log normal random distribution. Cet acte traite de la représentation des solutions itérées aux interfaces de la méthode de décomposition de domaine de type Schwarz afin d’approximer de manière adaptative son opérateur d’erreur aux interfaces des sous domaines. Ceci permet de construire de manière économique l’accélération de la convergence de la méthode itérative en étendant la technique d’accélération de la convergence de Aitken au cas
Stade, Eric
2005-01-01
A reader-friendly, systematic introduction to Fourier analysis Rich in both theory and application, Fourier Analysis presents a unique and thorough approach to a key topic in advanced calculus. This pioneering resource tells the full story of Fourier analysis, including its history and its impact on the development of modern mathematical analysis, and also discusses essential concepts and today's applications. Written at a rigorous level, yet in an engaging style that does not dilute the material, Fourier Analysis brings two profound aspects of the discipline to the forefront: the wealth of ap
Huang, Yong; Song, Cheol; Liu, Xuan; Kang, Jin U.
2013-03-01
A motion-compensated hand-held common-path Fourier-domain optical coherence tomography imaging probe has been developed for image guided intervention during microsurgery. A hand-held prototype instrument was designed and fabricated by integrating an imaging fiber probe inside a stainless steel needle which is attached to the ceramic shaft of a piezoelectric motor housed in an aluminum handle. The fiber probe obtains A-scan images. The distance information was extracted from the A-scans to track the sample surface distance and a fixed distance was maintained by a feedback motor control which effectively compensated hand tremor and target movements in the axial direction. Graphical user interface, real-time data processing, and visualization based on a CPU-GPU hybrid programming architecture were developed and used in the implantation of this system. To validate the system, free-hand optical coherence tomography images using various samples were obtained. The system can be easily integrated into microsurgical tools and robotics for a wide range of clinical applications. Such tools could offer physicians the freedom to easily image sites of interest with reduced risk and higher image quality.
Xiao, Qing; Hou, Jue; Fu, Ling
2012-06-01
A Fourier domain optical coherence tomography (OCT) system with 1310 nm light was demonstrated to study inflammatory human skin and the skin coated with a moisturizer in vivo. By using a graphics processing unit (GPU), the display rate could reach 20 frames/s with 1000 A-scans contained in one image. The field of view (FOV) of the cross-sectional image is 7 mm in the lateral direction and the penetration depth is ˜1 mm in skin. The result shows that, in inflammatory skin, the epidermis became thicker and had a decreased scattering; furthermore, the region of the severe lesion present an uneven thickness of the epidermis compared with the peripheral area. For the result of a finger tip coated with the moisturizer, the antireflection effect was significant and the stratum corneum became more transparent. In this letter, we demonstrated that real-time display with a large FOV could enable screening of a large tissue area; thereby increasing the dermatologic diagnostic potential of the method by permitting a comparison of the lesion and the normal peripheral region.
Adaptive Matrices and Filters for Color Texture Classification
Giotis, Ioannis; Bunte, Kerstin; Petkov, Nicolai; Biehl, Michael
In this paper we introduce an integrative approach towards color texture classification and recognition using a supervised learning framework. Our approach is based on Generalized Learning Vector Quantization (GLVQ), extended by an adaptive distance measure, which is defined in the Fourier domain,
Directory of Open Access Journals (Sweden)
Rolle T
2011-07-01
Full Text Available Teresa Rolle, Cristina Briamonte, Daniela Curto, Federico Maria GrignoloEye Clinic, Section of Ophthalmology, Department of Clinical Physiopathology, University of Torino, Torino, ItalyAims: To evaluate the capability of Fourier-domain optical coherence tomography (FD-OCT to detect structural damage in patients with preperimetric glaucoma.Methods: A total of 178 Caucasian subjects were enrolled in this cohort study: 116 preperimetric glaucoma patients and 52 healthy subjects. Using three-dimensional FD-OCT, the participants underwent imaging of the ganglion cell complex (GCC and the optic nerve head. Sensitivity, specificity, likelihood ratios, and predictive values were calculated for all parameters at the first and fifth percentiles. Areas under the curves (AUCs were generated for all parameters and were compared (Delong test. For both the GCC and the optic nerve head protocols, the OR logical disjunction (Boolean logic operator was calculated.Results: The AUCs didn’t significantly differ. Macular global loss volume had the largest AUC (0.81. Specificities were high at both the fifth and first percentiles (up to 97%, but sensitivities were low, especially at the first percentile (55%–27%.Conclusion: Macular and papillary diagnostic accuracies did not differ significantly based on the 95% confidence interval. The computation of the Boolean OR operator has been found to boost diagnostic accuracy. Using the software-provided classification, sensitivity and diagnostic accuracy were low for both the retinal nerve fiber layer and the GCC scans. FD-OCT does not seem to be decisive for early detection of structural damage in patients with no functional impairment. This suggests that there is a need for analysis software to be further refined to enhance glaucoma diagnostic capability.Keywords: OCT, RNFL, GCC, diagnostic accuracy
Institute of Scientific and Technical Information of China (English)
刘清宇; 卫红凯
2015-01-01
利用线性调频(Linear Frequency Modulation, LFM)信号在分数阶Fourier域上的聚焦性，通过搜索可实现LFM信号的检测和参数估计。通常采用步进式搜索法，效率低下。为了克服该缺点，通过对分数阶Fourier域优化问题的研究，将免疫算法引入到分数阶Fourier变换极值搜索中。仿真结果表明：该方法优于传统的步进式搜索法。%Based on the concentrated characteristics of linear frequency modulation (LFM) signal in the fractional Fourier domain, the detection and parameter estimation of LFM signal are usually realized by step-based searching method for extremum searching in the fractional Fourier domain. In order to resolve the disadvantage of low efficiency of the step-based searching method, Immune Algorithm is introduced to the fractional Fourier transform for extremum searching with the study of fractional Fourier optimization. Simulation results show that the performance of the Im-mune algorithm is better than that of the traditional step-based method.
A FAST ALGORITHM OF DISCRETE GENERALIZED FOURIER TRANSFORMS ON HEXAGON DOMAINS%平行六边形区域上的快速离散傅立叶变换
Institute of Scientific and Technical Information of China (English)
孙家昶; 姚继锋
2004-01-01
In this paper, we propose a fast algorithm for computing the DGFT (Discrete Generalized Fourier Transforms) on hexagon domains [6], based on the geometric properties of the domain. Our fast algorithm (FDGFT) reduces the computation complexity of DGFT from O(N4) to O(N2 log N). In particulary, for N =2P23P34P45P56P6, the floating point computation working amount equals to(17/2P2 + 16p3 + 135/8p4 + 2424/25p5 + 201/2P6)3N2. Numerical examples are given to access our analysis.
Computational color technology
Kang, Henry R
2006-01-01
Henry Kang provides the fundamental color principles and mathematical tools to prepare the reader for a new era of color reproduction, and for subsequent applications in multispectral imaging, medical imaging, remote sensing, and machine vision. This book is intended to bridge the gap between color science and computational color technology, putting color adaptation, color constancy, color transforms, color display, and color rendition in the domain of vector-matrix representations and theories. Computational Color Technology deals with color digital images on the spectral level using vector-m
DEFF Research Database (Denmark)
Guan, Pengyu; Mulvad, Hans Christian Hansen; Tomiyama, Yutaro
2011-01-01
developed an ultrafast timedomain optical Fourier transformation technique in a round-trip configuration. By applying this technique to subpicosecond pulses, transmission impairments were greatly reduced, and BER performance below FEC limit was obtained with increased system margin. Copyright © 2011...
Sui, Liansheng; Liu, Benqing; Wang, Qiang; Li, Ye; Liang, Junli
2015-12-01
A color image encryption scheme is proposed based on Yang-Gu mixture amplitude-phase retrieval algorithm and two-coupled logistic map in gyrator transform domain. First, the color plaintext image is decomposed into red, green and blue components, which are scrambled individually by three random sequences generated by using the two-dimensional Sine logistic modulation map. Second, each scrambled component is encrypted into a real-valued function with stationary white noise distribution in the iterative amplitude-phase retrieval process in the gyrator transform domain, and then three obtained functions are considered as red, green and blue channels to form the color ciphertext image. Obviously, the ciphertext image is real-valued function and more convenient for storing and transmitting. In the encryption and decryption processes, the chaotic random phase mask generated based on logistic map is employed as the phase key, which means that only the initial values are used as private key and the cryptosystem has high convenience on key management. Meanwhile, the security of the cryptosystem is enhanced greatly because of high sensitivity of the private keys. Simulation results are presented to prove the security and robustness of the proposed scheme.
Han, Jae-Ho; Xuan, Liu; Kang, Jin U.; Song, Chul-Gyu
2010-02-01
In this paper, we have demonstrated a polarization sensitive subcutaneous and muscle imaging based on common path optical coherence tomography (CP-OCT) using near infrared source. The axial and lateral resolutions of our PS-OCT system are 9μm and 6μm, respectively. The internal structural information has been extracted by the real-time signal analysis (Fourier Transform) from the modulated spectral intensity depending on the beam and tissue birefringence. Preliminary results using fresh beef and in vivo rat show that we can visualize the birefringence effect of the tissue collagen fibers in the samples for better image contrast and sensitivity for detection of hidden dermal structures. Compared to conventional CP-OCT, our proposed PS-OCT could provide depth-resolved images, which reflect tissue birefringence.
Fourier transform profilometry based on mean envelope extraction
Zhang, Xiaoxuan; Huang, Shujun; Gao, Nan; Zhang, Zonghua
2017-02-01
Based on an image pre-processing algorithm, a three-dimensional (3D) object measurement method is proposed by combining time domain and frequency domain analysis. Firstly, extreme points of sinusoidal fringes under the disturbance of noise are accurately extracted. Secondly, mean envelope of the fringe is obtained through appropriate interpolation method and then removed. Thirdly, phase information is extracted by using specific filtering in Fourier spectrum of the pre-processed fringe pattern. Finally, simulated and experimental results show a good property of the proposed method in accuracy and measurement range. The proposed method can achieve 3D shape of objects having large slopes and/or discontinuous surfaces from one-shot acquisition by using color fringe projection technique and will have wide applications in the fields of fast measurement.
Fourier Lucas-Kanade algorithm.
Lucey, Simon; Navarathna, Rajitha; Ashraf, Ahmed Bilal; Sridharan, Sridha
2013-06-01
In this paper, we propose a framework for both gradient descent image and object alignment in the Fourier domain. Our method centers upon the classical Lucas & Kanade (LK) algorithm where we represent the source and template/model in the complex 2D Fourier domain rather than in the spatial 2D domain. We refer to our approach as the Fourier LK (FLK) algorithm. The FLK formulation is advantageous when one preprocesses the source image and template/model with a bank of filters (e.g., oriented edges, Gabor, etc.) as 1) it can handle substantial illumination variations, 2) the inefficient preprocessing filter bank step can be subsumed within the FLK algorithm as a sparse diagonal weighting matrix, 3) unlike traditional LK, the computational cost is invariant to the number of filters and as a result is far more efficient, and 4) this approach can be extended to the Inverse Compositional (IC) form of the LK algorithm where nearly all steps (including Fourier transform and filter bank preprocessing) can be precomputed, leading to an extremely efficient and robust approach to gradient descent image matching. Further, these computational savings translate to nonrigid object alignment tasks that are considered extensions of the LK algorithm, such as those found in Active Appearance Models (AAMs).
Implementation of quantum and classical discrete fractional Fourier transforms.
Weimann, Steffen; Perez-Leija, Armando; Lebugle, Maxime; Keil, Robert; Tichy, Malte; Gräfe, Markus; Heilmann, René; Nolte, Stefan; Moya-Cessa, Hector; Weihs, Gregor; Christodoulides, Demetrios N; Szameit, Alexander
2016-03-23
Fourier transforms, integer and fractional, are ubiquitous mathematical tools in basic and applied science. Certainly, since the ordinary Fourier transform is merely a particular case of a continuous set of fractional Fourier domains, every property and application of the ordinary Fourier transform becomes a special case of the fractional Fourier transform. Despite the great practical importance of the discrete Fourier transform, implementation of fractional orders of the corresponding discrete operation has been elusive. Here we report classical and quantum optical realizations of the discrete fractional Fourier transform. In the context of classical optics, we implement discrete fractional Fourier transforms of exemplary wave functions and experimentally demonstrate the shift theorem. Moreover, we apply this approach in the quantum realm to Fourier transform separable and path-entangled biphoton wave functions. The proposed approach is versatile and could find applications in various fields where Fourier transforms are essential tools.
Institute of Scientific and Technical Information of China (English)
谢志华; 曾杰
2012-01-01
This paper proposes a novel temperature normalization method in Fourier domain, which can lessen the effect on infrared face recognition from ambient temperature. Firstly, the infrared face images in different ambient temperatures are transformed to Fourier domain. Secondly, based on statistical theory, the variances of phase spectrum and amplitude spectrum of the infrared face are used to describe the extent affected by the ambient temperature. Then, to achieve the robust information, those parts with big variances in the phase spectrum and amplitude spectrum are discarded and replaced by corresponding mean parts in training database. The main idea of this process is that one can set a suitable threshold for the variance of phase spectrum and amplitude spectrum and find those characteristic points that should be replaced. Finally, in order to verify the effectiveness of our temperature normalization method, the normalized infrared face is applied to the traditional face recognition system based on classic PCA method. Experimental results show that our normalization method can obtain stable information in infrared face and improve the performance of the infrared face recognition system.%为了减少环境温度对红外人脸图像的影响,本文提出了一种基于傅里叶变换的红外人脸图像温度归一化方法.首先,对不同环境温度下的红外人脸图像变换到傅里叶域,得到幅度谱和相位谱.其次,基于统计分析理论,幅频系数和相频系数的方差用于表示不同特征受环境温度影响的程度.为了达到归一化的目的,对方差较大的幅频系数和相频系数用训练样本的均值进行替换.最后,为了验证温度归一化的有效性,将归一化的红外人脸图像用于传统的基于PCA的红外人脸识别系统.实验结果表明,本文提出的归一化方法可以提取稳定的红外人脸特征,提高了环境温度变化下红外人脸识别的识别率.
Directory of Open Access Journals (Sweden)
Nabanita Barua
2016-01-01
Full Text Available Context: Analysis of diagnostic ability of macular ganglionic cell complex and retinal nerve fiber layer (RNFL in glaucoma. Aim: To correlate functional and structural parameters and comparing predictive value of each of the structural parameters using Fourier-domain (FD optical coherence tomography (OCT among primary open angle glaucoma (POAG and ocular hypertension (OHT versus normal population. Setting and Design: Single centric, cross-sectional study done in 234 eyes. Materials and Methods: Patients were enrolled in three groups: POAG, ocular hypertensive and normal (40 patients in each group. After comprehensive ophthalmological examination, patients underwent standard automated perimetry and FD-OCT scan in optic nerve head and ganglion cell mode. The relationship was assessed by correlating ganglion cell complex (GCC parameters with mean deviation. Results were compared with RNFL parameters. Statistical Analysis: Data were analyzed with SPSS, analysis of variance, t-test, Pearson′s coefficient, and receiver operating curve. Results: All parameters showed strong correlation with visual field (P 0.5 when compared with other parameters. None of the parameters showed significant diagnostic capability to detect OHT from normal population. In diagnosing early glaucoma from OHT and normal population, only inferior GCC had statistically significant AUC value (0.715. Conclusion: In this study, GCC and RNFL parameters showed equal predictive capability in perimetric versus normal group. In early stage, inferior GCC was the best parameter. In OHT population, single day cross-sectional imaging was not valuable.
Transformadas Discretas de Fourier
Alpízar-Brenes, Geisel; Calderón-Arce, Cindy; Soto-Quirós, Juan Pablo
2015-01-01
Proyecto de Investigación (VIE-5402-1440-4301). Este proyecto presenta un marco matem atico-computacional para el desarrollo de un conjunto de de niciones derivadas de la transformada discreta de Fourier (TDF), que son la funci on discreta de ambig uedad, la transformada discreta de Zak, la transformada discreta de Fourier en tiempo corto, la transformada discreta chirp-Fourier, la transformada discreta de Fourier de quaterniones, la transformada discreta de Cohen, la transform...
Research progress on discretization of fractional Fourier transform
Institute of Scientific and Technical Information of China (English)
TAO Ran; ZHANG Feng; WANG Yue
2008-01-01
As the fractional Fourier transform has attracted a considerable amount of atten-tion in the area of optics and signal processing,the discretization of the fractional Fourier transform becomes vital for the application of the fractional Fourier trans-form.Since the discretization of the fractional Fourier transform cannot be obtained by directly sampling in time domain and the fractional Fourier domain,the discre-tization of the fractional Fourier transform has been investigated recently.A sum-mary of discretizations of the fractional Fourier transform developed in the last nearly two decades is presented in this paper.The discretizations include sampling in the fractional Fourier domain,discrete-time fractional Fourier transform,frac-tional Fourier series,discrete fractional Fourier transform (including 3 main types:linear combination-type;sampling-type;and eigen decomposition-type),and other discrete fractional signal transform.It is hoped to offer a doorstep for the readers who are interested in the fractional Fourier transform.
Content adaptive illumination for Fourier ptychography.
Bian, Liheng; Suo, Jinli; Situ, Guohai; Zheng, Guoan; Chen, Feng; Dai, Qionghai
2014-12-01
Fourier ptychography (FP) is a recently reported technique, for large field-of-view and high-resolution imaging. Specifically, FP captures a set of low-resolution images, under angularly varying illuminations, and stitches them together in the Fourier domain. One of FP's main disadvantages is its long capturing process, due to the requisite large number of incident illumination angles. In this Letter, utilizing the sparsity of natural images in the Fourier domain, we propose a highly efficient method, termed adaptive Fourier ptychography (AFP), which applies content adaptive illumination for FP, to capture the most informative parts of the scene's spatial spectrum. We validate the effectiveness and efficiency of the reported framework, with both simulated and real experiments. Results show that the proposed AFP could shorten the acquisition time of conventional FP, by around 30%-60%.
Image restoration based on the discrete fraction Fourier transform
Yan, Peimin; Mo, Yu L.; Liu, Hong
2001-09-01
The fractional Fourier transform is the powerful tool for time-variant signal analysis. For space-variant degradation and non-stationary processes the filtering in fractional Fourier domains permits reduction of the error compared with ordinary Fourier domain filtering. In this paper the concept of filtering in fractional Fourier domains is applied to the problem of estimating degraded images. Efficient digital implementation using discrete Hermite eigenvectors can provide similar results to match the continuous outputs. Expressions for the 2D optimal filter function in fractional domains will be given for transform domains characterized by the two rotation angle parameters of the 2D fractional Fourier transform. The proposed method is used to restore images that have several degradations in the experiments. The results show that the method presented in this paper is valid.
Principles of Fourier analysis
Howell, Kenneth B
2001-01-01
Fourier analysis is one of the most useful and widely employed sets of tools for the engineer, the scientist, and the applied mathematician. As such, students and practitioners in these disciplines need a practical and mathematically solid introduction to its principles. They need straightforward verifications of its results and formulas, and they need clear indications of the limitations of those results and formulas.Principles of Fourier Analysis furnishes all this and more. It provides a comprehensive overview of the mathematical theory of Fourier analysis, including the development of Fourier series, "classical" Fourier transforms, generalized Fourier transforms and analysis, and the discrete theory. Much of the author''s development is strikingly different from typical presentations. His approach to defining the classical Fourier transform results in a much cleaner, more coherent theory that leads naturally to a starting point for the generalized theory. He also introduces a new generalized theory based ...
Fourier Analysis of Blazar Variability
Finke, Justin D
2014-01-01
Blazars display strong variability on multiple timescales and in multiple radiation bands. Their variability is often characterized by power spectral densities (PSDs) and time lags plotted as functions of the Fourier frequency. We develop a new theoretical model based on the analysis of the electron transport (continuity) equation, carried out in the Fourier domain. The continuity equation includes electron cooling and escape, and a derivation of the emission properties includes light travel time effects associated with a radiating blob in a relativistic jet. The model successfully reproduces the general shapes of the observed PSDs and predicts specific PSD and time lag behaviors associated with variability in the synchrotron, synchrotron self-Compton (SSC), and external Compton (EC) emission components, from sub-mm to gamma-rays. We discuss applications to BL Lacertae objects and to flat-spectrum radio quasars (FSRQs), where there are hints that some of the predicted features have already been observed. We a...
Adaptive optics implementation with a Fourier reconstructor.
Glazer, Oded; Ribak, Erez N; Mirkin, Leonid
2007-02-01
Adaptive optics takes its servo feedback error cue from a wavefront sensor. The common Hartmann-Shack spot grid that represents the wavefront slopes is usually analyzed by finding the spot centroids. In a novel application, we used the Fourier decomposition of a spot pattern to find deviations from grid regularity. This decomposition was performed either in the Fourier domain or in the image domain, as a demodulation of the grid of spots. We analyzed the system, built a control loop for it, and tested it thoroughly. This allowed us to close the loop on wavefront errors caused by turbulence in the optical system.
Zhang, Ping
2015-01-01
A comprehensive treatment of color-induced graph colorings is presented in this book, emphasizing vertex colorings induced by edge colorings. The coloring concepts described in this book depend not only on the property required of the initial edge coloring and the kind of objects serving as colors, but also on the property demanded of the vertex coloring produced. For each edge coloring introduced, background for the concept is provided, followed by a presentation of results and open questions dealing with this topic. While the edge colorings discussed can be either proper or unrestricted, the resulting vertex colorings are either proper colorings or rainbow colorings. This gives rise to a discussion of irregular colorings, strong colorings, modular colorings, edge-graceful colorings, twin edge colorings and binomial colorings. Since many of the concepts described in this book are relatively recent, the audience for this book is primarily mathematicians interested in learning some new areas of graph colorings...
Fourier transformation for pedestrians
Butz, Tilman
2006-01-01
Meant to serve an "entertaining textbook," this book belongs to a rare genre. It is written for all students and practitioners who deal with Fourier transformation. Fourier series as well as continuous and discrete Fourier transformation are covered, and particular emphasis is placed on window functions. Many illustrations and easy-to-solve exercises make the book especially accessible, and its humorous style will add to the pleasure of learning from it.
Color digital image watermarking based on Contourlet transform domain%一种Contourlet变换域彩色图像数字水印算法
Institute of Scientific and Technical Information of China (English)
何冰
2015-01-01
As an important means of copyright protection,digital watermarking technology has been widely used,but the practical watermark algorithm is scant,especially the relevant algorithm of color image and video image processing. Taking fully into account of the characteristics of human visual system,a binary watermark image is embedded into the low frequency compo-nent(after DWT transform)of the protected image in the color space according to the feature of carrier image,the quantity of the embedded binary watermark information can be adaptively increased according to the actual requirement. Based on the digi-tal watermark embedding algorithm research in Contourlet domain,the embedded process and watermark extraction process of the algorithm are implemented through Matlab software emulation. The emulation result proves that the proposed algorithm can improve the practical application of digital watermarking technology in the real life.%数字水印技术作为版权保护的一种有效手段,在信息安全领域已有一定的实际应用,但实用性的水印算法还较少,特别是与彩色图像及视频图像处理的相关算法凤毛麟角.依靠人类的视觉敏感特性,在彩色图像空间上将一幅二值水印图像根据载体图像的特征,选择性的嵌入到受保护图像的DWT变换后的低频分量中,所嵌入的二值水印信息量可以根据实际需要自适应的增加.在Contourlet域水印的嵌入算法研究基础上,提出并通过Matlab软件仿真完成算法的嵌入过程和水印提取过程.仿真实验证明所提出的算法能够有效提高数字水印技术在现实生活中的实际应用.
Fourier Series Operating Package
Charnow, Milton L.
1961-01-01
This report presents a computer program for multiplying, adding, differentiating, integrating, "barring" and scalarly multiplying "literal" Fourier series as such, and for extracting the coefficients of specified terms.
Adaptive Fourier Decomposition Based Time-Frequency Analysis
Institute of Scientific and Technical Information of China (English)
Li-Ming Zhang
2014-01-01
The attempt to represent a signal simultaneously in time and frequency domains is full of challenges. The recently proposed adaptive Fourier decomposition (AFD) offers a practical approach to solve this problem. This paper presents the principles of the AFD based time-frequency analysis in three aspects: instantaneous frequency analysis, frequency spectrum analysis, and the spectrogram analysis. An experiment is conducted and compared with the Fourier transform in convergence rate and short-time Fourier transform in time-frequency distribution. The proposed approach performs better than both the Fourier transform and short-time Fourier transform.
Zhu, Dong; Kinoshita, Shuichi; Cai, Dongsheng; Cole, James B
2009-11-01
We use the nonstandard-finite-difference time-domain (NS-FDTD) method to investigate the interaction of light with the complicated microstructures in the Morpho butterfly scales, which produce the well-known brilliant blue coloring. The NS-FDTD algorithm is particularly suitable to analyze such complex structures because the calculation can be performed in a short time with high accuracy on a relatively coarse numerical grid. We analyze (1) the microstructure obtained directly by binarizing an electron microgram of the cross section of a scale, (2) the reflection and diffraction properties of three model structures--flat, alternating, and tree-shaped alternating multilayers, and (3) an array of alternating multilayers with random noise superposed on the height of the structures. We found that the actual microstructure well reproduced the reflection spectrum in a blue region by integrating the reflection intensities over all the reflection angles. Under normal incidence, the flat multilayer mainly stresses on multilayer interference except for shorter wavelengths, while alternating multilayer rather enhances the effect of diffraction grating due to longitudinally repeating structure by strongly suppressing the reflection toward the normal direction. In the array of alternating multilayers, the reflection into larger angles is considerably suppressed and the spectral shape becomes different from that expected for a single alternating multilayer. This suppression mainly comes from the scattering of reflected light by adjacent structures, which is particularly prominent for the TM mode. Thus a clear difference between the TE and TM modes is observed with respect to the origin of spectral shape, though the obtained spectra are similar to each other. Finally, the polarization dependence of the reflection and the importance of the alternating multilayer are discussed.
Sterken, C.
2003-03-01
This paper gives a short account of some key elements in the life of Jean Baptiste Joseph Fourier (1768-1830), specifically his relation to Napoleon Bonaparte. The mathematical approach to Fourier series and the original scepticism by French mathematicians are briefly illustrated.
Generalized Fourier transforms classes
DEFF Research Database (Denmark)
Berntsen, Svend; Møller, Steen
2002-01-01
The Fourier class of integral transforms with kernels $B(\\omega r)$ has by definition inverse transforms with kernel $B(-\\omega r)$. The space of such transforms is explicitly constructed. A slightly more general class of generalized Fourier transforms are introduced. From the general theory...
Fourier Series Optimization Opportunity
Winkel, Brian
2008-01-01
This note discusses the introduction of Fourier series as an immediate application of optimization of a function of more than one variable. Specifically, it is shown how the study of Fourier series can be motivated to enrich a multivariable calculus class. This is done through discovery learning and use of technology wherein students build the…
Fourier-Bessel rotational invariant eigenimages.
Zhao, Zhizhen; Singer, Amit
2013-05-01
We present an efficient and accurate algorithm for principal component analysis (PCA) of a large set of two-dimensional images and, for each image, the set of its uniform rotations in the plane and its reflection. The algorithm starts by expanding each image, originally given on a Cartesian grid, in the Fourier-Bessel basis for the disk. Because the images are essentially band limited in the Fourier domain, we use a sampling criterion to truncate the Fourier-Bessel expansion such that the maximum amount of information is preserved without the effect of aliasing. The constructed covariance matrix is invariant to rotation and reflection and has a special block diagonal structure. PCA is efficiently done for each block separately. This Fourier-Bessel-based PCA detects more meaningful eigenimages and has improved denoising capability compared to traditional PCA for a finite number of noisy images.
... rose in full bloom. If you have a color vision defect, you may see these colors differently than most people. There are three main kinds of color vision defects. Red-green color vision defects are the most ...
α-bandlimited diffuser in fractional Fourier optics
Patiño-Vanegas, Alberto; Durand, Pierre-Emmanuel; Torres, Rafael; Pellat-Finet, Pierre
2016-04-01
We propose a method for calculating appropriate α-band limited diffusers using the fractional Fourier transform. In order to do this, we implement a method for performing a numerical interpolation in the fractional Fourier domain. Such diffusers with compact support in the Fresnel regime may be used in fractional Fourier optical systems where the use of diffusers produce speckles, e.g. digital holography or optical encryption. Numerical simulations are presented.
Fourier analysis an introduction
Stein, Elias M
2003-01-01
This first volume, a three-part introduction to the subject, is intended for students with a beginning knowledge of mathematical analysis who are motivated to discover the ideas that shape Fourier analysis. It begins with the simple conviction that Fourier arrived at in the early nineteenth century when studying problems in the physical sciences--that an arbitrary function can be written as an infinite sum of the most basic trigonometric functions.The first part implements this idea in terms of notions of convergence and summability of Fourier series, while highlighting applications such as th
Solving Fractional Partial Differential Equations with Corrected Fourier Series Method
Directory of Open Access Journals (Sweden)
Nor Hafizah Zainal
2014-01-01
Full Text Available The corrected Fourier series (CFS is proposed for solving partial differential equations (PDEs with fractional time derivative on a finite domain. In the previous work, we have been solving partial differential equations by using corrected Fourier series. The fractional derivatives are described in Riemann sense. Some numerical examples are presented to show the solutions.
Debnath, Lokenath
2012-01-01
This article deals with a brief biographical sketch of Joseph Fourier, his first celebrated work on analytical theory of heat, his first great discovery of Fourier series and Fourier transforms. Included is a historical development of Fourier series and Fourier transforms with their properties, importance and applications. Special emphasis is made…
Fourier transformation for pedestrians
Butz, Tilman
2015-01-01
This book is an introduction to Fourier Transformation with a focus on signal analysis, based on the first edition. It is well suited for undergraduate students in physics, mathematics, electronic engineering as well as for scientists in research and development. It gives illustrations and recommendations when using existing Fourier programs and thus helps to avoid frustrations. Moreover, it is entertaining and you will learn a lot unconsciously. Fourier series as well as continuous and discrete Fourier transformation are discussed with particular emphasis on window functions. Filter effects of digital data processing are illustrated. Two new chapters are devoted to modern applications. The first deals with data streams and fractional delays and the second with the back-projection of filtered projections in tomography. There are many figures and mostly easy to solve exercises with solutions.
Digital Fourier analysis fundamentals
Kido, Ken'iti
2015-01-01
This textbook is a thorough, accessible introduction to digital Fourier analysis for undergraduate students in the sciences. Beginning with the principles of sine/cosine decomposition, the reader walks through the principles of discrete Fourier analysis before reaching the cornerstone of signal processing: the Fast Fourier Transform. Saturated with clear, coherent illustrations, "Digital Fourier Analysis - Fundamentals" includes practice problems and thorough Appendices for the advanced reader. As a special feature, the book includes interactive applets (available online) that mirror the illustrations. These user-friendly applets animate concepts interactively, allowing the user to experiment with the underlying mathematics. For example, a real sine signal can be treated as a sum of clockwise and counter-clockwise rotating vectors. The applet illustration included with the book animates the rotating vectors and the resulting sine signal. By changing parameters such as amplitude and frequency, the reader ca...
Fourier transform mass spectrometry.
Scigelova, Michaela; Hornshaw, Martin; Giannakopulos, Anastassios; Makarov, Alexander
2011-07-01
This article provides an introduction to Fourier transform-based mass spectrometry. The key performance characteristics of Fourier transform-based mass spectrometry, mass accuracy and resolution, are presented in the view of how they impact the interpretation of measurements in proteomic applications. The theory and principles of operation of two types of mass analyzer, Fourier transform ion cyclotron resonance and Orbitrap, are described. Major benefits as well as limitations of Fourier transform-based mass spectrometry technology are discussed in the context of practical sample analysis, and illustrated with examples included as figures in this text and in the accompanying slide set. Comparisons highlighting the performance differences between the two mass analyzers are made where deemed useful in assisting the user with choosing the most appropriate technology for an application. Recent developments of these high-performing mass spectrometers are mentioned to provide a future outlook.
Generalized fiber Fourier optics.
Cincotti, Gabriella
2011-06-15
A twofold generalization of the optical schemes that perform the discrete Fourier transform (DFT) is given: new passive planar architectures are presented where the 2 × 2 3 dB couplers are replaced by M × M hybrids, reducing the number of required connections and phase shifters. Furthermore, the planar implementation of the discrete fractional Fourier transform (DFrFT) is also described, with a waveguide grating router (WGR) configuration and a properly modified slab coupler.
Fan beam image reconstruction with generalized Fourier slice theorem.
Zhao, Shuangren; Yang, Kang; Yang, Kevin
2014-01-01
For parallel beam geometry the Fourier reconstruction works via the Fourier slice theorem (or central slice theorem, projection slice theorem). For fan beam situation, Fourier slice can be extended to a generalized Fourier slice theorem (GFST) for fan-beam image reconstruction. We have briefly introduced this method in a conference. This paper reintroduces the GFST method for fan beam geometry in details. The GFST method can be described as following: the Fourier plane is filled by adding up the contributions from all fanbeam projections individually; thereby the values in the Fourier plane are directly calculated for Cartesian coordinates such avoiding the interpolation from polar to Cartesian coordinates in the Fourier domain; inverse fast Fourier transform is applied to the image in Fourier plane and leads to a reconstructed image in spacial domain. The reconstructed image is compared between the result of the GFST method and the result from the filtered backprojection (FBP) method. The major differences of the GFST and the FBP methods are: (1) The interpolation process are at different data sets. The interpolation of the GFST method is at projection data. The interpolation of the FBP method is at filtered projection data. (2) The filtering process are done in different places. The filtering process of the GFST is at Fourier domain. The filtering process of the FBP method is the ramp filter which is done at projections. The resolution of ramp filter is variable with different location but the filter in the Fourier domain lead to resolution invariable with location. One advantage of the GFST method over the FBP method is in short scan situation, an exact solution can be obtained with the GFST method, but it can not be obtained with the FBP method. The calculation of both the GFST and the FBP methods are at O(N^3), where N is the number of pixel in one dimension.
Institute of Scientific and Technical Information of China (English)
徐会法; 刘锋; 张鑫
2011-01-01
fractional Fourier domain. First, introduce the detection and parameter estimation theories of multi-component LFM signals based on the elimination one by one method and clustering analysis method respectively, and analyze their advantages and disadvantages. And the novel detection method is presented combing elimination one by one method with clustering analysis method, use plane to cut the peaks of the multi-component LFM signals in the (u,a) plane, and a clustering algorithm named broad first search neighbors (BFSN) is introduced to detect the peaks. So the peaks of the LFM signals with approximative energy can be detected simultaneously. Next, use elimination one by one method to eliminate the strong signals detected. Repeat the above process until all the LFM signals have been detected. So the novel method improves the detection efficiency and the parameter estimation precision of the FRFT for stronger signals and it also eliminate the shading effects of strong signals to weak signals. The plane cutting method reduces the input data-set pointers of the BFSN clustering algorithm, and it reduces the computation cost of the novel method. Finally, simulations results verify the effectiveness of the method.
Liflyand, E.
2012-01-01
We study an extension to Fourier transforms of the old problem on absolute convergence of the re-expansion in the sine (cosine) Fourier series of an absolutely convergent cosine (sine) Fourier series. The results are obtained by revealing certain relations between the Fourier transforms and their Hilbert transforms.
Energy Technology Data Exchange (ETDEWEB)
Krapez, J.C.; Spagnolo, L. [Politechnique di Bari (Italy); Friess, M. [Deutsches Luft- und Raumfahrtzentrum eV (DLR), Stuttgart (Germany); Maier, H.P. [Stuttgart Univ., MPA (Germany); Neuer, G. [Institut fur Kernenergetik und Energiesysteme, Universitat Stuttgart (Germany)
2003-07-01
The through-thickness thermal diffusivity can be evaluated by the classical flash method. If an homogeneous and extended source is used to irradiate the surface and a thermographic camera is used to monitor the temperature evolution of the opposite side, a map of the through-thickness thermal diffusivity can be obtained in a single experiment and without any contact with the sample under inspection. In order to measure the in-plane thermal diffusivity of a plate-like sample or in one of the principal directions of its plane, a thermal gradient across the plane of the material has to be settled. The ratio of the Fourier transform of temperature at two different spatial frequencies is an exponential function of time multiplied by the diffusivity in the considered principal direction. This can be used to evaluate the diffusivity in an homogenous material. In order to maximize the signal-to-noise ratio, it is better if heat is absorbed over a series of periodic parallel strips (grid flash method). When the material presents a transverse gradient of conductivity, we propose, as a first approach, to perform the Fourier analysis over a sliding window corresponding to one period of the grid pattern. This method allowed us to quantify in situ the diffusivity decrease in a tensile composite sample due to the stress-induced density increase of transverse microcracks. We finally analysed a more rigorous method for transverse conductivity profile inversion. It is based on a perturbation method. The analytical expression of the 'transfer function' between the Fourier transform of the temperature contrast and the Fourier transform of conductivity was established. We validated the proposed inverse technique on simulated and noise-corrupted thermograms. The approach is robust and the simulated profiles are very well resolved. (authors)
Rudin, Walter
2011-01-01
In the late 1950s, many of the more refined aspects of Fourier analysis were transferred from their original settings (the unit circle, the integers, the real line) to arbitrary locally compact abelian (LCA) groups. Rudin's book, published in 1962, was the first to give a systematic account of these developments and has come to be regarded as a classic in the field. The basic facts concerning Fourier analysis and the structure of LCA groups are proved in the opening chapters, in order to make the treatment relatively self-contained.
Fourier and Laplace Transforms
Beerends, R.J.; Morsche, ter H.G.; Berg, van den J.C.
2003-01-01
This textbook presents in a unified manner the fundamentals of both continuous and discrete versions of the Fourier and Laplace transforms. These transforms play an important role in the analysis of all kinds of physical phenomena. As a link between the various applications of these transforms the a
Introduction to Fourier Optics
Huggins, Elisha
2007-01-01
Much like a physical prism, which displays the frequency components of a light wave, Fourier analysis can be thought of as a mathematical prism that can tell us what harmonics or frequency components are contained in a recording of a sound wave. We wrote the MacScope II program so that the user could not only see a plot of the harmonic amplitudes…
Introduction to Fourier Optics
Huggins, Elisha
2007-01-01
Much like a physical prism, which displays the frequency components of a light wave, Fourier analysis can be thought of as a mathematical prism that can tell us what harmonics or frequency components are contained in a recording of a sound wave. We wrote the MacScope II program so that the user could not only see a plot of the harmonic amplitudes…
Bilinear Fourier restriction theorems
Demeter, Ciprian
2012-01-01
We provide a general scheme for proving $L^p$ estimates for certain bilinear Fourier restrictions outside the locally $L^2$ setting. As an application, we show how such estimates follow for the lacunary polygon. In contrast with prior approaches, our argument avoids any use of the Rubio de Francia Littlewood--Paley inequality.
Fast Fourier Orthogonalization
Ducas, L.; Prest, T.; Abramov, S.A.; Zima, E.V.; Gao, X-S.
2016-01-01
The classical fast Fourier transform (FFT) allows to compute in quasi-linear time the product of two polynomials, in the {\\em circular convolution ring} R[x]/(x^d−1) --- a task that naively requires quadratic time. Equivalently, it allows to accelerate matrix-vector products when the matrix is *circ
Multi-color imaging of magnetic Co/Pt heterostructures
Directory of Open Access Journals (Sweden)
Felix Willems
2017-01-01
Full Text Available We present an element specific and spatially resolved view of magnetic domains in Co/Pt heterostructures in the extreme ultraviolet spectral range. Resonant small-angle scattering and coherent imaging with Fourier-transform holography reveal nanoscale magnetic domain networks via magnetic dichroism of Co at the M2,3 edges as well as via strong dichroic signals at the O2,3 and N6,7 edges of Pt. We demonstrate for the first time simultaneous, two-color coherent imaging at a free-electron laser facility paving the way for a direct real space access to ultrafast magnetization dynamics in complex multicomponent material systems.
Institute of Scientific and Technical Information of China (English)
严双红
2007-01-01
About one in 12 boys is color-blind, and one in every 400 girls, so in each school class there are likely to be at least one or two people who are color-blind. Because they are color- blind from birth, most people do not know that they are color-
Generation of spatiotemporal colored noise
García Ojalvo, Jordi; Ramírez de la Piscina Millán, Laureano; Sancho, Jose Maria
1992-01-01
We develop an algorithm to simulate a Gaussian stochastic process that is non-δ-correlated in both space and time coordinates. The colored noise obeys a linear reaction-diffusion Langevin equation with Gaussian white noise. This equation is exactly simulated in a discrete Fourier space. Peer Reviewed
A Fourier analysis of extreme events
DEFF Research Database (Denmark)
Mikosch, Thomas Valentin; Zhao, Yuwei
2014-01-01
The extremogram is an asymptotic correlogram for extreme events constructed from a regularly varying stationary sequence. In this paper, we define a frequency domain analog of the correlogram: a periodogram generated from a suitable sequence of indicator functions of rare events. We derive basic ...... properties of the periodogram such as the asymptotic independence at the Fourier frequencies and use this property to show that weighted versions of the periodogram are consistent estimators of a spectral density derived from the extremogram....
Generic Quantum Fourier Transforms
Moore, Cristopher; Russell, A; Moore, Cristopher; Rockmore, Daniel; Russell, Alexander
2003-01-01
The quantum Fourier transform (QFT) is the principal algorithmic tool underlying most efficient quantum algorithms. We present a generic framework for the construction of efficient quantum circuits for the QFT by ``quantizing'' the separation of variables technique that has been so successful in the study of classical Fourier transform computations. Specifically, this framework applies the existence of computable Bratteli diagrams, adapted factorizations, and Gel'fand-Tsetlin bases to offer efficient quantum circuits for the QFT over a wide variety a finite Abelian and non-Abelian groups, including all group families for which efficient QFTs are currently known and many new group families. Moreover, the method gives rise to the first subexponential-size quantum circuits for the QFT over the linear groups GL_k(q), SL_k(q), and the finite groups of Lie type, for any fixed prime power q.
Grafakos, Loukas
2014-01-01
The main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces. It covers classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood–Paley theory. The primary readership is intended to be graduate students in mathematics with the prerequisite including satisfactory completion of courses in real and complex variables. The coverage of topics and exposition style are designed to leave no gaps in understanding and stimulate further study. This third edition includes new Sections 3.5, 4.4, 4.5 as well as a new chapter on “Weighted Inequalities,” which has been moved from GTM 250, 2nd Edition. Appendices I and B.9 are also new to this edition. Countless corrections and improvements have been made to the material from the second edition. Additions and improvements include: more examples and applications, new and more relevant hints for the existing exercises, new exercises, and...
Fourier techniques and applications
1985-01-01
The first systematic methods of Fourier analysis date from the early eighteenth century with the work of Joseph Fourier on the problem of the flow of heat. (A brief history is contained in the first paper.) Given the initial tempera ture at all points of a region, the problem was to determine the changes in the temperature distribution over time. Understanding and predicting these changes was important in such areas as the handling of metals and the determination of geological and atmospheric temperatures. Briefly, Fourier noticed that the solution of the heat diffusion problem was simple if the initial temperature dis tribution was sinusoidal. He then asserted that any distri bution can be decomposed into a sum of sinusoids, these being the harmonics of the original function. This meant that the general solution could now be obtained by summing the solu tions of the component sinusoidal problems. This remarkable ability of the series of sinusoids to describe all "reasonable" functions, the sine qua n...
Quaternion Fourier transforms for signal and image processing
Ell, Todd A; Sangwine, Stephen J
2014-01-01
Based on updates to signal and image processing technology made in the last two decades, this text examines the most recent research results pertaining to Quaternion Fourier Transforms. QFT is a central component of processing color images and complex valued signals. The book's attention to mathematical concepts, imaging applications, and Matlab compatibility render it an irreplaceable resource for students, scientists, researchers, and engineers.
Local properties of Fourier series
Hüseyin Bor
2000-01-01
A theorem on local property of |N¯,pn|k summability of factored Fourier series, which generalizes some known results, and also a general theorem concerning the |N¯,pn|k summability factors of Fourier series have been proved.
Generalized Fourier slice theorem for cone-beam image reconstruction.
Zhao, Shuang-Ren; Jiang, Dazong; Yang, Kevin; Yang, Kang
2015-01-01
The cone-beam reconstruction theory has been proposed by Kirillov in 1961, Tuy in 1983, Feldkamp in 1984, Smith in 1985, Pierre Grangeat in 1990. The Fourier slice theorem is proposed by Bracewell 1956, which leads to the Fourier image reconstruction method for parallel-beam geometry. The Fourier slice theorem is extended to fan-beam geometry by Zhao in 1993 and 1995. By combining the above mentioned cone-beam image reconstruction theory and the above mentioned Fourier slice theory of fan-beam geometry, the Fourier slice theorem in cone-beam geometry is proposed by Zhao 1995 in short conference publication. This article offers the details of the derivation and implementation of this Fourier slice theorem for cone-beam geometry. Especially the problem of the reconstruction from Fourier domain has been overcome, which is that the value of in the origin of Fourier space is 0/0. The 0/0 type of limit is proper handled. As examples, the implementation results for the single circle and two perpendicular circle source orbits are shown. In the cone-beam reconstruction if a interpolation process is considered, the number of the calculations for the generalized Fourier slice theorem algorithm is O(N^4), which is close to the filtered back-projection method, here N is the image size of 1-dimension. However the interpolation process can be avoid, in that case the number of the calculations is O(N5).
Fourier transforms principles and applications
Hansen, Eric W
2014-01-01
Fourier Transforms: Principles and Applications explains transform methods and their applications to electrical systems from circuits, antennas, and signal processors-ably guiding readers from vector space concepts through the Discrete Fourier Transform (DFT), Fourier series, and Fourier transform to other related transform methods. Featuring chapter end summaries of key results, over two hundred examples and four hundred homework problems, and a Solutions Manual this book is perfect for graduate students in signal processing and communications as well as practicing engineers.
Real Clifford Windowed Fourier Transform
Institute of Scientific and Technical Information of China (English)
Mawardi BAHRI; Sriwulan ADJI; Ji Man ZHAO
2011-01-01
We study the windowed Fourier transform in the framework of Clifford analysis, which we call the Clifford windowed Fourier transform (CWFT). Based on the spectral representation of the Clifford Fourier transform (CFT), we derive several important properties such as shift, modulation,reconstruction formula, orthogonality relation, isometry, and reproducing kernel. We also present an example to show the differences between the classical windowed Fourier transform (WFT) and the CWFT. Finally, as an application we establish a Heisenberg type uncertainty principle for the CWFT.
Fourier optics through the looking glass of digital computers
Yaroslavsky, Leonid P.
2011-10-01
Optical transforms are represented in computers by their discrete versions. In particular, Fourier optics is represented through Discrete Fourier Transform (DFT) and Discrete Cosine Transform (DCT). Being discrete representation of the optical Fourier transform, these transforms feature a number of peculiarities that cast a new light on such fundamental properties of the Fourier Transform as sampling theorem and the uncertainty principle. In this paper, we formulate the Discrete Sampling Theorem and the discrete uncertainty principle, demonstrate that discrete signals can be both bandlimited in DFT or DCT domains and have strictly limited support in signal domain and present examples of such "bandlimited/ space-limited" signals that remain to be so for whatever large of their samples.
Fourier spectra from exoplanets with polar caps and ocean glint
Visser, P M
2015-01-01
The weak orbital-phase dependent reflection signal of an exoplanet contains information on the planet surface, such as the distribution of continents and oceans on terrestrial planets. This light curve is usually studied in the time domain, but because the signal from a stationary surface is (quasi)periodic, analysis of the Fourier series may provide an alternative, complementary approach. We study Fourier spectra from reflected light curves for geometrically simple configurations. Depending on its atmospheric properties, a rotating planet in the habitable zone could have circular polar ice caps. Tidally locked planets, on the other hand, may have symmetric circular oceans facing the star. These cases are interesting because the high-albedo contrast at the sharp edges of the ice-sheets and the glint from the host star in the ocean may produce recognizable light curves with orbital periodicity, which could also be interpreted in the Fourier domain. We derive a simple general expression for the Fourier coeffici...
National Aeronautics and Space Administration — Satellite-derived Ocean Color Data sets from historical and currently operational NASA and International Satellite missions including the NASA Coastal Zone Color...
Entropy, color, and color rendering.
Price, Luke L A
2012-12-01
The Shannon entropy [Bell Syst. Tech J.27, 379 (1948)] of spectral distributions is applied to the problem of color rendering. With this novel approach, calculations for visual white entropy, spectral entropy, and color rendering are proposed, indices that are unreliant on the subjectivity inherent in reference spectra and color samples. The indices are tested against real lamp spectra, showing a simple and robust system for color rendering assessment. The discussion considers potential roles for white entropy in several areas of color theory and psychophysics and nonextensive entropy generalizations of the entropy indices in mathematical color spaces.
Thermal stabilization of static single-mirror Fourier transform spectrometers
Schardt, Michael; Schwaller, Christian; Tremmel, Anton J.; Koch, Alexander W.
2017-05-01
Fourier transform spectroscopy has become a standard method for spectral analysis of infrared light. With this method, an interferogram is created by two beam interference which is subsequently Fourier-transformed. Most Fourier transform spectrometers used today provide the interferogram in the temporal domain. In contrast, static Fourier transform spectrometers generate interferograms in the spatial domain. One example of this type of spectrometer is the static single-mirror Fourier transform spectrometer which offers a high etendue in combination with a simple, miniaturized optics design. As no moving parts are required, it also features a high vibration resistance and high measurement rates. However, it is susceptible to temperature variations. In this paper, we therefore discuss the main sources for temperature-induced errors in static single-mirror Fourier transform spectrometers: changes in the refractive index of the optical components used, variations of the detector sensitivity, and thermal expansion of the housing. As these errors manifest themselves in temperature-dependent wavenumber shifts and intensity shifts, they prevent static single-mirror Fourier transform spectrometers from delivering long-term stable spectra. To eliminate these shifts, we additionally present a work concept for the thermal stabilization of the spectrometer. With this stabilization, static single-mirror Fourier transform spectrometers are made suitable for infrared process spectroscopy under harsh thermal environmental conditions. As the static single-mirror Fourier transform spectrometer uses the so-called source-doubling principle, many of the mentioned findings are transferable to other designs of static Fourier transform spectrometers based on the same principle.
Geusebroek, J.M.; van den Boomgaard, R.; Smeulders, A.W.M.; Geerts, H.
2001-01-01
This paper presents the measurement of colored object reflectance, under different, general assumptions regarding the imaging conditions. We exploit the Gaussian scale-space paradigm for color images to define a framework for the robust measurement of object reflectance from color images. Object ref
Mulligan, Jeffrey B.
2017-01-01
A color algebra refers to a system for computing sums and products of colors, analogous to additive and subtractive color mixtures. We would like it to match the well-defined algebra of spectral functions describing lights and surface reflectances, but an exact correspondence is impossible after the spectra have been projected to a three-dimensional color space, because of metamerism physically different spectra can produce the same color sensation. Metameric spectra are interchangeable for the purposes of addition, but not multiplication, so any color algebra is necessarily an approximation to physical reality. Nevertheless, because the majority of naturally-occurring spectra are well-behaved (e.g., continuous and slowly-varying), color algebras can be formulated that are largely accurate and agree well with human intuition. Here we explore the family of algebras that result from associating each color with a member of a three-dimensional manifold of spectra. This association can be used to construct a color product, defined as the color of the spectrum of the wavelength-wise product of the spectra associated with the two input colors. The choice of the spectral manifold determines the behavior of the resulting system, and certain special subspaces allow computational efficiencies. The resulting systems can be used to improve computer graphic rendering techniques, and to model various perceptual phenomena such as color constancy.
Fourier transforms in spectroscopy
Kauppinen, Jyrki
2000-01-01
This modern approach to the subject is clearly and logically structured, and gives readers an understanding of the essence of Fourier transforms and their applications. All important aspects are included with respect to their use with optical spectroscopic data. Based on popular lectures, the authors provide the mathematical fundamentals and numerical applications which are essential in practical use. The main part of the book is dedicated to applications of FT in signal processing and spectroscopy, with IR and NIR, NMR and mass spectrometry dealt with both from a theoretical and practical poi
Fast Fourier transform telescope
Tegmark, Max; Zaldarriaga, Matias
2009-04-01
We propose an all-digital telescope for 21 cm tomography, which combines key advantages of both single dishes and interferometers. The electric field is digitized by antennas on a rectangular grid, after which a series of fast Fourier transforms recovers simultaneous multifrequency images of up to half the sky. Thanks to Moore’s law, the bandwidth up to which this is feasible has now reached about 1 GHz, and will likely continue doubling every couple of years. The main advantages over a single dish telescope are cost and orders of magnitude larger field-of-view, translating into dramatically better sensitivity for large-area surveys. The key advantages over traditional interferometers are cost (the correlator computational cost for an N-element array scales as Nlog2N rather than N2) and a compact synthesized beam. We argue that 21 cm tomography could be an ideal first application of a very large fast Fourier transform telescope, which would provide both massive sensitivity improvements per dollar and mitigate the off-beam point source foreground problem with its clean beam. Another potentially interesting application is cosmic microwave background polarization.
Hackel, L.A.; Hermann, M.R.; Dane, C.B.; Tiszauer, D.H.
1995-12-12
A solid state laser is frequency tripled to 0.3 {micro}m. A small portion of the laser is split off and generates a Stokes seed in a low power oscillator. The low power output passes through a mask with the appropriate hole pattern. Meanwhile, the bulk of the laser output is focused into a larger stimulated Brillouin scattering (SBS) amplifier. The low power beam is directed through the same cell in the opposite direction. The majority of the amplification takes place at the focus which is the fourier transform plane of the mask image. The small holes occupy large area at the focus and thus are preferentially amplified. The amplified output is now imaged onto the multichip module where the holes are drilled. Because of the fourier plane amplifier, only about 1/10th the power of a competitive system is needed. This concept allows less expensive masks to be used in the process and requires much less laser power. 1 fig.
Hackel, Lloyd A.; Hermann, Mark R.; Dane, C. Brent; Tiszauer, Detlev H.
1995-01-01
A solid state laser is frequency tripled to 0.3 .mu.m. A small portion of the laser is split off and generates a Stokes seed in a low power oscillator. The low power output passes through a mask with the appropriate hole pattern. Meanwhile, the bulk of the laser output is focused into a larger stimulated Brillouin scattering (SBS) amplifier. The low power beam is directed through the same cell in the opposite direction. The majority of the amplification takes place at the focus which is the fourier transform plane of the mask image. The small holes occupy large area at the focus and thus are preferentially amplified. The amplified output is now imaged onto the multichip module where the holes are drilled. Because of the fourier plane amplifier, only .about.1/10th the power of a competitive system is needed. This concept allows less expensive masks to be used in the process and requires much less laser power.
Color Categories and Color Appearance
Webster, Michael A.; Kay, Paul
2012-01-01
We examined categorical effects in color appearance in two tasks, which in part differed in the extent to which color naming was explicitly required for the response. In one, we measured the effects of color differences on perceptual grouping for hues that spanned the blue-green boundary, to test whether chromatic differences across the boundary…
Color Categories and Color Appearance
Webster, Michael A.; Kay, Paul
2012-01-01
We examined categorical effects in color appearance in two tasks, which in part differed in the extent to which color naming was explicitly required for the response. In one, we measured the effects of color differences on perceptual grouping for hues that spanned the blue-green boundary, to test whether chromatic differences across the boundary…
Wrolstad, Ronald E.; Smith, Daniel E.
Color, flavor, and texture are the three principal quality attributes that determine food acceptance, and color has a far greater influence on our judgment than most of us appreciate. We use color to determine if a banana is at our preferred ripeness level, and a discolored meat product can warn us that the product may be spoiled. The marketing departments of our food corporations know that, for their customers, the color must be "right." The University of California Davis scorecard for wine quality designates four points out of 20, or 20% of the total score, for color and appearance (1). Food scientists who establish quality control specifications for their product are very aware of the importance of color and appearance. While subjective visual assessment and use of visual color standards are still used in the food industry, instrumental color measurements are extensively employed. Objective measurement of color is desirable for both research and industrial applications, and the ruggedness, stability, and ease of use of today's color measurement instruments have resulted in their widespread adoption.
Fourier Transform Spectrometer System
Campbell, Joel F. (Inventor)
2014-01-01
A Fourier transform spectrometer (FTS) data acquisition system includes an FTS spectrometer that receives a spectral signal and a laser signal. The system further includes a wideband detector, which is in communication with the FTS spectrometer and receives the spectral signal and laser signal from the FTS spectrometer. The wideband detector produces a composite signal comprising the laser signal and the spectral signal. The system further comprises a converter in communication with the wideband detector to receive and digitize the composite signal. The system further includes a signal processing unit that receives the composite signal from the converter. The signal processing unit further filters the laser signal and the spectral signal from the composite signal and demodulates the laser signal, to produce velocity corrected spectral data.
Processing of Color Words Activates Color Representations
Richter, Tobias; Zwaan, Rolf A.
2009-01-01
Two experiments were conducted to investigate whether color representations are routinely activated when color words are processed. Congruency effects of colors and color words were observed in both directions. Lexical decisions on color words were faster when preceding colors matched the color named by the word. Color-discrimination responses…
Alexandrov, Mikhail D.; Cairns, Brian; Mishchenko, Michael I.
2012-01-01
We present a novel technique for remote sensing of cloud droplet size distributions. Polarized reflectances in the scattering angle range between 135deg and 165deg exhibit a sharply defined rainbow structure, the shape of which is determined mostly by single scattering properties of cloud particles, and therefore, can be modeled using the Mie theory. Fitting the observed rainbow with such a model (computed for a parameterized family of particle size distributions) has been used for cloud droplet size retrievals. We discovered that the relationship between the rainbow structures and the corresponding particle size distributions is deeper than it had been commonly understood. In fact, the Mie theory-derived polarized reflectance as a function of reduced scattering angle (in the rainbow angular range) and the (monodisperse) particle radius appears to be a proxy to a kernel of an integral transform (similar to the sine Fourier transform on the positive semi-axis). This approach, called the rainbow Fourier transform (RFT), allows us to accurately retrieve the shape of the droplet size distribution by the application of the corresponding inverse transform to the observed polarized rainbow. While the basis functions of the proxy-transform are not exactly orthogonal in the finite angular range, this procedure needs to be complemented by a simple regression technique, which removes the retrieval artifacts. This non-parametric approach does not require any a priori knowledge of the droplet size distribution functional shape and is computationally fast (no look-up tables, no fitting, computations are the same as for the forward modeling).
Scarfone, A. M.
2017-08-01
We present a new formulation of Fourier transform in the picture of the κ-algebra derived in the framework of the κ-generalized statistical mechanics. The κ-Fourier transform is obtained from a κ-Fourier series recently introduced by Scarfone (2013). The kernel of this transform, that reduces to the usual exponential phase in the κ → 0 limit, is composed by a κ-deformed phase and a damping factor that gives a wavelet-like behaviour. We show that the κ-Fourier transform is isomorph to the standard Fourier transform through a changing of time and frequency variables. Nevertheless, the new formalism is useful to study, according to Fourier analysis, those functions defined in the realm of the κ-algebra. As a relevant application, we discuss the central limit theorem for the κ-sum of n-iterate statistically independent random variables.
Quadrature formulas for Fourier coefficients
Bojanov, Borislav
2009-09-01
We consider quadrature formulas of high degree of precision for the computation of the Fourier coefficients in expansions of functions with respect to a system of orthogonal polynomials. In particular, we show the uniqueness of a multiple node formula for the Fourier-Tchebycheff coefficients given by Micchelli and Sharma and construct new Gaussian formulas for the Fourier coefficients of a function, based on the values of the function and its derivatives. © 2009 Elsevier B.V. All rights reserved.
Yau, Donald
2016-01-01
The subject of this book is the theory of operads and colored operads, sometimes called symmetric multicategories. A (colored) operad is an abstract object which encodes operations with multiple inputs and one output and relations between such operations. The theory originated in the early 1970s in homotopy theory and quickly became very important in algebraic topology, algebra, algebraic geometry, and even theoretical physics (string theory). Topics covered include basic graph theory, basic category theory, colored operads, and algebras over colored operads. Free colored operads are discussed in complete detail and in full generality. The intended audience of this book includes students and researchers in mathematics and other sciences where operads and colored operads are used. The prerequisite for this book is minimal. Every major concept is thoroughly motivated. There are many graphical illustrations and about 150 exercises. This book can be used in a graduate course and for independent study.
Directory of Open Access Journals (Sweden)
Dominique Lafon
2011-05-01
Full Text Available The goal of this article is to present specific capabilities and limitations of the use of color digital images in a characterization process. The whole process is investigated, from the acquisition of digital color images to the analysis of the information relevant to various applications in the field of material characterization. A digital color image can be considered as a matrix of pixels with values expressed in a vector-space (commonly 3 dimensional space whose specificity, compared to grey-scale images, is to ensure a coding and a representation of the output image (visualisation printing that fits the human visual reality. In a characterization process, it is interesting to regard color image attnbutes as a set of visual aspect measurements on a material surface. Color measurement systems (spectrocolorimeters, colorimeters and radiometers and cameras use the same type of light detectors: most of them use Charge Coupled Devices sensors. The difference between the two types of color data acquisition systems is that color measurement systems provide a global information of the observed surface (average aspect of the surface: the color texture is not taken into account. Thus, it seems interesting to use imaging systems as measuring instruments for the quantitative characterization of the color texture.
Research progress of the fractional Fourier transform in signal processing
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The fractional Fourier transform is a generalization of the classical Fourier transform, which is introduced from the mathematic aspect by Namias at first and has many applications in optics quickly. Whereas its potential appears to have remained largely unknown to the signal processing community until 1990s. The fractional Fourier transform can be viewed as the chirp-basis expansion directly from its definition, but essentially it can be interpreted as a rotation in the time-frequency plane, i.e. the unified time-frequency transform. With the order from 0 increasing to 1, the fractional Fourier transform can show the characteristics of the signal changing from the time domain to the frequency domain. In this research paper, the fractional Fourier transform has been comprehensively and systematically treated from the signal processing point of view. Our aim is to provide a course from the definition to the applications of the fractional Fourier transform, especially as a reference and an introduction for researchers and interested readers.
An Optical Watermarking Solution for Color Personal Identification Pictures
Yi-zhou, Tan; Shui-hua, Huang; Ben-jian, Sheng; Zhong-ming, Pan; 10.1117/12.839630
2013-01-01
This paper presents a new approach for embedding authentication information into image on printed materials based on optical projection technique. Our experimental setup consists of two parts, one is a common camera, and the other is a LCD projector, which project a pattern on personnel's body (especially on the face). The pattern, generated by a computer, act as the illumination light source with sinusoidal distribution and it is also the watermark signal. For a color image, the watermark is embedded into the blue channel. While we take pictures (256 *256 and 512*512, 567*390 pixels, respectively), an invisible mark is embedded directly into magnitude oefficients of Discrete Fourier transform (DFT) at exposure moment. Both optical an d digital correlation is suitable for detection of this type of watermark. The decoded watermark is a set of concentric circles or sectors in the DFT domain (middle frequencies region) which is robust to photographing, printing and scanning. The unlawful people modify or replace...
Reflective Fourier ptychography.
Pacheco, Shaun; Zheng, Guoan; Liang, Rongguang
2016-02-01
The Fourier ptychography technique in reflection mode has great potential applications in tissue imaging and optical inspection, but the current configuration either has a limitation on cut-off frequency or is not practical. By placing the imaging aperture stop outside the illumination path, the illumination numerical aperture (NA) can be greater than the imaging NA of the objective lens. Thus, the cut-off frequency achieved in the proposed optical system is greater than twice the objective's NA divided by the wavelength (2NAobj/λ ), which is the diffraction limit for the cut-off frequency in an incoherent epi-illumination configuration. We experimentally demonstrated that the synthesized NA is increased by a factor of 4.5 using the proposed optical concept. The key advantage of the proposed system is that it can achieve high-resolution imaging over a large field of view with a simple objective. It will have a great potential for applications in endoscopy, biomedical imaging, surface metrology, and industrial inspection.
Reconstruction in Fourier space
Burden, A.; Percival, W. J.; Howlett, C.
2015-10-01
We present a fast iterative fast Fourier transform (FFT) based reconstruction algorithm that allows for non-parallel redshift-space distortions (RSDs). We test our algorithm on both N-body dark matter simulations and mock distributions of galaxies designed to replicate galaxy survey conditions. We compare solenoidal and irrotational components of the redshift distortion and show that an approximation of this distortion leads to a better estimate of the real-space potential (and therefore faster convergence) than ignoring the RSD when estimating the displacement field. Our iterative reconstruction scheme converges in two iterations for the mock samples corresponding to Baryon Oscillation Spectroscopic Survey CMASS Data Release 11 when we start with an approximation of the RSD. The scheme takes six iterations when the initial estimate, measured from the redshift-space overdensity, has no RSD correction. Slower convergence would be expected for surveys covering a larger angle on the sky. We show that this FFT based method provides a better estimate of the real-space displacement field than a configuration space method that uses finite difference routines to compute the potential for the same grid resolution. Finally, we show that a lognormal transform of the overdensity, used as a proxy for the linear overdensity, is beneficial in estimating the full displacement field from a dense sample of tracers. However, the lognormal transform of the overdensity does not perform well when estimating the displacements from sparser simulations with a more realistic galaxy density.
Grafakos, Loukas
2014-01-01
This text is addressed to graduate students in mathematics and to interested researchers who wish to acquire an in depth understanding of Euclidean Harmonic analysis. The text covers modern topics and techniques in function spaces, atomic decompositions, singular integrals of nonconvolution type, and the boundedness and convergence of Fourier series and integrals. The exposition and style are designed to stimulate further study and promote research. Historical information and references are included at the end of each chapter. This third edition includes a new chapter entitled "Multilinear Harmonic Analysis" which focuses on topics related to multilinear operators and their applications. Sections 1.1 and 1.2 are also new in this edition. Numerous corrections have been made to the text from the previous editions and several improvements have been incorporated, such as the adoption of clear and elegant statements. A few more exercises have been added with relevant hints when necessary. Reviews fr...
POINTWISE FOURIER INVERSION OF DISTRIBUTIONS
Institute of Scientific and Technical Information of China (English)
F.J.González Vieli
2008-01-01
We show that,given a tempered distribution T whose Fourier transform is a function of polynomial growth and a point x in Rn at which T has the value τ(in the sense of Lojasiewicz),the Fourier integral of T at x is summable in Bochner-Riesz means to τ.
Wavelet-fractional Fourier transforms
Institute of Scientific and Technical Information of China (English)
Yuan Lin
2008-01-01
This paper extends the definition of fractional Fourier transform (FRFT) proposed by Namias V by using other orthonormal bases for L2 (R) instead of Hermite-Ganssian functions.The new orthonormal basis is gained indirectly from multiresolution analysis and orthonormal wavelets. The so defined FRFT is called wavelets-fractional Fourier transform.
Digital Fourier analysis advanced techniques
Kido, Ken'iti
2015-01-01
This textbook is a thorough, accessible introduction to advanced digital Fourier analysis for advanced undergraduate and graduate students. Assuming knowledge of the Fast Fourier Transform, this book covers advanced topics including the Hilbert transform, cepstrum analysis, and the two-dimensional Fourier transform. Saturated with clear, coherent illustrations, "Digital Fourier Analysis - Advanced Techniques" includes practice problems and thorough Appendices. As a central feature, the book includes interactive applets (available online) that mirror the illustrations. These user-friendly applets animate concepts interactively, allowing the user to experiment with the underlying mathematics. The applet source code in Visual Basic is provided online, enabling advanced students to tweak and change the programs for more sophisticated results. A complete, intuitive guide, "Digital Fourier Analysis - Advanced Techniques" is an essential reference for students in science and engineering.
On the Alignment of Shapes Represented by Fourier Descriptors
DEFF Research Database (Denmark)
Sjöstrand, Karl; Ericsson, Anders; Larsen, Rasmus
2006-01-01
The representation of shapes by Fourier descriptors is a time-honored technique that has received relatively little attention lately. Nevertheless, it has many benefits and is applicable for describing a range of medical structures in two dimensions. Delineations in medical applications often...... consist of continuous outlines of structures, where no information of correspondence between samples exist. In this article, we discuss an alignment method that works directly with the functional representation of Fourier descriptors, and that is optimal in a least-squares sense. With corresponding...... represented by common landmarks can be constructed in an automatic fashion. If the aligned Fourier descriptors are inverse transformed from the frequency domain to the spatial domain, a set of roughly aligned landmarks are obtained. The positions of these are then adjusted along the contour of the objects...
Synthetic aperture ultrasound Fourier beamformation using virtual sources
DEFF Research Database (Denmark)
Moghimirad, Elahe; Villagómez Hoyos, Carlos Armando; Mahloojifar, Ali
2016-01-01
An efficient Fourier beamformation algorithm is presented for multistatic synthetic aperture ultrasound imaging using virtual sources (FBV). The concept is based on the frequency domain wavenumber algorithm from radar and sonar and is extended to a multi-element transmit/receive configuration using...
Slow Mapping: Color Word Learning as a Gradual Inductive Process
Wagner, Katie; Dobkins, Karen; Barner, David
2013-01-01
Most current accounts of color word acquisition propose that the delay between children's first production of color words and adult-like understanding is due to problems abstracting color as a domain of meaning. Here we present evidence against this hypothesis, and show that, from the time children produce color words in a labeling task they use…
Optical/digital color photography based on white-light information processing
Institute of Scientific and Technical Information of China (English)
罗罡; 刘福来; 林列; 方志良; 王肇圻; 母国光; 翁志成
2001-01-01
The achievement in optical/digital color photography based on white-light information processing including the color-encoding camera, the color image decoder, the integral window Fourier algorithm of the Fourier transform in digital decoding, the color correction of the retrieval color image and the fusion of zero order diffraction is reported. This technique has found its important applications in the fields of aerial reconnaissance photography and far-distance ground photography due to its features of large information capacity, convenience in archival storage, the capability of color enhancement, particularly easy transportation by Internet.
Fourier Analysis and Structure Determination: Part I: Fourier Transforms.
Chesick, John P.
1989-01-01
Provides a brief introduction with some definitions and properties of Fourier transforms. Shows relations, ways of understanding the mathematics, and applications. Notes proofs are not included but references are given. First of three part series. (MVL)
National Research Council Canada - National Science Library
Foster, David H
2011-01-01
... despite changes in the spectrum of the illumination. At about the same time, new models of color constancy appeared, along with physiological data on cortical mechanisms and photographic colorimetric measurements of natural scenes...
Rius Tormo, Palmira
2010-01-01
Póster presentado en el IX Congreso Nacional del Color, Alicante, 29-30 junio, 1-2 julio 2010. La exposición que se propone tiene como núcleo principal el color y muestra las posibilidades expresivas que aporta a los diferentes materiales. Las 7 obras presentadas buscan la armonía estética y la fuerza simbólica.
Gegenfurtner, Karl R; Kiper, Daniel C
2003-01-01
Color vision starts with the absorption of light in the retinal cone photoreceptors, which transduce electromagnetic energy into electrical voltages. These voltages are transformed into action potentials by a complicated network of cells in the retina. The information is sent to the visual cortex via the lateral geniculate nucleus (LGN) in three separate color-opponent channels that have been characterized psychophysically, physiologically, and computationally. The properties of cells in the retina and LGN account for a surprisingly large body of psychophysical literature. This suggests that several fundamental computations involved in color perception occur at early levels of processing. In the cortex, information from the three retino-geniculate channels is combined to enable perception of a large variety of different hues. Furthermore, recent evidence suggests that color analysis and coding cannot be separated from the analysis and coding of other visual attributes such as form and motion. Though there are some brain areas that are more sensitive to color than others, color vision emerges through the combined activity of neurons in many different areas.
Fourier analysis and stochastic processes
Brémaud, Pierre
2014-01-01
This work is unique as it provides a uniform treatment of the Fourier theories of functions (Fourier transforms and series, z-transforms), finite measures (characteristic functions, convergence in distribution), and stochastic processes (including arma series and point processes). It emphasises the links between these three themes. The chapter on the Fourier theory of point processes and signals structured by point processes is a novel addition to the literature on Fourier analysis of stochastic processes. It also connects the theory with recent lines of research such as biological spike signals and ultrawide-band communications. Although the treatment is mathematically rigorous, the convivial style makes the book accessible to a large audience. In particular, it will be interesting to anyone working in electrical engineering and communications, biology (point process signals) and econometrics (arma models). A careful review of the prerequisites (integration and probability theory in the appendix, Hilbert spa...
Fourier series and orthogonal functions
Davis, Harry F
1963-01-01
This incisive text deftly combines both theory and practical example to introduce and explore Fourier series and orthogonal functions and applications of the Fourier method to the solution of boundary-value problems. Directed to advanced undergraduate and graduate students in mathematics as well as in physics and engineering, the book requires no prior knowledge of partial differential equations or advanced vector analysis. Students familiar with partial derivatives, multiple integrals, vectors, and elementary differential equations will find the text both accessible and challenging.
Dynamic measurement of deformation using Fourier transform digital holographic interferometry
Gao, Xinya; Wu, Sijin; Yang, Lianxiang
2013-10-01
Digital holographic interferometry (DHI) is a well-established optical technique for measurement of nano-scale deformations. It has become more and more important due to the rapid development of applications in aerospace engineering and biomedicine. Traditionally, phase shift technique is used to quantitatively measure the deformations in DHI. However, it cannot be applied in dynamic measurement. Fourier transform phase extraction method, which can determine the phase distribution from only a single hologram, becomes a promising method to extract transient phases in DHI. This paper introduces a digital holographic interferometric system based on 2D Fourier transform phase extraction method, with which deformations of objects can be measured quickly. In the optical setup, the object beam strikes a CCD via a lens and aperture, and the reference beam is projected on the CCD through a single-mode fiber. A small inclination angle between the diverging reference beam and optical axial is introduced in order to physically separate the Fourier components in frequency domain. Phase maps are then obtained by the utilization of Fourier transform and windowed inverse Fourier transform. The capability of the Fourier transform DHI is discussed by theoretical discussion as well as experiments.
... present from birth) color vision problems: Achromatopsia -- complete color blindness , seeing only shades of gray Deuteranopia -- difficulty telling ... Vision test - color; Ishihara color vision test Images Color blindness tests References Bowling B. Hereditary fundus dystrophies. In: ...
Modeling human color categorization: Color discrimination and color memory
Heskes, T.; van den Broek, Egon; Lucas, P.; Hendriks, Maria A.; Vuurpijl, L.G.; Puts, M.J.H.; Wiegerinck, W.
2003-01-01
Color matching in Content-Based Image Retrieval is done using a color space and measuring distances between colors. Such an approach yields non-intuitive results for the user. We introduce color categories (or focal colors), determine that they are valid, and use them in two experiments. The experim
Modeling human color categorization: Color discrimination and color memory
Heskes, T.; van den Broek, Egon; Lucas, P.; Hendriks, Maria A.; Vuurpijl, L.G.; Puts, M.J.H.; Wiegerinck, W.
2003-01-01
Color matching in Content-Based Image Retrieval is done using a color space and measuring distances between colors. Such an approach yields non-intuitive results for the user. We introduce color categories (or focal colors), determine that they are valid, and use them in two experiments. The
Institute of Scientific and Technical Information of China (English)
王飞; 赵镇南; 李喜琪; 姜春晖; 孙兴怀; 史国华; 钱韶红
2012-01-01
Objective To discuss the imaging ability of different anterior optical coherence tomography (OCT) systems.Methods It was a cross-sectional study.Six normal volunteers (12 eyes,24 directions) were involved in this cross-sectional study.Three different OCT systems were used to acquire images of their eyes.The important structures:scleral spur,Schlemm's canal,anterior segment angle recess and Schwalbe line were defined.The trabecular-iris angle (TIA500),angle opening distance at 500 μm (AOD500),the area of the trabeculo-iris space at 500 μm (TISA500),the widest diameter of Schlemm's canal,and the area and circumference of Schlemm's canal were measured if possible.Results Using real-time Fourier-domain anterior segment OCT,the scleral spur,Schlemm's canal,anterior segment angle recess and the Schwalbe line were defined in 8 eyes (67％) 13 positions (54％),12 eyes (100％) 22 positions (92％),12 eyes (100％) 24 positions (100％),and 6 eyes (50％) 9 positions (38％),respectively.Using RTV-ue 100 OCT,Schlemm's canal and the Schwalbe line could be defined in 8 eyes (67％) 8 positions (33％) and 10 eyes (83％) 19 positions (79％),respectively.The scleral spur and anterior segment angle recess could not be seen.The scleral spur and anterior segment angle recess were defined in 12 eyes (100％) 21 positions (88％) and 12 eyes (100％) 24positions (100％),respectively using Visante OCT,but Schwalbe's line and Schlemm's canal could not be defined.There was a significant difference in their ability to define important structures (scleral spur,P＜0.01; Schlemm's canal,P＜0.01; anterior segment angle recess,P＜0.01; and Schwalbe line,P＜0.01).The TIA500,AOD500 and TISA500 measured by Real-time Fourier-domain anterior segment OCT and Visante OCT were similar,and the area and widest diameter of Schlemm's canal measured by Real-time Fourier-domain anterior segment OCT and RTV-ue 100 OCT were also similar.The differences were not significant.Conclusion All three
Energy Technology Data Exchange (ETDEWEB)
Wilczek, F. [Institute for Advanced Study, Princeton, NJ (United States)
1997-09-22
The asymptotic freedom of QCD suggests that at high density - where one forms a Fermi surface at very high momenta - weak coupling methods apply. These methods suggest that chiral symmetry is restored and that an instability toward color triplet condensation (color superconductivity) sets in. Here I attempt, using variational methods, to estimate these effects more precisely. Highlights include demonstration of a negative pressure in the uniform density chiral broken phase for any non-zero condensation, which we take as evidence for the philosophy of the MIT bag model; and demonstration that the color gap is substantial - several tens of MeV - even at modest densities. Since the superconductivity is in a pseudoscalar channel, parity is spontaneously broken.
On Associative Meanings of Color-Related English Words from the Per-spective of Cognitive Metaphor
Institute of Scientific and Technical Information of China (English)
邹强珍
2014-01-01
As an important metaphor, metaphor of color-related English words regards color domain as source domain, and maps the color domain to non-colored abstract domain. This enables us to understand, think and discuss color-related concept. This paper studies the basic color-related English words through cognitive metaphor. The process of exploring the associative mean-ings of the color-related English words is in nature to understand the cultural connotation of color-related English words by means of cognitive metaphor under different cultural backgrounds.
DEFF Research Database (Denmark)
Haberland, Hartmut
2005-01-01
The domain concept, originally suggested by Schmidt-Rohr in the 1930’s (as credited in Fishman’s writings in the 1970s), was an attempt to sort out different areas of language use in multilingual societies, which are relevant for language choice. In Fishman’s version, domains were considered...... not described in terms of domains, and recent research e.g. about the multilingual communities in the Danish-German border area seems to confirm this....
Fractional Fourier transform-based optical encryption with treble random phase-encoding
Xin, Yi; Tao, Ran; Wang, Yue
2008-03-01
We propose a new architecture of optical encryption technique using the fractional Fourier transform with three statistically independent random phase masks. Compared with the existing double-phase encoding method in the fractional Fourier-domain, the proposed extra phase mask in the last fractional Fourier domain makes the architecture symmetrical, and additive processing to the encrypted image can be turned into complex stationary white noise after decryption, and enlarge the key space without any degradation of its robustness to blind decryption. This property can be utilized to improve the quality of the recover image. Simulation results have verified the validity.
Institute of Scientific and Technical Information of China (English)
南楠; 步鹏; 郭昕; 王向朝
2012-01-01
A three-dimensional (3D) full-range complex Fourier domain optical coherence tomography (FDOCT) system based on sinusoidal phase-modulating method is developed for vivo imaging of human skin. A complex spectral interferogram is retrieved based on Fourier transform analysis and bandpass filter of phase-modulated interference spectra, which is recorded with sinusoidal phase modulation introduced during lateral beam scanning. With the system, the depth imaging range is doubled and the signal-to-noise ratio degrading with the lateral scanning is avoided. Also the system is suitable for vivo imaging. 3D vivo full-range OCX images of human skin is achieved with the proposed system. In the images, the stratum corneum, the epidermis and the upper dermis can be clearly identified. By optimizing the sampling number in one modulation period, the complex conjugate rejection ratio is improved, which is about 36 dB.%基于正弦相位调制建立了用于人体皮肤在体三维成像的全深度复频域光学相干层析(FDOCT)成像系统.通过在不同横向位置获取的干涉谱信号中引入正弦相位调制,利用傅里叶变换结合带通滤波的方法重建复干涉谱信号,使成像深度范围扩大为原来的两倍,且适合对活体组织进行在体成像.通过优化相位调制周期内的采样点数,提高了镜像抑制比.基于该系统在体获得了人体皮肤的三维全深度层析图,图中角质层、表皮层及真皮乳突层等皮肤层状结构清晰可见,镜像消除比约为36dB.
A class of Fourier integrals based on the electric potential of an elongated dipole.
Skianis, Georgios Aim
2014-01-01
In the present paper the closed expressions of a class of non tabulated Fourier integrals are derived. These integrals are associated with a group of functions at space domain, which represent the electric potential of a distribution of elongated dipoles which are perpendicular to a flat surface. It is shown that the Fourier integrals are produced by the Fourier transform of the Green's function of the potential of the dipole distribution, times a definite integral in which the distribution of the polarization is involved. Therefore the form of this distribution controls the expression of the Fourier integral. Introducing various dipole distributions, the respective Fourier integrals are derived. These integrals may be useful in the quantitative interpretation of electric potential anomalies produced by elongated dipole distributions, at spatial frequency domain.
Fourier Series, the DFT and Shape Modelling
DEFF Research Database (Denmark)
Skoglund, Karl
2004-01-01
This report provides an introduction to Fourier series, the discrete Fourier transform, complex geometry and Fourier descriptors for shape analysis. The content is aimed at undergraduate and graduate students who wish to learn about Fourier analysis in general, as well as its application to shape...
Fourier processing of quantum light
Poem, Eilon; Lahini, Yoav; Silberberg, Yaron
2012-01-01
It is shown that a classical optical Fourier processor can be used for the shaping of quantum correlations between two or more photons, and the class of Fourier masks applicable in the multiphoton Fourier space is identified. This concept is experimentally demonstrated using two types of periodic phase masks illuminated with path-entangled photon pairs, a highly non-classical state of light. Applied first were sinusoidal phase masks, emulating two-particle quantum walk on a periodic lattice, yielding intricate correlation patterns with various spatial bunching and anti-bunching effects depending on the initial state. Then, a periodic Zernike-like filter was applied on top of the sinusoidal phase masks. Using this filter, phase information lost in the original correlation measurements was retrieved.
Fast Numerical Nonlinear Fourier Transforms
Wahls, Sander
2014-01-01
The nonlinear Fourier transform, which is also known as the forward scattering transform, decomposes a periodic signal into nonlinearly interacting waves. In contrast to the common Fourier transform, these waves no longer have to be sinusoidal. Physically relevant waveforms are often available for the analysis instead. The details of the transform depend on the waveforms underlying the analysis, which in turn are specified through the implicit assumption that the signal is governed by a certain evolution equation. For example, water waves generated by the Korteweg-de Vries equation can be expressed in terms of cnoidal waves. Light waves in optical fiber governed by the nonlinear Schr\\"dinger equation (NSE) are another example. Nonlinear analogs of classic problems such as spectral analysis and filtering arise in many applications, with information transmission in optical fiber, as proposed by Yousefi and Kschischang, being a very recent one. The nonlinear Fourier transform is eminently suited to address them ...
Fourier transforms in generalized Fock spaces
Directory of Open Access Journals (Sweden)
John Schmeelk
1990-01-01
Full Text Available A classical Fock space consists of functions of the form,Φ↔(ϕ0,ϕ1,…,ϕq,…,where ϕ0∈C and ϕq∈L2(R3q, q≥1. We will replace the ϕq, q≥1 with q-symmetric rapid descent test functions within tempered distribution theory. This space is a natural generalization of a classical Fock space as seen by expanding functionals having generalized Taylor series. The particular coefficients of such series are multilinear functionals having tempered distributions as their domain. The Fourier transform will be introduced into this setting. A theorem will be proven relating the convergence of the transform to the parameter, s, which sweeps out a scale of generalized Fock spaces.
Finkelstein, Robert J
2009-01-01
Previous studies have suggested complementary models of the elementary particles as (a) quantum knots and (b) preonic nuclei that are field and particle descriptions, respectively, of the same particles. This earlier work, carried out in the context of standard electroweak (SU(2) x U(1)) physics, is here extended to the strong interactions by the introduction of color (SU(3)) charges.
Johnson, Heidi S. S.; Maki, Jennifer A.
2009-01-01
This article reports a study conducted by members of the WellU Academic Integration Subcommittee of The College of St. Scholastica's College's Healthy Campus Initiative plan whose purpose was to determine whether changing color in the classroom could have a measurable effect on students. One simple improvement a school can make in a classroom is…
Combination Restoration for Motion-blurred Color Videos under Limited Transmission Bandwidth
Directory of Open Access Journals (Sweden)
Shi Li
2009-10-01
Full Text Available Color video images degraded in a deterministic way by motion-blurring can be restored by the new algorithm in real-time by using color components combination to fit to the limited transmission bandwidth. The image motion PSF of each surface of YUV422 image can be obtained based on the color space conversion model. The Y, U, V planes are packed to construct a 2 dimensional complex array. Through the decomposition of frequency domain, the Y, U, V frequency can be had respectively by performing Fourier transform a time on the specific complex array. The resulting frequencies will be filtered by Wiener filter to generate the final restored images. The proposed algorithm can restore 1024x1024 24-bit motionblurred color video images at 18 ms/frame speed on GPU, and the PSNR of the restored frame is 31.45. The experiment results show that the proposed algorithm is 3X speed compared to the traditional algorithm, and it reduces the bandwidth of video data stream 1/3.
Static Fourier transform infrared spectrometer.
Schardt, Michael; Murr, Patrik J; Rauscher, Markus S; Tremmel, Anton J; Wiesent, Benjamin R; Koch, Alexander W
2016-04-01
Fourier transform spectroscopy has established itself as the standard method for spectral analysis of infrared light. Here we present a robust and compact novel static Fourier transform spectrometer design without any moving parts. The design is well suited for measurements in the infrared as it works with extended light sources independent of their size. The design is experimentally evaluated in the mid-infrared wavelength region between 7.2 μm and 16 μm. Due to its large etendue, its low internal light loss, and its static design it enables high speed spectral analysis in the mid-infrared.
Multi-channel sampling theorems for band-limited signals with fractional Fourier transform
Institute of Scientific and Technical Information of China (English)
2008-01-01
Multi-channel sampling for band-limited signals is fundamental in the theory of multi-channel parallel A/D environment and multiplexing wireless communication environment. As the fractional Fourier transform has been found wide applications in signal processing fields, it is necessary to consider the multi-channel sampling theorem based on the fractional Fourier transform. In this paper, the multi-channel sampling theorem for the fractional band-limited signal is firstly proposed, which is the generalization of the well-known sampling theorem for the fractional Fourier transform. Since the periodic nonuniformly sampled signal in the fractional Fourier domain has valuable applications, the reconstruction expression for the periodic nonuniformly sampled signal has been then obtained by using the derived multi-channel sampling theorem and the specific space-shifting and phase-shifting properties of the fractional Fourier transform. Moreover, by designing different fractional Fourier filters, we can obtain reconstruction methods for other sampling strategies.
Beaulieu, Gabriel; Duchêne, Eric
2012-01-01
Coloring games are combinatorial games where the players alternate painting uncolored vertices of a graph one of $k > 0$ colors. Each different ruleset specifies that game's coloring constraints. This paper investigates six impartial rulesets (five new), derived from previously-studied graph coloring schemes, including proper map coloring, oriented coloring, 2-distance coloring, weak coloring, and sequential coloring. For each, we study the outcome classes for special cases and general computational complexity. In some cases we pay special attention to the Grundy function.
Fourier transform of delayed fluorescence as an indicator of herbicide concentration.
Guo, Ya; Tan, Jinglu
2014-12-21
It is well known that delayed fluorescence (DF) from Photosystem II (PSII) of plant leaves can be potentially used to sense herbicide pollution and evaluate the effect of herbicides on plant leaves. The research of using DF as a measure of herbicides in the literature was mainly conducted in time domain and qualitative correlation was often obtained. Fourier transform is often used to analyze signals. Viewing DF signal in frequency domain through Fourier transform may allow separation of signal components and provide a quantitative method for sensing herbicides. However, there is a lack of an attempt to use Fourier transform of DF as an indicator of herbicide. In this work, the relationship between the Fourier transform of DF and herbicide concentration was theoretically modelled and analyzed, which immediately yielded a quantitative method to measure herbicide concentration in frequency domain. Experiments were performed to validate the developed method.
A Borderline Random Fourier Series
Talagrand, Michel
1995-01-01
Consider a mean zero random variable $X$, and an independent sequence $(X_n)$ distributed like $X$. We show that the random Fourier series $\\sum_{n\\geq 1} n^{-1} X_n \\exp(2i\\pi nt)$ converges uniformly almost surely if and only if $E(|X|\\log\\log(\\max(e^e, |X|))) < \\infty$.
Fourier Series and Elliptic Functions
Fay, Temple H.
2003-01-01
Non-linear second-order differential equations whose solutions are the elliptic functions "sn"("t, k"), "cn"("t, k") and "dn"("t, k") are investigated. Using "Mathematica", high precision numerical solutions are generated. From these data, Fourier coefficients are determined yielding approximate formulas for these non-elementary functions that are…
Fourier Analysis of Musical Intervals
LoPresto, Michael C.
2008-01-01
Use of a microphone attached to a computer to capture musical sounds and software to display their waveforms and harmonic spectra has become somewhat commonplace. A recent article in "The Physics Teacher" aptly demonstrated the use of MacScope in just such a manner as a way to teach Fourier analysis. A logical continuation of this project is to…
Utilizing Bochners Theorem for Constrained Evaluation of Missing Fourier Data
Nemirovsky, Jonathan
2015-01-01
A method is presented for estimating unknown Fourier domain (k-space) data using a small number of samples in that space. The method is derived from Bochners Theorem, and is termed: Bochner Inequality Completion of K-Space (BICKS). It is suitable for filling the k-space of a real and nonnegative unknown quantity, and applicable even when the sampling rate is substantially lower than the Nyquist sampling rate. The BICKS method is demonstrated in the context of medical imaging, but it is also applicable to many other scientific areas that utilize signal processing in Fourier domain. The results indicate that filling a highly undersampled k-space using BICKS enables high quality image reconstruction.
Non-Fourier heat conduction in an exponentially graded slab
Raveshi, M. R.
2016-03-01
The present article investigates one-dimensional non-Fourier heat conduction in a functionally graded material by using the differential transformation method. The studied geometry is a finite functionally graded slab, which is initially at a uniform temperature and suddenly experiences a temperature rise at one side, while the other side is kept insulated. A general non-Fourier heat transfer equation related to the functionally graded slab is derived. The problem is solved in the Laplace domain analytically, and the final results in the time domain are obtained by using numerical inversion of the Laplace transform. The obtained results are compared with the exact solution to verify the accuracy of the proposed method, which shows excellent agreement.
Optimized Fourier representations for three-dimensional magnetic surfaces
Energy Technology Data Exchange (ETDEWEB)
Hirshman, S.P.; Meier, H.K.
1984-11-01
The selection of an optimal parametric angle theta describing a closed magnetic flux surface is considered with regard to accelerating the convergence rate of the Fourier series for the Cartesian coordinates x(theta,phi) identical with R - R/sub 0/ and y(theta,phi) identical with Z - Z/sub 0/. Geometric criteria are developed based on the Hamiltonian invariants of Keplerian orbits. These criteria relate the rate of curve traversal (tangential speed) to the curvature (normal acceleration) so as to provide increased angular resolution in regions of largest curvature. They are, however, limited to either convex or starlike domains and do not provide rapid convergence for complex domains with alternating convex and concave regions. A generally applicable constraint criterion, based directly on minimizing the width of the x and y Fourier spectra, is also derived. A variational principle is given for implementing these constraints numerically. Application to the representation of three-dimensional magnetic flux surfaces is discussed.
Ultrafast ranging lidar based on real-time Fourier transformation.
Xia, Haiyun; Zhang, Chunxi
2009-07-15
Real-time Fourier-transformation-based ranging lidar using a mode-locked femtosecond fiber laser is demonstrated. The object signal and the reference signal are guided from a fiber Mach-Zehnder interferometer into a dispersive element. The two optical pulses extend and overlap with each other temporally, which yields a microwave pulse on the photodetector with its frequency proportional to the time delay between the two signals. The temporal interferograms are transformed from the time domain into the frequency domain using a time-to-frequency conversion function obtained in the calibration process. The Fourier transform is used in the data processing. A range resolution of 334 nm at a sampling rate of 48.6 MHz over a distance of 16 cm is demonstrated in the laboratory.
Application of fast Fourier transformation in thermoluminescence thermogram reconstruction
Pla, C.; Podgorsak, E. B.
1984-03-01
A thermoluminescence (TL) thermogram reconstruction technique based on fast Fourier transformation (FFT) techniques is presented. Only the first few terms of the real and imaginary ``frequency arrays,'' representing the thermogram in the frequency domain, are used for thermogram reconstruction by an inverse transformation. A method to determine the optimum number of FFT terms is discussed and a reconstruction study performed on six commonly used TL materials.
Fourier analysis for rotating-element ellipsometers.
Cho, Yong Jai; Chegal, Won; Cho, Hyun Mo
2011-01-15
We introduce a Fourier analysis of the waveform of periodic light-irradiance variation to capture Fourier coefficients for multichannel rotating-element ellipsometers. In this analysis, the Fourier coefficients for a sample are obtained using a discrete Fourier transform on the exposures. The analysis gives a generic function that encompasses the discrete Fourier transform or the Hadamard transform, depending on the specific conditions. Unlike the Hadamard transform, a well-known data acquisition method that is used only for conventional multichannel rotating-element ellipsometers with line arrays with specific readout-mode timing, this Fourier analysis is applicable to various line arrays with either nonoverlap or overlap readout-mode timing. To assess the effects of the novel Fourier analysis, the Fourier coefficients for a sample were measured with a custom-built rotating-polarizer ellipsometer, using this Fourier analysis with various numbers of scans, integration times, and rotational speeds of the polarizer.
Full Text Available ... One Use Facts About Colored Contacts and Halloween Safety Colored Contact Lens Facts Over-the-Counter Costume ... use of colored contact lenses , from the U.S. Food and Drug Administration (FDA). Are the colored lenses ...
Fourier-positivity constraints on QCD dipole models
Directory of Open Access Journals (Sweden)
Bertrand G. Giraud
2016-09-01
Full Text Available Fourier-positivity (F-positivity, i.e. the mathematical property that a function has a positive Fourier transform, can be used as a constraint on the parametrization of QCD dipole-target cross-sections or Wilson line correlators in transverse position space r. They are Bessel transforms of positive transverse momentum dependent gluon distributions. Using mathematical F-positivity constraints on the limit r→0 behavior of the dipole amplitudes, we identify the common origin of the violation of F-positivity for various, however phenomenologically convenient, dipole models. It is due to the behavior r2+ϵ, ϵ>0 softer, even slightly, than color transparency. F-positivity seems thus to conflict with the present dipole formalism when it includes a QCD running coupling constant α(r.
A Graphical Presentation to Teach the Concept of the Fourier Transform
Besalu, E.
2006-01-01
A study was conducted to visualize the reason why the Fourier transform technique is useful to detect the originating frequencies of a complicated superposition of waves. The findings reveal that students respond well when instructors adapt pictorial presentation to show how the time-domain function is transformed into the frequency domain.
Fourier Transform Near Infrared Spectrometry: Using Interferograms To Determine Chemical Composition
Hoy, R. M.; McClure, W. Fred
1989-12-01
Previous research conducted in this laboratory has demonstrated several advantages accrued by transforming near infrared spectra from the wavelength domain to the Fourier domain. Those advantages include: [1] smoothing wavelength domain data without loss of end points, [2] correcting for particle size phenomena encountered in solid sample analyses by simply omitting the mean term Fourier coefficient from the "retransformation process", [3] minimizing the multicollinearity problem prevalent in wavelength space, [4] generating wavelength-space derivatives from Fourier space without loss of end points, [5] performing band enhancements via Fourier self-deconvolution, [6] identifying sample type using Fourier vectors, [7] estimating chemical composition using only the first few Fourier coefficients, [8] cutting of computer storage requirements by more than 96%, [9] cutting of calibration time by more than 96%, hence [10] reducing the drudgery of maintaining calibrations. That the first 12 Fourier coefficients contain sufficient information to determine chemical constituents in many products has turned out to be a major advantage leading us to understand that the chemical absorption information in the wavelength spectrum of a sample obtained with an interferometer was also present in the interferogram.
Motion-corrected Fourier ptychography
Bian, Liheng; Guo, Kaikai; Suo, Jinli; Yang, Changhuei; Chen, Feng; Dai, Qionghai
2016-01-01
Fourier ptychography (FP) is a recently proposed computational imaging technique for high space-bandwidth product imaging. In real setups such as endoscope and transmission electron microscope, the common sample motion largely degrades the FP reconstruction and limits its practicability. In this paper, we propose a novel FP reconstruction method to efficiently correct for unknown sample motion. Specifically, we adaptively update the sample's Fourier spectrum from low spatial-frequency regions towards high spatial-frequency ones, with an additional motion recovery and phase-offset compensation procedure for each sub-spectrum. Benefiting from the phase retrieval redundancy theory, the required large overlap between adjacent sub-spectra offers an accurate guide for successful motion recovery. Experimental results on both simulated data and real captured data show that the proposed method can correct for unknown sample motion with its standard deviation being up to 10% of the field-of-view scale. We have released...
From Fourier analysis to wavelets
Gomes, Jonas
2015-01-01
This text introduces the basic concepts of function spaces and operators, both from the continuous and discrete viewpoints. Fourier and Window Fourier Transforms are introduced and used as a guide to arrive at the concept of Wavelet transform. The fundamental aspects of multiresolution representation, and its importance to function discretization and to the construction of wavelets is also discussed. Emphasis is given on ideas and intuition, avoiding the heavy computations which are usually involved in the study of wavelets. Readers should have a basic knowledge of linear algebra, calculus, and some familiarity with complex analysis. Basic knowledge of signal and image processing is desirable. This text originated from a set of notes in Portuguese that the authors wrote for a wavelet course on the Brazilian Mathematical Colloquium in 1997 at IMPA, Rio de Janeiro.
Compact Microwave Fourier Spectrum Analyzer
Savchenkov, Anatoliy; Matsko, Andrey; Strekalov, Dmitry
2009-01-01
A compact photonic microwave Fourier spectrum analyzer [a Fourier-transform microwave spectrometer, (FTMWS)] with no moving parts has been proposed for use in remote sensing of weak, natural microwave emissions from the surfaces and atmospheres of planets to enable remote analysis and determination of chemical composition and abundances of critical molecular constituents in space. The instrument is based on a Bessel beam (light modes with non-zero angular momenta) fiber-optic elements. It features low power consumption, low mass, and high resolution, without a need for any cryogenics, beyond what is achievable by the current state-of-the-art in space instruments. The instrument can also be used in a wide-band scatterometer mode in active radar systems.
Fourier's Law in Quantum Mechanics
Seligman, Thomas H
2010-01-01
We derive Fourier's law for a completely coherent quantum system coupled locally to two heat baths at different temperatures. We solve the master equation to first order in the temperature difference. We show that the heat conductance can be expressed as a thermodynamic equilibrium coefficient taken at some intermediate temperature. We use that expression to show that for temperatures large compared to the mean level spacing of the system, the heat conductance is inversely proportional to the length of the system.
A More Accurate Fourier Transform
Courtney, Elya
2015-01-01
Fourier transform methods are used to analyze functions and data sets to provide frequencies, amplitudes, and phases of underlying oscillatory components. Fast Fourier transform (FFT) methods offer speed advantages over evaluation of explicit integrals (EI) that define Fourier transforms. This paper compares frequency, amplitude, and phase accuracy of the two methods for well resolved peaks over a wide array of data sets including cosine series with and without random noise and a variety of physical data sets, including atmospheric $\\mathrm{CO_2}$ concentrations, tides, temperatures, sound waveforms, and atomic spectra. The FFT uses MIT's FFTW3 library. The EI method uses the rectangle method to compute the areas under the curve via complex math. Results support the hypothesis that EI methods are more accurate than FFT methods. Errors range from 5 to 10 times higher when determining peak frequency by FFT, 1.4 to 60 times higher for peak amplitude, and 6 to 10 times higher for phase under a peak. The ability t...
Color blindness and Rorschach color responsivity.
Corsino, B V
1985-10-01
Color vision deficits occur in 10% of the American white male population. Thus, color blindness may invalidate diagnostic hypotheses generated from Rorschach data. The Rorschach protocols of 43 white, college male color-blind subjects were compared to the protocols of normally sighted controls. The color-blind group manifested fewer pure "C" responses. No significant between group differences emerged for any of the other primary Rorschach color variables. Pure "C" responses rarely figure prominently in Rorschach evaluations, and the apparent lowered frequency of these responses by the color-blind is insufficient to warrant modification of current Rorschach practice. The data suggest that color blindness is unlikely to confound Rorschach assessment.
An introduction to Fourier series and integrals
Seeley, Robert T
2006-01-01
This compact guide emphasizes the relationship between physics and mathematics, introducing Fourier series in the way that Fourier himself used them: as solutions of the heat equation in a disk. 1966 edition.
Fourier techniques in X-ray timing
M. van der Klis
1988-01-01
Basic principles of Fourier techniques often used in X-ray time series analysis are reviewed. The relation between the discrete Fourier transform and the continuous Fourier transform is discussed to introduce the concepts of windowing and aliasing. The relation is derived between the power spectrum
Dantas, José L; Camata, Thiago V; Brunetto, Maria A C; Moraes, Antonio C; Abrão, Taufik; Altimari, Leandro R
2010-01-01
Frequency domain analyses of changes in electromyographic (EMG) signals over time are frequently used to assess muscle fatigue. Fourier based approaches are typically used in these analyses, yet Fourier analysis assumes signal stationarity, which is unlikely during dynamic contractions. Wavelet based methods of signal analysis do not assume stationarity and may be more appropriate for joint time-frequency domain analysis. The purpose of this study was to compare Short-Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT) in assessing muscle fatigue in isometric and dynamic exercise. The results of this study indicate that CWT and STFT analyses give similar fatigue estimates (slope of median frequency) in isometric and dynamic exercise (P>0.05). However, the results of the variance was lower for both types of exercise in CWT compared to STFT (P signal analysis using STFT. Thus, the stationarity assumption may not be the sole factor responsible for affecting the Fourier based estimates.
Precise and fast spatial-frequency analysis using the iterative local Fourier transform.
Lee, Sukmock; Choi, Heejoo; Kim, Dae Wook
2016-09-19
The use of the discrete Fourier transform has decreased since the introduction of the fast Fourier transform (fFT), which is a numerically efficient computing process. This paper presents the iterative local Fourier transform (ilFT), a set of new processing algorithms that iteratively apply the discrete Fourier transform within a local and optimal frequency domain. The new technique achieves 210 times higher frequency resolution than the fFT within a comparable computation time. The method's superb computing efficiency, high resolution, spectrum zoom-in capability, and overall performance are evaluated and compared to other advanced high-resolution Fourier transform techniques, such as the fFT combined with several fitting methods. The effectiveness of the ilFT is demonstrated through the data analysis of a set of Talbot self-images (1280 × 1024 pixels) obtained with an experimental setup using grating in a diverging beam produced by a coherent point source.
Inverse design of nanostructured surfaces for color effects
DEFF Research Database (Denmark)
Andkjær, Jacob Anders; Johansen, Villads Egede; Friis, Kasper Storgaard;
2014-01-01
We propose an inverse design methodology for systematic design of nanostructured surfaces for color effects. The methodology is based on a 2D topology optimization formulation based on frequency-domain finite element simulations for E and/or H polarized waves. The goal of the optimization...... is to maximize color intensity in prescribed direction(s) for a prescribed color (RGB) vector. Results indicate that nanostructured surfaces with any desirable color vector can be generated; that complex structures can generate more intense colors than simple layerings; that angle independent colorings can...
Fractional Fourier Transform Applied to Digital Images Encryption
Vilardy, Juan M.; Torres, Cesar O.; Mattos, Lorenzo
2008-04-01
In the present paper a digital algorithm was developed to make phase encryption of digital indexed images to color using the fractional Fourier transform (the images in RGB are converted to indexed before to encrypt). The indexed images are represented by a matrix of M×N pixels (where M defines the height and N is the Width of the image) and a color map (it's a matrix of C×3 elements, where C indicates the colors number of the image and the number 3 indicates the three columns associated with the color components: Red, Green and Blue of each pixel of the matrix of M×N) associated to the matrix of pixels to suitably represent the color information of the image. The indexed image (matrix of M×N pixels) to encrypt is placed as the phase of a complex exponential, then is transformed three times and multiplied in intermediate steps by two random phase masks statistically independent thus to obtain the encrypted image, for decrypt the coding image the encryption procedure is applied in the inverse sense to the conjugated complex of the encrypted image, then is taken the negative of the phase of the resulting function of the decryption process and the original image is obtained this way that had been encrypted; For the color map equal procedure is applied in the encryption/decryption process described previously for the matrix of M×N pixels. In the implemented cryptographic algorithm five keys are used, constituted by three fractional orders and two random phase masks, all these keys are necessary for a correct decryption providing a dependability to the transference of images by means of the communications nets.
Aperture scanning Fourier ptychographic microscopy
Ou, Xiaoze; Chung, Jaebum; Horstmeyer, Roarke; Yang, Changhuei
2016-01-01
Fourier ptychographic microscopy (FPM) is implemented through aperture scanning by an LCOS spatial light modulator at the back focal plane of the objective lens. This FPM configuration enables the capturing of the complex scattered field for a 3D sample both in the transmissive mode and the reflective mode. We further show that by combining with the compressive sensing theory, the reconstructed 2D complex scattered field can be used to recover the 3D sample scattering density. This implementation expands the scope of application for FPM and can be beneficial for areas such as tissue imaging and wafer inspection. PMID:27570705
Novel Micro Fourier Transform Spectrometers
Institute of Scientific and Technical Information of China (English)
KONG Yan-mei; LIANG Jing-qiu; LIANG Zhong-zhu; WANG-Bo; ZHANG Jun
2008-01-01
The miniaturization of spectrometer opens a new application area with real-time and on-site measurements. The Fourier transform spectrometer(FTS) is much attractive considering its particular advantages among the approaches. This paper reviews the current status of micro FTS in worldwide and describes its developments; In addition, analyzed are the key problems in designing and fabricating FTS to be settled during the miniaturization. Finally, a novel model of micro FTS with no moving parts is proposed and analyzed, which may provide new concepts for the design of spectrometers.
Fourier-transform optical microsystems
Collins, S. D.; Smith, R. L.; Gonzalez, C.; Stewart, K. P.; Hagopian, J. G.; Sirota, J. M.
1999-01-01
The design, fabrication, and initial characterization of a miniature single-pass Fourier-transform spectrometer (FTS) that has an optical bench that measures 1 cm x 5 cm x 10 cm is presented. The FTS is predicated on the classic Michelson interferometer design with a moving mirror. Precision translation of the mirror is accomplished by microfabrication of dovetailed bearing surfaces along single-crystal planes in silicon. Although it is miniaturized, the FTS maintains a relatively high spectral resolution, 0.1 cm-1, with adequate optical throughput.
Fourier analysis and its applications
Folland, Gerald B
2009-01-01
This book presents the theory and applications of Fourier series and integrals, eigenfunction expansions, and related topics, on a level suitable for advanced undergraduates. It includes material on Bessel functions, orthogonal polynomials, and Laplace transforms, and it concludes with chapters on generalized functions and Green's functions for ordinary and partial differential equations. The book deals almost exclusively with aspects of these subjects that are useful in physics and engineering, and includes a wide variety of applications. On the theoretical side, it uses ideas from modern ana
JPL Fourier transform ultraviolet spectrometer
Cageao, R. P.; Friedl, R. R.; Sander, Stanley P.; Yung, Y. L.
1994-01-01
The Fourier Transform Ultraviolet Spectrometer (FTUVS) is a new high resolution interferometric spectrometer for multiple-species detection in the UV, visible and near-IR. As an OH sensor, measurements can be carried out by remote sensing (limb emission and column absorption), or in-situ sensing (long-path absorption or laser-induced fluorescence). As a high resolution detector in a high repetition rate (greater than 10 kHz) LIF system, OH fluorescence can be discriminated against non-resonant background emission and laser scatter, permitting (0, 0) excitation.
Fourier-Transform Infrared Spectrometer
Schindler, R. A.
1986-01-01
Fourier-transform spectrometer provides approximately hundredfold increase in luminosity at detector plane over that achievable with older instruments of this type. Used to analyze such weak sources as pollutants and other low-concentration substances in atmosphere. Interferometer creates fringe patterns on two distinct arrays of light detectors, which observe different wavelength bands. Objective lens focuses scene on image plane, which contains optical chopper. To make instrument less susceptible to variations in scene under observation, field and detector lenses focus entrance aperture, rather that image, onto detector array.
Fourier Transform Methods. Chapter 4
Kaplan, Simon G.; Quijada, Manuel A.
2015-01-01
This chapter describes the use of Fourier transform spectrometers (FTS) for accurate spectrophotometry over a wide spectral range. After a brief exposition of the basic concepts of FTS operation, we discuss instrument designs and their advantages and disadvantages relative to dispersive spectrometers. We then examine how common sources of error in spectrophotometry manifest themselves when using an FTS and ways to reduce the magnitude of these errors. Examples are given of applications to both basic and derived spectrophotometric quantities. Finally, we give recommendations for choosing the right instrument for a specific application, and how to ensure the accuracy of the measurement results..
High-Rate Data-Hiding Robust to Linear Filtering for Colored Hosts
Directory of Open Access Journals (Sweden)
Pérez-González Fernando
2009-01-01
Full Text Available The discrete Fourier transform-rational dither modulation (DFT-RDM has been proposed as a way to provide robustness to linear-time-invariant (LTI filtering for quantization-based watermarking systems. This scheme has been proven to provide high rates for white Gaussian hosts but those rates considerably decrease for nonwhite hosts. In this paper the theoretical analysis of DFT-RDM is generalized to colored Gaussian hosts supplied with an explanation of the performance degradation with respect to white Gaussian hosts. Moreover the characterization of the watermark-to-noise ratio in the frequency domain is shown as an useful tool to give a simple and intuitive measure of performance. Afterwards an extension of DFT-RDM is proposed to improve its performance for colored hosts without assuming any additional knowledge on the attack filter. Our analysis is validated by experiments and the results of several simulations for different attack filters confirm the performance improvement afforded by the whitening operation for both Gaussian colored hosts and audio tracks.
Modeling human color categorization
van den Broek, Egon; Schouten, Th.E.; Kisters, P.M.F.
2008-01-01
A unique color space segmentation method is introduced. It is founded on features of human cognition, where 11 color categories are used in processing color. In two experiments, human subjects were asked to categorize color stimuli into these 11 color categories, which resulted in markers for a Colo
Modeling human color categorization
van den Broek, Egon; Schouten, Th.E.; Kisters, P.M.F.
A unique color space segmentation method is introduced. It is founded on features of human cognition, where 11 color categories are used in processing color. In two experiments, human subjects were asked to categorize color stimuli into these 11 color categories, which resulted in markers for a
Rotation, scale and translation invariant pattern recognition system for color images
Barajas-García, Carolina; Solorza-Calderón, Selene; Álvarez-Borrego, Josué
2016-12-01
This work presents a color image pattern recognition system invariant to rotation, scale and translation. The system works with three 1D signatures, one for each RGB color channel. The signatures are constructed based on Fourier transform, analytic Fourier-Mellin transform and Hilbert binary rings mask. According with the statistical theory of box-plots, the pattern recognition system has a confidence level at least of 95.4%.
[Continuum based fast Fourier transform processing of infrared spectrum].
Liu, Qing-Jie; Lin, Qi-Zhong; Wang, Qin-Jun; Li, Hui; Li, Shuai
2009-12-01
To recognize ground objects with infrared spectrum, high frequency noise removing is one of the most important phases in spectrum feature analysis and extraction. A new method for infrared spectrum preprocessing was given combining spectrum continuum processing and Fast Fourier Transform (CFFT). Continuum was firstly removed from the noise polluted infrared spectrum to standardize hyper-spectra. Then the spectrum was transformed into frequency domain (FD) with fast Fourier transform (FFT), separating noise information from target information After noise eliminating from useful information with a low-pass filter, the filtered FD spectrum was transformed into time domain (TD) with fast Fourier inverse transform. Finally the continuum was recovered to the spectrum, and the filtered infrared spectrum was achieved. Experiment was performed for chlorite spectrum in USGS polluted with two kinds of simulated white noise to validate the filtering ability of CFFT by contrast with cubic function of five point (CFFP) in time domain and traditional FFT in frequency domain. A circle of CFFP has limited filtering effect, so it should work much with more circles and consume more time to achieve better filtering result. As for conventional FFT, Gibbs phenomenon has great effect on preprocessing result at edge bands because of special character of rock or mineral spectra, while works well at middle bands. Mean squared error of CFFT is 0. 000 012 336 with cut-off frequency of 150, while that of FFT and CFFP is 0. 000 061 074 with cut-off frequency of 150 and 0.000 022 963 with 150 working circles respectively. Besides the filtering result of CFFT can be improved by adjusting the filter cut-off frequency, and has little effect on working time. The CFFT method overcomes the Gibbs problem of FFT in spectrum filtering, and can be more convenient, dependable, and effective than traditional TD filter methods.
Pointwise convergence of Fourier series
Arias de Reyna, Juan
2002-01-01
This book contains a detailed exposition of Carleson-Hunt theorem following the proof of Carleson: to this day this is the only one giving better bounds. It points out the motivation of every step in the proof. Thus the Carleson-Hunt theorem becomes accessible to any analyst.The book also contains the first detailed exposition of the fine results of Hunt, Sjölin, Soria, etc on the convergence of Fourier Series. Its final chapters present original material. With both Fefferman's proof and the recent one of Lacey and Thiele in print, it becomes more important than ever to understand and compare these two related proofs with that of Carleson and Hunt. These alternative proofs do not yield all the results of the Carleson-Hunt proof. The intention of this monograph is to make Carleson's proof accessible to a wider audience, and to explain its consequences for the pointwise convergence of Fourier series for functions in spaces near $äcal Lü^1$, filling a well-known gap in the literature.
Seismic Shear Energy Reflection By Radon-Fourier Transform
Directory of Open Access Journals (Sweden)
Malik Umairia
2016-01-01
Full Text Available Seismic waves split in an anisotropic medium, instead of rotating horizontal component to principal direction, Radon-Fourier is derived to observe the signature of shear wave reflection. Synthetic model with fracture is built and discretized using finite difference scheme for spatial and time domain. Common depth point (CDP with single shot gives traces and automatic gain is preprocessed before Radon Transform (RT, a filtering technique gives radon domain. It makes easier to observe fractures at specific incidence and improves its quality in some way by removing the noise. A comparison of synthetic data and BF-data is performed on the basis of root means square error (RMS values. The RMS error is minimum at the 10th trace in radon domain.
Safari, M J; Afarideh, H; Jamili, S; Bayat, E
2016-01-01
A Discrete Fourier Transform Method (DFTM) for discrimination between the signal of neutrons and gamma rays in organic scintillation detectors is presented. The method is based on the transformation of signals into the frequency domain using the sine and cosine Fourier transforms in combination with the discrete Fourier transform. The method is largely benefited from considerable differences that usually is available between the zero-frequency components of sine and cosine and the norm of the amplitude of the DFT for neutrons and gamma-ray signals. Moreover, working in frequency domain naturally results in considerable suppression of the unwanted effects of various noise sources that is expected to be effective in time domain methods. The proposed method could also be assumed as a generalized nonlinear weighting method that could result in a new class of pulse shape discrimination methods, beyond definition of the DFT. A comparison to the traditional Charge Integration Method (CIM), as well as the Frequency G...
Embedding Color Watermarks in Color Images
Directory of Open Access Journals (Sweden)
Wu Tung-Lin
2003-01-01
Full Text Available Robust watermarking with oblivious detection is essential to practical copyright protection of digital images. Effective exploitation of the characteristics of human visual perception to color stimuli helps to develop the watermarking scheme that fills the requirement. In this paper, an oblivious watermarking scheme that embeds color watermarks in color images is proposed. Through color gamut analysis and quantizer design, color watermarks are embedded by modifying quantization indices of color pixels without resulting in perceivable distortion. Only a small amount of information including the specification of color gamut, quantizer stepsize, and color tables is required to extract the watermark. Experimental results show that the proposed watermarking scheme is computationally simple and quite robust in face of various attacks such as cropping, low-pass filtering, white-noise addition, scaling, and JPEG compression with high compression ratios.
Color vision and color formation in dragonflies.
Futahashi, Ryo
2016-10-01
Dragonflies including damselflies are colorful and large-eyed insects, which show remarkable sexual dimorphism, color transition, and color polymorphism. Recent comprehensive visual transcriptomics has unveiled an extraordinary diversity of opsin genes within the lineage of dragonflies. These opsin genes are differentially expressed between aquatic larvae and terrestrial adults, as well as between dorsal and ventral regions of adult compound eyes. Recent topics of color formation in dragonflies are also outlined. Non-iridescent blue color is caused by coherent light scattering from the quasiordered nanostructures, whereas iridescent color is produced by multilayer structures. Wrinkles or wax crystals sometimes enhances multilayer structural colors. Sex-specific and stage-specific color differences in red dragonflies is attributed to redox states of ommochrome pigments.
... medlineplus.gov/ency/article/003139.htm Urine - abnormal color To use the sharing features on this page, please enable JavaScript. The usual color of urine is straw-yellow. Abnormally colored urine ...
... page: //medlineplus.gov/ency/article/003224.htm Skin color - patchy To use the sharing features on this page, please enable JavaScript. Patchy skin color is areas where the skin color is irregular. ...
Backprojection by upsampled Fourier series expansion and interpolated FFT.
Tabei, M; Ueda, M
1992-01-01
A fast backprojection method through the use of interpolated fast Fourier transform (FFT) is presented. The computerized tomography (CT) reconstruction by the convolution backprojection (CBP) method has produced precise images. However, the backprojection part of the conventional CBP method is not very efficient. The authors propose an alternative approach to interpolating and backprojecting the convolved projections onto the image frame. First, the upsampled Fourier series expansion of the convolved projection is calculated. Then, using a Gaussian function, it is projected by the aliasing-free interpolation of FFT bins onto a rectangular grid in the frequency domain. The total amount of computation in this procedure for a 512x512 image is 1/5 of the conventional backprojection method with linear interpolation. This technique also allows the arbitrary control of the frequency characteristics.
DEFF Research Database (Denmark)
Hjørland, Birger
2017-01-01
The domain-analytic approach to knowledge organization (KO) (and to the broader field of library and information science, LIS) is outlined. The article reviews the discussions and proposals on the definition of domains, and provides an example of a domain-analytic study in the field of art studie....... Varieties of domain analysis as well as criticism and controversies are presented and discussed....
Fernandez-Maloigne, Christine; Macaire, Ludovic
2013-01-01
This collective work identifies the latest developments in the field of the automatic processing and analysis of digital color images.For researchers and students, it represents a critical state of the art on the scientific issues raised by the various steps constituting the chain of color image processing.It covers a wide range of topics related to computational color imaging, including color filtering and segmentation, color texture characterization, color invariant for object recognition, color and motion analysis, as well as color image and video indexing and retrieval. <
Choi, Kyongsik; Kim, Hwi; Lee, Byoungho
2004-10-18
A novel full-color autostereoscopic three-dimensional (3D) display system has been developed using color-dispersion-compensated (CDC) synthetic phase holograms (SPHs) on a phase-type spatial light modulator. To design the CDC phase holograms, we used a modified iterative Fourier transform algorithm with scaling constants and phase quantization level constraints. We obtained a high diffraction efficiency (~90.04%), a large signal-to-noise ratio (~9.57dB), and a low reconstruction error (~0.0011) from our simulation results. Each optimized phase hologram was synthesized with each CDC directional hologram for red, green, and blue wavelengths for full-color autostereoscopic 3D display. The CDC SPHs were composed and modulated by only one phase-type spatial light modulator. We have demonstrated experimentally that the designed CDC SPHs are able to generate full-color autostereoscopic 3D images and video frames very well, without any use of glasses.
Quantum Fourier transform in computational basis
Zhou, S. S.; Loke, T.; Izaac, J. A.; Wang, J. B.
2017-03-01
The quantum Fourier transform, with exponential speed-up compared to the classical fast Fourier transform, has played an important role in quantum computation as a vital part of many quantum algorithms (most prominently, Shor's factoring algorithm). However, situations arise where it is not sufficient to encode the Fourier coefficients within the quantum amplitudes, for example in the implementation of control operations that depend on Fourier coefficients. In this paper, we detail a new quantum scheme to encode Fourier coefficients in the computational basis, with fidelity 1 - δ and digit accuracy ɛ for each Fourier coefficient. Its time complexity depends polynomially on log (N), where N is the problem size, and linearly on 1/δ and 1/ɛ . We also discuss an application of potential practical importance, namely the simulation of circulant Hamiltonians.
The multiple-parameter fractional Fourier transform
Institute of Scientific and Technical Information of China (English)
LANG Jun; TAO Ran; RAN QiWen; WANG Yue
2008-01-01
The fractional Fourier transform (FRFT) has multiplicity, which is intrinsic in frac-tional operator. A new source for the multiplicity of the weight-type fractional Fou-rier transform (WFRFT) is proposed, which can generalize the weight coefficients of WFRFT to contain two vector parameters MN,∈ZM. Therefore a generalized frac-tional Fourier transform can be defined, which is denoted by the multiple-parameter fractional Fourier transform (MPFRFT). It enlarges the multiplicity of the FRFT, which not only includes the conventional FRFT and general multi-fractional Fourier transform as special cases, but also introduces new fractional Fourier transforms. It provides a unified framework for the FRFT, and the method is also available for fractionalizing other linear operators. In addition, numerical simulations of the MPFRFT on the Hermite-Gaussian and rectangular functions have been performed as a simple application of MPFRFT to signal processing.
The Fourier Transform on Quantum Euclidean Space
Directory of Open Access Journals (Sweden)
Kevin Coulembier
2011-05-01
Full Text Available We study Fourier theory on quantum Euclidean space. A modified version of the general definition of the Fourier transform on a quantum space is used and its inverse is constructed. The Fourier transforms can be defined by their Bochner's relations and a new type of q-Hankel transforms using the first and second q-Bessel functions. The behavior of the Fourier transforms with respect to partial derivatives and multiplication with variables is studied. The Fourier transform acts between the two representation spaces for the harmonic oscillator on quantum Euclidean space. By using this property it is possible to define a Fourier transform on the entire Hilbert space of the harmonic oscillator, which is its own inverse and satisfies the Parseval theorem.
Texture of lipid bilayer domains
DEFF Research Database (Denmark)
Jensen, Uffe Bernchou; Brewer, Jonathan R.; Midtiby, Henrik Skov
2009-01-01
chains. By imaging the intensity variations as a function of the polarization angle, we map the lateral variations of the lipid tilt within domains. Results reveal that gel domains are composed of subdomains with different lipid tilt directions. We have applied a Fourier decomposition method......We investigate the texture of gel (g) domains in binary lipid membranes composed of the phospholipids DPPC and DOPC. Lateral organization of lipid bilayer membranes is a topic of fundamental and biological importance. Whereas questions related to size and composition of fluid membrane domain...... are well studied, the possibility of texture in gel domains has so far not been examined. When using polarized light for two-photon excitation of the fluorescent lipid probe Laurdan, the emission intensity is highly sensitive to the angle between the polarization and the tilt orientation of lipid acyl...
THE FOURIER SERIES MODEL IN MAP ANALYSIS.
During the past several years the double Fourier Series has been applied to the analysis of contour-type maps as an alternative to the more commonly...used polynomial model. The double Fourier Series has high potential in the study of areal variations, inasmuch as a succession of trend maps based on...and it is shown that the double Fourier Series can be used to summarize the directional properties of areally-distributed data. An Appendix lists
Handbook of Fourier analysis & its applications
Marks, Robert J
2009-01-01
Fourier analysis has many scientific applications - in physics, number theory, combinatorics, signal processing, probability theory, statistics, option pricing, cryptography, acoustics, oceanography, optics and diffraction, geometry, and other areas. In signal processing and related fields, Fourier analysis is typically thought of as decomposing a signal into its component frequencies and their amplitudes. This practical, applications-based professional handbook comprehensively covers the theory and applications of Fourier Analysis, spanning topics from engineering mathematics, signal process
Magneto-sensor circuit efficiency incremented by Fourier-transformation
Talukdar, Abdul Hafiz Ibne
2011-10-01
In this paper detection by recognized intelligent algorithm for different magnetic films with the aid of a cost-effective and simple high efficient circuit are realized. Well-known, magnetic films generate oscillating frequencies when they stay a part of an LC- oscillatory circuit. These frequencies can be further analyzed to gather information about their magnetic properties. For the first time in this work we apply the signal analysis in frequency domain to create the Fourier frequency spectra which was used to detect the sample properties and their recognition. In this paper we have summarized both the simulation and experimental results. © 2011 Elsevier Ltd. All rights reserved.
Transfer Function Identification Using Orthogonal Fourier Transform Modeling Functions
Morelli, Eugene A.
2013-01-01
A method for transfer function identification, including both model structure determination and parameter estimation, was developed and demonstrated. The approach uses orthogonal modeling functions generated from frequency domain data obtained by Fourier transformation of time series data. The method was applied to simulation data to identify continuous-time transfer function models and unsteady aerodynamic models. Model fit error, estimated model parameters, and the associated uncertainties were used to show the effectiveness of the method for identifying accurate transfer function models from noisy data.
Color identification testing device
Brawner, E. L.; Martin, R.; Pate, W.
1970-01-01
Testing device, which determines ability of a technician to identify color-coded electric wires, is superior to standard color blindness tests. It tests speed of wire selection, detects partial color blindness, allows rapid testing, and may be administered by a color blind person.
Lucassen, M.P.; Gevers, T.; Gijsenij, A.
2011-01-01
Several studies have recorded color emotions in subjects viewing uniform color (UC) samples. We conduct an experiment to measure and model how these color emotions change when texture is added to the color samples. Using a computer monitor, our subjects arrange samples along four scales: warm-cool,
Lucassen, M.P.; Gevers, T.; Gijsenij, A.
2011-01-01
Several studies have recorded color emotions in subjects viewing uniform color (UC) samples. We conduct an experiment to measure and model how these color emotions change when texture is added to the color samples. Using a computer monitor, our subjects arrange samples along four scales: warm-cool,
Ma, Q.; Tipping, R. H.; Lavrentieva, N. N.
2012-01-01
By adopting a concept from signal processing, instead of starting from the correlation functions which are even, one considers the causal correlation functions whose Fourier transforms become complex. Their real and imaginary parts multiplied by 2 are the Fourier transforms of the original correlations and the subsequent Hilbert transforms, respectively. Thus, by taking this step one can complete the two previously needed transforms. However, to obviate performing the Cauchy principal integrations required in the Hilbert transforms is the greatest advantage. Meanwhile, because the causal correlations are well-bounded within the time domain and band limited in the frequency domain, one can replace their Fourier transforms by the discrete Fourier transforms and the latter can be carried out with the FFT algorithm. This replacement is justified by sampling theory because the Fourier transforms can be derived from the discrete Fourier transforms with the Nyquis rate without any distortions. We apply this method in calculating pressure induced shifts of H2O lines and obtain more reliable values. By comparing the calculated shifts with those in HITRAN 2008 and by screening both of them with the pair identity and the smooth variation rules, one can conclude many of shift values in HITRAN are not correct.
Spectral imaging of multi-color chromogenic dyes in pathological specimens.
Macville, M.V.E.; Laak, J.A.W.M. van der; Speel, E.J.; Katzir, N.; Garini, Y.; Soenksen, D.; McNamara, G.; Wilde, P.C.M. de; Hanselaar, A.G.J.M.; Hopman, A.H.N.; Ried, T.
2001-01-01
We have investigated the use of spectral imaging for multi-color analysis of permanent cytochemical dyes and enzyme precipitates on cytopathological specimens. Spectral imaging is based on Fourier-transform spectroscopy and digital imaging. A pixel-by-pixel spectrum-based color classification is pre
Sensory Drive, Color, and Color Vision.
Price, Trevor D
2017-08-01
Colors often appear to differ in arbitrary ways among related species. However, a fraction of color diversity may be explained because some signals are more easily perceived in one environment rather than another. Models show that not only signals but also the perception of signals should regularly evolve in response to different environments, whether these primarily involve detection of conspecifics or detection of predators and prey. Thus, a deeper understanding of how perception of color correlates with environmental attributes should help generate more predictive models of color divergence. Here, I briefly review our understanding of color vision in vertebrates. Then I focus on opsin spectral tuning and opsin expression, two traits involved in color perception that have become amenable to study. I ask how opsin tuning is correlated with ecological differences, notably the light environment, and how this potentially affects perception of conspecific colors. Although opsin tuning appears to evolve slowly, opsin expression levels are more evolutionarily labile but have been difficult to connect to color perception. The challenge going forward will be to identify how physiological differences involved in color vision, such as opsin expression levels, translate into perceptual differences, the selection pressures that have driven those differences, and ultimately how this may drive evolution of conspecific colors.
Klein, Georg A
2010-01-01
This unique book starts with a short historical overview of the development of the theories of color vision and applications of industrial color physics. The three dominant factors producing color - light source, color sample, and observer - are described in detail. The standardized color spaces are shown and related color values are applied to characteristic color qualities of absorption as well as of effect colorants. The fundamentals of spectrometric and colorimetric measuring techniques together with specific applications are described. Theoretical models for radiative transfer in transparent, translucent, and opaque layers are detailed; the two, three, and multi-flux approximations are presented for the first time in a coherent formalism. These methods constitute the fundamentals not only for the important classical methods, but also modern methods of recipe prediction applicable to all known colorants. The text is supplied with 52 tables, more than 200 partially colored illustrations, an appendix, and a...
Structural color mechanism in the Papilio blumei butterfly.
Lo, Mei-Ling; Lee, Cheng-Chung
2014-02-01
The structural color found in biological systems has complicated nanostructure. It is very important to determine its color mechanism. In this study, the 2D photonic crystal structures of the Papilio blumei butterfly were constructed, and the corresponding reflectance spectra were simulated by the finite-difference time-domain method. The structural color of the butterfly depends on the incident angle of light, film thickness, film material (film refractive index), and the size of the air hole (effective refractive index). Analysis of simulations can help us understand the hue, brightness, and saturation of structural color on the butterfly wing. As a result, the analysis can help us fabricate expected structural color.
A dendritic lattice neural network for color image segmentation
Urcid, Gonzalo; Lara-Rodríguez, Luis David; López-Meléndez, Elizabeth
2015-09-01
A two-layer dendritic lattice neural network is proposed to segment color images in the Red-Green-Blue (RGB) color space. The two layer neural network is a fully interconnected feed forward net consisting of an input layer that receives color pixel values, an intermediate layer that computes pixel interdistances, and an output layer used to classify colors by hetero-association. The two-layer net is first initialized with a finite small subset of the colors present in the input image. These colors are obtained by means of an automatic clustering procedure such as k-means or fuzzy c-means. In the second stage, the color image is scanned on a pixel by pixel basis where each picture element is treated as a vector and feeded into the network. For illustration purposes we use public domain color images to show the performance of our proposed image segmentation technique.
Stable Probability Distributions and their Domains of Attraction
J.L. Geluk (Jaap); L.F.M. de Haan (Laurens)
1997-01-01
textabstractThe theory of stable probability distributions and their domains of attraction is derived in a direct way (avoiding the usual route via infinitely divisible distributions) using Fourier transforms. Regularly varying functions play an important role in the exposition.
Frequency-Domain Optical Mammogram
2002-10-01
the tumor. * Combination of the above two points into a composite false-color breast image containing structural information (from the second...Antonangeli, A. Savoia, T. Parasassi, and N. Rosato, " Plastique : a synchrotron radiation beamline for time resolved fluorescence in the frequency domain
The Effect of pH and Color Stability of Anthocyanin on Food Colorant
Wahyuningsih, S.; Wulandari, L.; Wartono, M. W.; Munawaroh, H.; Ramelan, A. H.
2017-04-01
Anthocyanins are naturally occurring pigments of red and purple. Red anthocyanin pigments provide a strong and sharp and widely applied in various industries such as food coloring or drink. Anthocyanins isolated by maceration, extraction and thin layer chromatography (TLC). The extract has been obtained from the initial stages of maceration then separated into several fractions by chromatography to isolate fractions colored dark red. Identification of chemical compounds with TLC (Thin Layer Chromatography) is able to distinguish the fraction of anthocyanin produced. FTIR (Fourier Transform Infrared Spectroscopy) used to identification of the functional group of a compound. The UV-Vis absorption spectra have to produce maximum absorbance values that describe the intensity of anthocyanin spectra in different colors for different pH. Anthocyanins are more stable at low pH (acidic conditions) which gives a red pigment. Meanwhile, the higher the pH value of anthocyanin will provide color fading of the color blue. So as a food colorant, anthocyanin with a low pH or height pH has a significant effect on the food colorant.
Fourier analysis and synthesis tomography.
Energy Technology Data Exchange (ETDEWEB)
Wagner, Kelvin H. (University of Colorado at Boulder, Boulder, CO); Sinclair, Michael B.; Feldkuhn, Daniel (University of Colorado at Boulder, Boulder, CO)
2010-05-01
Most far-field optical imaging systems rely on a lens and spatially-resolved detection to probe distinct locations on the object. We describe and demonstrate a novel high-speed wide-field approach to imaging that instead measures the complex spatial Fourier transform of the object by detecting its spatially-integrated response to dynamic acousto-optically synthesized structured illumination. Tomographic filtered backprojection is applied to reconstruct the object in two or three dimensions. This technique decouples depth-of-field and working-distance from resolution, in contrast to conventional imaging, and can be used to image biological and synthetic structures in fluoresced or scattered light employing coherent or broadband illumination. We discuss the electronically programmable transfer function of the optical system and its implications for imaging dynamic processes. Finally, we present for the first time two-dimensional high-resolution image reconstructions demonstrating a three-orders-of-magnitude improvement in depth-of-field over conventional lens-based microscopy.
Programs for high-speed Fourier, Mellin and Fourier-Bessel transforms
Ikhabisimov, D. K.; Debabov, A. S.; Kolosov, B. I.; Usikov, D. A.
1979-01-01
Several FORTRAN program modules for performing one-dimensional and two-dimensional discrete Fourier transforms, Mellin, and Fourier-Bessel transforms are described along with programs that realize the algebra of high speed Fourier transforms on a computer. The programs can perform numerical harmonic analysis of functions, synthesize complex optical filters on a computer, and model holographic image processing methods.
The multipliers of multiple trigonometric Fourier series
Ydyrys, Aizhan; Sarybekova, Lyazzat; Tleukhanova, Nazerke
2016-11-01
We study the multipliers of multiple Fourier series for a regular system on anisotropic Lorentz spaces. In particular, the sufficient conditions for a sequence of complex numbers {λk}k∈Zn in order to make it a multiplier of multiple trigonometric Fourier series from Lp[0; 1]n to Lq[0; 1]n , p > q. These conditions include conditions Lizorkin theorem on multipliers.
1-Convergence of Complex Double Fourier Series
Indian Academy of Sciences (India)
Kulwinder Kaur; S S Bhatia; Babu Ram
2003-11-01
It is proved that the complex double Fourier series of an integrable function (, ) with coefficients {} satisfying certain conditions, will converge in 1-norm. The conditions used here are the combinations of Tauberian condition of Hardy–Karamata kind and its limiting case. This paper extends the result of Bray [1] to complex double Fourier series.
Two modified discrete chirp Fourier transform schemes
Institute of Scientific and Technical Information of China (English)
樊平毅; 夏香根
2001-01-01
This paper presents two modified discrete chirp Fourier transform (MDCFT) schemes.Some matched filter properties such as the optimal selection of the transform length, and its relationship to analog chirp-Fourier transform are studied. Compared to the DCFT proposed previously, theoretical and simulation results have shown that the two MDCFTs can further improve the chirp rate resolution of the detected signals.
Fourier-transform Ghost Imaging with Hard X-rays
Yu, Hong; Han, Shensheng; Xie, Honglan; Du, Guohao; Xiao, Tiqiao; Zhu, Daming
2016-01-01
Knowledge gained through X-ray crystallography fostered structural determination of materials and greatly facilitated the development of modern science and technology in the past century. Atomic details of sample structures is achievable by X-ray crystallography, however, it is only applied to crystalline structures. Imaging techniques based on X-ray coherent diffraction or zone plates are capable of resolving the internal structure of non-crystalline materials at nanoscales, but it is still a challenge to achieve atomic resolution. Here we demonstrate a novel lensless Fourier-transform ghost imaging method with pseudo-thermal hard X-rays by measuring the second-order intensity correlation function of the light. We show that high resolution Fourier-transform diffraction pattern of a complex structure can be achieved at Fresnel region, and the amplitude and phase distributions of a sample in spatial domain can be retrieved successfully. The method of lensless X-ray Fourier-transform ghost imaging extends X-ray...
Xi, Jiaxin; Liu, Ning
2017-09-01
Vibration characteristic of timing chain system is very important for an engine. In this study, we used a bush roller chain drive system as an example to explain how to use mulitybody dynamic techniques and short-time Fourier transform to investigate vibration characteristics of timing chain system. Multibody dynamic simulation data as chain tension force and external excitation sources curves were provided for short-time Fourier transform study. The study results of short-time Fourier transform illustrate that there are two main vibration frequency domain of timing chain system, one is the low frequency vibration caused by crankshaft sprocket velocity and camshaft sprocket torque. Another is vibration around 1000Hz lead by hydraulic tensioner. Hence, short-time Fourier transform method is useful for basic research of vibration characteristics for timing chain system.
From "Dirac combs" to Fourier-positivity
Giraud, Bertrand G
2015-01-01
Motivated by various problems in physics and applied mathematics, we look for constraints and properties of real Fourier-positive functions, i.e. with positive Fourier transforms. Properties of the "Dirac comb" distribution and of its tensor products in higher dimensions lead to Poisson resummation, allowing for a useful approximation formula of a Fourier transform in terms of a limited number of terms. A connection with the Bochner theorem on positive definiteness of Fourier-positive functions is discussed. As a practical application, we find simple and rapid analytic algorithms for checking Fourier-positivity in 1- and (radial) 2-dimensions among a large variety of real positive functions. This may provide a step towards a classification of positive positive-definite functions.
Fractional Fourier processing of quantum light.
Sun, Yifan; Tao, Ran; Zhang, Xiangdong
2014-01-13
We have extended Fourier transform of quantum light to a fractional Fourier processing, and demonstrated that a classical optical fractional Fourier processor can be used for the shaping of quantum correlations between two or more photons. Comparing the present method with that of Fourier processing, we find that fractional Fourier processing for quantum light possesses many advantages. Based on such a method, not only quantum correlations can be shaped more rich, but also the initial states can be easily identified. Moreover, the twisted phase information can be recovered and quantum states are easily controlled in performing quantum information experiments. Our findings open up new avenues for the manipulation of correlations between photons in optical quantum information processing.
Wavelength-domain RF photonic signal processing
Gao, Lu
This thesis presents a novel approach to RF-photonic signal processing applications based on wavelength-domain optical signal processing techniques using broadband light sources as the information carriers, such as femtosecond lasers and white light sources. The wavelength dimension of the broadband light sources adds an additional degree of freedom to conventional optical signal processing systems. Two novel wavelength-domain optical signal processing systems are presented and demonstrated in this thesis. The first wavelength-domain RF photonic signal processing system is a wavelength-compensated squint-free photonic multiple beam-forming system for wideband RF phased-array antennas. Such a photonic beam-forming system employs a new modulation scheme developed in this thesis, which uses traveling-wave tunable filters to modulate wideband RF signals onto broadband optical light sources in a frequency-mapped manner. The wavelength dimension of the broadband light sources provides an additional dimension in the wavelength-compensated Fourier beam-forming system for mapping the received RF frequencies to the linearly proportional optical frequencies, enabling true-time-delay beam forming, as well as other novel RF-photonic signal processing functions such as tunable filtering and frequency down conversion. A new slow-light mechanism, the SLUGGISH light, has also been discovered with an effective slow-light velocity of 86 m/s and a record time-bandwidth product of 20. Experimental demonstration of true-time-delay beam forming based on the SLUGGISH light effect has also been presented in this thesis. In the second wavelength-domain RF photonic signal processing system, the wavelength dimension increases the information carrying capacity by spectrally multiplexing multiple wavelength channels in a wavelength-division-multiplexing fiber-optic communication system. A novel ultrafast all-optical 3R (Re-amplification, Retiming, Re-shaping) wavelength converter based on
Short-time Fourier transform laser Doppler holography
Atlan, Michael
2012-01-01
We report a demonstration of laser Doppler holography at a sustained acquisition rate of 250 Hz on a 1 Megapixel complementary metal-oxide-semiconductor (CMOS) sensor array and image display at 10 Hz frame rate. The holograms are optically acquired in off-axis configuration, with a frequency-shifted reference beam. Wide-field imaging of optical fluctuations in a 250 Hz frequency band is achieved by turning time-domain samplings to the dual domain via short-time temporal Fourier transformation. The measurement band can be positioned freely within the low radio-frequency spectrum by tuning the frequency of the reference beam in real-time. Video-rate image rendering is achieved by streamline image processing with commodity computer graphics hardware. This experimental scheme is validated by a non-contact vibrometry experiment.
Single-exposure color digital holography
Feng, Shaotong; Wang, Yanhui; Zhu, Zhuqing; Nie, Shouping
2010-11-01
In this paper, we report a method for color image reconstruction by recording only one single multi-wavelength hologram. In the recording process, three lasers of different wavelengths emitting in the red, green and blue regions are used for illuminating on the object and the object diffraction fields will arrive at the hologram plane simultaneously. Three reference beams with different spatial angles will interfere with the corresponding object diffraction fields on the hologram plane, respectively. Finally, a series of sub-holograms incoherently overlapped on the CCD to be recorded as a multi-wavelength hologram. Angular division multiplexing is employed to reference beams so that the spatial spectra of the multiple recordings will be separated in the Fourier plane. In the reconstruction process, the multi-wavelength hologram will be Fourier transformed into its Fourier plane, where the spatial spectra of different wavelengths are separated and can be easily extracted by employing frequency filtering. The extracted spectra are used to reconstruct the corresponding monochromatic complex amplitudes, which will be synthesized to reconstruct the color image. For singleexposure recording technique, it is convenient for applications on the real-time image processing fields. However, the quality of the reconstructed images is affected by speckle noise. How to improve the quality of the images needs for further research.
Directory of Open Access Journals (Sweden)
Vahid Bagheri
2014-11-01
Full Text Available This paper introduce a new data SONAR classification method based on Short-Time Fractional Fourier Transform (STFrFT analysis. The passive SONAR system receives the acoustic signals radiated by vessels and attempts to categorize them as a function of the similarities between vessels of the same class.Here, a time-frequency processing and feature extraction method is developed in order to improve the performance of a feedforwardneural network, which is used to classify five classes of vessels.Processing of time-varying signals in fractional fourier domain allows us to estimate the signal with higher concentration than conventional fourier domain, making the technique robust against additive noise, maintaining same computational complexity. With the purpose of dimension reduction and classification improvement, we use Linear Discriminant Analysis (LDA technique. The feasibility of the proposed technique (STFrFTLDA has been tested experimentally using a real database. The experimental results show the superiority of the proposed method
Image encryption based on the reality-preserving multiple-parameter fractional Fourier transform
Lang, Jun
2012-05-01
In recent years, a number of methods have been proposed in the literature for the encryption of two-dimensional information by using the fractional Fourier transform, but most of their encryptions are complex values and need digital hologram technique to record information, which is inconvenient for digital transmission. In this paper, we propose a new approach for image encryption based on the real-valuedness and decorrelation property of the reality-preserving multiple-parameter fractional Fourier transform in order to meet the requirements of the secure image transmission. In the proposed scheme, the original and encrypted images are respectively in the spatial domain and the reality-preserving multiple-parameter fractional Fourier transformed domain determined by the encryption keys. Numerical simulations are performed to demonstrate that the proposed method is reliable and more robust to blind decryption than several existing methods.
Institute of Scientific and Technical Information of China (English)
QI Lin; TAO Ran; ZHOU Siyong; WANG Yue
2004-01-01
This paper presents a new method for the detection and parameter estimation of multicomponent LFM signals based on the fractional Fourier transform. For the optimization in the fractional Fourier domain, an algorithm based on Quasi-Newton method is proposed which consists of two steps of searching, leading to a reduction in computation without loss of accuracy. And for multicomponent signals, we further propose a signal separation technique in the fractional Fourier domain which can effectively suppress the interferences on the detection of the weak components brought by the stronger components. The statistical analysis of the estimate errors is also performed which perfects the method theoretically, and finally, simulation results are provided to show the validity of our method.
Perception of Coloration in Diotic Reverberant Noise.
Pierce, Linda K.
These experiments explored the perception, termed coloration, of the frequency domain characterization of reverberant sound. The beginning premise was that the standard deviation, (sigma), of the room frequency response, H(f), was a good measure of coloration. Using simulated rooms, reverberant noise stimuli were created which differed only in their perceived frequency spectra and not in their perceived temporal characteristics. Four experiments were run. In two experiments subjects heard pairs of reverberant noises representing different rooms and made difference judgments; data from these experiments were analyzed using multidimensional scaling techniques. It was determined that coloration has both quantity and quality. Both quantity and quality of coloration are derived primarily from the early reflections, i.e., the first 10 msec, of a room's impulse response, h(t). Quantity of coloration is related to the standard deviation of H(f), but is best described by a model which uses a critical band-like filter to smooth H(f) before calculating the standard deviation, (sigma)(,CB). Quantity of coloration can be manipulated with little variation in coloration quality by varying the reflectivity, (beta), of the surfaces in a given room. Quality of coloration is a complex pitch-like quality associated with the particular reflections in a room. Differences in quality between rooms were described accurately by calculating the standard deviation of the difference, (sigma)(,CBDIF), between two smoothed room spectra. In the third experiment, subjects judged quantity of coloration in two tasks, a paired comparison task and an absolute judgment task, and (sigma)(,CB) was substantiated as a measure of quantity of coloration. In the last experiment, a Thurstone paired comparison task and analysis was used to determine that the range of the coloration quantity continuum is about 5 1/2 jnd's.
Ushenko, A G; Dubolazov, O V; Ushenko, V A; Novakovskaya, O Yu; Olar, O V
2016-04-20
The optical model of polycrystalline networks of human tissue has been proposed. The values of statistical parameters (statistical moments of the first to fourth order) characterizing the polarization-inhomogeneous images of skin surface in the Fourier domain have been measured. The diagnostic criteria of pathological processes in human skin and the differentiation of its severity degree have been determined.
Modeling cavities exhibiting strong lateral confinement using open geometry Fourier modal method
DEFF Research Database (Denmark)
Häyrynen, Teppo; Gregersen, Niels
2016-01-01
We have developed a computationally eﬃcient Fourier-Bessel expansion based open geometry formalism for modeling the optical properties of rotationally symmetric photonic nanostructures. The lateral computation domain is assumed inﬁnite so that no artiﬁcial boundary conditions are needed. Instead...
Zarabadi, Atefeh S; Pawliszyn, Janusz
2015-02-17
Analysis in the frequency domain is considered a powerful tool to elicit precise information from spectroscopic signals. In this study, the Fourier transformation technique is employed to determine the diffusion coefficient (D) of a number of proteins in the frequency domain. Analytical approaches are investigated for determination of D from both experimental and data treatment viewpoints. The diffusion process is modeled to calculate diffusion coefficients based on the Fourier transformation solution to Fick's law equation, and its results are compared to time domain results. The simulations characterize optimum spatial and temporal conditions and demonstrate the noise tolerance of the method. The proposed model is validated by its application for the electropherograms from the diffusion path of a set of proteins. Real-time dynamic scanning is conducted to monitor dispersion by employing whole column imaging detection technology in combination with capillary isoelectric focusing (CIEF) and the imaging plug flow (iPF) experiment. These experimental techniques provide different peak shapes, which are utilized to demonstrate the Fourier transformation ability in extracting diffusion coefficients out of irregular shape signals. Experimental results confirmed that the Fourier transformation procedure substantially enhanced the accuracy of the determined values compared to those obtained in the time domain.
The Geostationary Fourier Transform Spectrometer
Key, Richard; Sander, Stanley; Eldering, Annmarie; Blavier, Jean-Francois; Bekker, Dmitriy; Manatt, Ken; Rider, David; Wu, Yen-Hung
2012-01-01
The Geostationary Fourier Transform Spectrometer (GeoFTS) is an imaging spectrometer designed for a geostationary orbit (GEO) earth science mission to measure key atmospheric trace gases and process tracers related to climate change and human activity. GEO allows GeoFTS to continuously stare at a region of the earth for frequent sampling to capture the variability of biogenic fluxes and anthropogenic emissions from city to continental spatial scales and temporal scales from diurnal, synoptic, seasonal to interannual. The measurement strategy provides a process based understanding of the carbon cycle from contiguous maps of carbon dioxide (CO2), methane (CH4), carbon monoxide (CO), and chlorophyll fluorescence (CF) collected many times per day at high spatial resolution (2.7kmx2.7km at nadir). The CO2/CH4/CO/CF measurement suite in the near infrared spectral region provides the information needed to disentangle natural and anthropogenic contributions to atmospheric carbon concentrations and to minimize uncertainties in the flow of carbon between the atmosphere and surface. The half meter cube size GeoFTS instrument is based on a Michelson interferometer design that uses all high TRL components in a modular configuration to reduce complexity and cost. It is self-contained and as independent of the spacecraft as possible with simple spacecraft interfaces, making it ideal to be a "hosted" payload on a commercial communications satellite mission. The hosted payload approach for measuring the major carbon-containing gases in the atmosphere from the geostationary vantage point will affordably advance the scientific understating of carbon cycle processes and climate change.
Fourier-wavelet restoration in PET/CT brain studies
Energy Technology Data Exchange (ETDEWEB)
Knesaurek, Karin, E-mail: karin.knesaurek@mssm.edu [Division of Nuclear Medicine, The Mount Sinai Medical Center, One Gustave L. Levy Place, New York, NY 10029 (United States)
2012-10-11
Our goal is to improve brain PET imaging through the application of a novel, hybrid Fourier-wavelet (WFT) restoration technique. The major limitation of PET studies is a relatively poor resolution in comparison with MRI and CT imaging and there is a need for improved PET imaging. A GE DLS PET/CT 16 slice system was used to acquire the studies. In order to create restoration filters the point source study was performed. The 6-fillable spheres and 3D Hoffman brain phantom studies were acquired and used to test and optimize the restoration approach. The patient data used in the study were acquired in a 3D PET mode, using the standard clinical protocol. Here, we have implemented Fourier-wavelet regularized restoration. In the Fourier domain, the inverse of modulation transfer function was multiplied by a Butterworth low-pass filter, order n=6 and cut-off frequency f=0.35 cycles/pixel. In addition, wavelet (Daubechies, order 2) noise suppression was applied by 'hard threshold'. Hot spheres and 3D Hoffman brain studies showed that the restoration process not only improves resolution and contrast but also improves quantification in 3D PET/CT imaging. The average contrast increase was 19% and the quantification improved in the range 8-20% depending on sphere size. In the restored images, there was no significant increase in noise when compared with the original images. The clinical studies followed brain phantom findings, i.e., the restored images had better contrast and resolution properties, when compared with the original images. The results of the study demonstrate that the quality and quantification of 3D brain {sup 18}F FDG PET images can be significantly improved by Fourier-wavelet (WFT) restoration filtering.
Fourier-wavelet restoration in PET/CT brain studies
Knešaurek, Karin
2012-10-01
Our goal is to improve brain PET imaging through the application of a novel, hybrid Fourier-wavelet (WFT) restoration technique. The major limitation of PET studies is a relatively poor resolution in comparison with MRI and CT imaging and there is a need for improved PET imaging. A GE DLS PET/CT 16 slice system was used to acquire the studies. In order to create restoration filters the point source study was performed. The 6-fillable spheres and 3D Hoffman brain phantom studies were acquired and used to test and optimize the restoration approach. The patient data used in the study were acquired in a 3D PET mode, using the standard clinical protocol. Here, we have implemented Fourier-wavelet regularized restoration. In the Fourier domain, the inverse of modulation transfer function was multiplied by a Butterworth low-pass filter, order n=6 and cut-off frequency f=0.35 cycles/pixel. In addition, wavelet (Daubechies, order 2) noise suppression was applied by “hard threshold”. Hot spheres and 3D Hoffman brain studies showed that the restoration process not only improves resolution and contrast but also improves quantification in 3D PET/CT imaging. The average contrast increase was 19% and the quantification improved in the range 8-20% depending on sphere size. In the restored images, there was no significant increase in noise when compared with the original images. The clinical studies followed brain phantom findings, i.e., the restored images had better contrast and resolution properties, when compared with the original images. The results of the study demonstrate that the quality and quantification of 3D brain 18F FDG PET images can be significantly improved by Fourier-wavelet (WFT) restoration filtering.
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
The poly-[2-methoxy,(5-2′-ethyl-hexyloxy)-p-phenylene vinylene](MEH-PPV) film is investigated by means of the Multi-Color Photon Echo(MCPE) technique. Under the three-order nonlinear response theory,the reason for the occurrence of the quantum beats in the time domain and the relations among signal wavevector,pulse sequence and response function are discussed. The analysis of the Raman spectrum of MEH-PPV and the fast Fourier transformation(FFT) results of photon echo(PE) signal dynamics demonstrate the coherent coupling between the C==C bonds and the CC-H bonds and the coherent coupling between the C-C stretching of the phenyl group and the C==C stretching of the vinylene group.
Persian Sign Language Recognition Using Radial Distance and Fourier Transform
Directory of Open Access Journals (Sweden)
Bahare Jalilian
2013-11-01
Full Text Available This paper provides a novel hand gesture recognition method to recognize 32 static signs of the Persian Sign Language (PSL alphabets. Accurate hand segmentation is the first and important step in sign language recognition systems. Here, we propose a method for hand segmentation that helps to build a better vision based sign language recognition system. The proposed method is based on YCbCr color space, single Gaussian model and Bayes rule. It detects region of hand in complex background and non-uniform illumination. Hand gesture features are extracted by radial distance and Fourier transform. Finally, the Euclidean distanceis used to compute the similarity between the input signs and all training feature vectors in the database. The system is tested on 480 posture images of the PSL, 15 images for each 32 signs. Experimental results show that our approach is capable to recognize all 32 PSL alphabets with 95.62% recognition rate.
Image encryption techniques based on the fractional Fourier transform
Hennelly, B. M.; Sheridan, J. T.
2003-11-01
The fractional Fourier transform, (FRT), is a generalisation of the Fourier transform which allows domains of mixed spatial frequency and spatial information to be examined. A number of method have recently been proposed in the literature for the encryption of two dimensional information using optical systems based on the FRT. Typically, these methods require random phase screen keys to decrypt the data, which must be stored at the receiver and must be carefully aligned with the received encrypted data. We have proposed a new technique based on a random shifting or Jigsaw transformation. This method does not require the use of phase keys. The image is encrypted by juxtaposition of sections of the image in various FRT domains. The new method has been compared numerically with existing methods and shows comparable or superior robustness to blind decryption. An optical implementation is also proposed and the sensitivity of the various encryption keys to blind decryption is quantified. We also present a second image encryption technique, which is based on a recently proposed method of optical phase retrieval using the optical FRT and one of its discrete counterparts. Numerical simulations of the new algorithm indicates that the sensitivity of the keys is much greater than any of the techniques currently available. In fact the sensitivity appears to be so high that optical implementation, based on existing optical signal processing technology, may be impossible. However, the technique has been shown to be a powerful method of 2-D image data encryption.
Voloshin, Vitaly I
2002-01-01
The theory of graph coloring has existed for more than 150 years. Historically, graph coloring involved finding the minimum number of colors to be assigned to the vertices so that adjacent vertices would have different colors. From this modest beginning, the theory has become central in discrete mathematics with many contemporary generalizations and applications. Generalization of graph coloring-type problems to mixed hypergraphs brings many new dimensions to the theory of colorings. A main feature of this book is that in the case of hypergraphs, there exist problems on both the minimum and th
Extremely simple holographic projection of color images
Makowski, Michal; Ducin, Izabela; Kakarenko, Karol; Suszek, Jaroslaw; Kolodziejczyk, Andrzej; Sypek, Maciej
2012-03-01
A very simple scheme of holographic projection is presented with some experimental results showing good quality image projection without any imaging lens. This technique can be regarded as an alternative to classic projection methods. It is based on the reconstruction real images from three phase iterated Fourier holograms. The illumination is performed with three laser beams of primary colors. A divergent wavefront geometry is used to achieve an increased throw angle of the projection, compared to plane wave illumination. Light fibers are used as light guidance in order to keep the setup as simple as possible and to provide point-like sources of high quality divergent wave-fronts at optimized position against the light modulator. Absorbing spectral filters are implemented to multiplex three holograms on a single phase-only spatial light modulator. Hence color mixing occurs without any time-division methods, which cause rainbow effects and color flicker. The zero diffractive order with divergent illumination is practically invisible and speckle field is effectively suppressed with phase optimization and time averaging techniques. The main advantages of the proposed concept are: a very simple and highly miniaturizable configuration; lack of lens; a single LCoS (Liquid Crystal on Silicon) modulator; a strong resistance to imperfections and obstructions of the spatial light modulator like dead pixels, dust, mud, fingerprints etc.; simple calculations based on Fast Fourier Transform (FFT) easily processed in real time mode with GPU (Graphic Programming).
Teaching Taekwondo in Physical Education: Incorporating the Color Belt System
Oh, Hyun-Ju; Hannon, James C.; Banks, Aaron
2006-01-01
Taekwondo is an excellent lifetime physical activity that provides both physical and mental benefits to its participants. The color belt system may be creatively used in physical education to encourage improvement in all learning domains. This article provides information on incorporating the color belt system into physical education, and provides…
Teaching Taekwondo in Physical Education: Incorporating the Color Belt System
Oh, Hyun-Ju; Hannon, James C.; Banks, Aaron
2006-01-01
Taekwondo is an excellent lifetime physical activity that provides both physical and mental benefits to its participants. The color belt system may be creatively used in physical education to encourage improvement in all learning domains. This article provides information on incorporating the color belt system into physical education, and provides…
Transform domain steganography with blind source separation
Jouny, Ismail
2015-05-01
This paper applies blind source separation or independent component analysis for images that may contain mixtures of text, audio, or other images for steganography purposes. The paper focuses on separating mixtures in the transform domain such as Fourier domain or the Wavelet domain. The study addresses the effectiveness of steganography when using linear mixtures of multimedia components and the ability of standard blind sources separation techniques to discern hidden multimedia messages. Mixing in the space, frequency, and wavelet (scale) domains is compared. Effectiveness is measured using mean square error rate between original and recovered images.
Implementation of Color Image Enhancement using DCT on TMS320C6713
Directory of Open Access Journals (Sweden)
Neeraj Kumar
2012-06-01
Full Text Available The paper underneath deals with image processing of color images using DSP processor (Texas Instrument product, TMS3206713. The basic process involve is to take input, a color image which is to be enhanced in DSP board and output its enhanced form which can be displayed on VM3224K2 Daughter kit (LCD. VM3224Daughter Kit is embedded with DSK6713 Kit just to display the respective images. Enhancement of color images can be carried out either in spatial domain or frequency domain. Enhancing color images in frequency domain is advantageous because individual color/frequency components can be modulated as per the requirement. Color images are analyzed into its constituent intensity and color components. Suitable scaling factor are employed for different components so that over all image is enhanced. Color images mostly uses JPEG compression format for saving bandwidth and memory space which uses popular discrete cosine transform (DCT. Hence it becomes necessary to investigate and propose new enhancement technique for the color image enhancement in compressed domain. In order to observe the colorfulness of the image, colorfulness metrics is adopted after enhancing the color image in compressed domain. The enhancement technique & proposed algorithm were well implemented practically on our hardware (TMS6713 kit. Implementation of algorithm& all computation of the paper is carried out in C-programming language.
Fourier transforms in radar and signal processing
Brandwood, David
2011-01-01
Fourier transforms are used widely, and are of particular value in the analysis of single functions and combinations of functions found in radar and signal processing. Still, many problems that could have been tackled by using Fourier transforms may have gone unsolved because they require integration that is difficult and tedious. This newly revised and expanded edition of a classic Artech House book provides you with an up-to-date, coordinated system for performing Fourier transforms on a wide variety of functions. Along numerous updates throughout the book, the Second Edition includes a crit
Harmonic functions on groups and Fourier algebras
Chu, Cho-Ho
2002-01-01
This research monograph introduces some new aspects to the theory of harmonic functions and related topics. The authors study the analytic algebraic structures of the space of bounded harmonic functions on locally compact groups and its non-commutative analogue, the space of harmonic functionals on Fourier algebras. Both spaces are shown to be the range of a contractive projection on a von Neumann algebra and therefore admit Jordan algebraic structures. This provides a natural setting to apply recent results from non-associative analysis, semigroups and Fourier algebras. Topics discussed include Poisson representations, Poisson spaces, quotients of Fourier algebras and the Murray-von Neumann classification of harmonic functionals.
Full Text Available ... lentes de contacto de color Sep. 26, 2013 It started as an impulsive buy from a souvenir ... Can Ruin Vision Eye Makeup Safety In fact, it is illegal to sell colored contact lenses without ...
Full Text Available ... colored contact lenses , from the U.S. Food and Drug Administration (FDA). Are the colored lenses you are ... from dry eye now have a completely new, drug-free alternative to lubricating eye drops and topical ...
Novozhilov, V Yu; Novozhilov, Victor; Novozhilov, Yuri
2002-01-01
We discuss specific features of color chiral solitons (asymptotics, possibility of confainment, quantization) at example of isolated SU(2) color skyrmions, i.e. skyrmions in a background field which is the vacuum field forming the gluon condensate.
Johnston, Jamie; Esposti, Federico; Lagnado, Leon
2012-08-21
Two complementary studies have resolved the circuitry underlying green-blue color discrimination in the retina. A blue-sensitive interneuron provides the inhibitory signal required for computing green-blue color opponency.
Institute of Scientific and Technical Information of China (English)
张俊斌
2006-01-01
Different colors affect us differently.The following will show us how they work. Experiment proves that math problems worked on yellow paper have fewer mistakes than problems written on other colors of paper.
Full Text Available ... Vision and Daily Eye Drops After One Use Facts About Colored Contacts and Halloween Safety Colored Contact Lens Facts Over-the-Counter Costume Contacts May Contain Chemicals ...
Fourier Series for Kample De Feriet Function
Directory of Open Access Journals (Sweden)
A. D. Wadhwa
1971-07-01
Full Text Available Some integrals involving Kampe de Feriet function have been evaluated. These integrals have further been employed to obtain some Fourier series for Kampe de Feriet functions. Some particular cases have also been discussed.
Composite Cyclotomic Fourier Transforms with Reduced Complexities
Wu, Xuebin; Chen, Ning; Yan, Zhiyuan; Wang, Ying
2010-01-01
Discrete Fourier transforms~(DFTs) over finite fields have widespread applications in digital communication and storage systems. Hence, reducing the computational complexities of DFTs is of great significance. Recently proposed cyclotomic fast Fourier transforms (CFFTs) are promising due to their low multiplicative complexities. Unfortunately, there are two issues with CFFTs: (1) they rely on efficient short cyclic convolution algorithms, which has not been investigated thoroughly yet, and (2) they have very high additive complexities when directly implemented. In this paper, we address both issues. One of the main contributions of this paper is efficient bilinear 11-point cyclic convolution algorithms, which allow us to construct CFFTs over GF$(2^{11})$. The other main contribution of this paper is that we propose composite cyclotomic Fourier transforms (CCFTs). In comparison to previously proposed fast Fourier transforms, our CCFTs achieve lower overall complexities for moderate to long lengths, and the imp...
Electronically-Scanned Fourier-Transform Spectrometer
Breckinridge, J. B.; Ocallaghan, F. G.
1984-01-01
Instrument efficient, lightweight, and stable. Fourier-transform spectrometer configuration uses electronic, instead of mechanical, scanning. Configuration insensitive to vibration-induced sampling errors introduced into mechanically scanned systems.
Wavelet-Fourier self-deconvolution
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Using a wavelet function as the filter function of Fourier self-deconvolution, a new me- thod of resolving overlapped peaks, wavelet-Fourier self-deconvolution, is founded. The properties of different wavelet deconvolution functions are studied. In addition, a cutoff value coefficient method of eliminating artificial peaks and wavelet method of removing shoulder peaks using the ratio of maximum peak to minimum peak is established. As a result, some problems in classical Fourier self-deconvolution are solved, such as the bad result of denoising, complicated processing, as well as usual appearance of artificial and shoulder peaks. Wavelet-Fourier self-deconvolution is applied to determination of multi-components in oscillographic chronopotentiometry. Experimental results show that the method has characteristics of simpler process and better effect of processing.
Wavelet-Fourier self-deconvolution
Institute of Scientific and Technical Information of China (English)
郑建斌; 张红权; 高鸿
2000-01-01
Using a wavelet function as the filter function of Fourier self-deconvolution, a new method of resolving overlapped peaks, wavelet-Fourier self-deconvolution, is founded. The properties of different wavelet deconvolution functions are studied. In addition, a cutoff value coefficient method of eliminating artificial peaks and wavelet method of removing shoulder peaks using the ratio of maximum peak to minimum peak is established. As a result, some problems in classical Fourier self-deconvolution are solved, such as the bad result of denoising, complicated processing, as well as usual appearance of artificial and shoulder peaks. Wavelet-Fourier self-deconvolution is applied to determination of multi-components in oscillographic chronopotentiometry. Experimental results show that the method has characteristics of simpler process and better effect of processing.
A new twist to fourier transforms
Meikle, Hamish D
2004-01-01
Making use of the inherent helix in the Fourier transform expression, this book illustrates both Fourier transforms and their properties in the round. The author draws on elementary complex algebra to manipulate the transforms, presenting the ideas in such a way as to avoid pages of complicated mathematics. Similarly, abbreviations are not used throughout and the language is kept deliberately clear so that the result is a text that is accessible to a much wider readership.The treatment is extended with the use of sampled data to finite and discrete transforms, the fast Fourier transform, or FFT, being a special case of a discrete transform. The application of Fourier transforms in statistics is illustrated for the first time using the examples operational research and later radar detection. In addition, a whole chapter on tapering or weighting functions is added for reference. The whole is rounded off by a glossary and examples of diagrams in three dimensions made possible by today's mathematics programs
Color: Implications in dentistry
Directory of Open Access Journals (Sweden)
Sikri Vimal
2010-01-01
Full Text Available The success of restorative dentistry is determined on the basis of functional and esthetic results. To achieve esthetics, four basic determinants are required in sequence; viz., position, contour, texture and color. The knowledge of the concept of color is essential for achieving good esthetics. This review compiles the various aspects of color, its measurements and shade matching in dentistry.
Hoang, M.A.; Geusebroek, J.M.; Chantler, M.
2002-01-01
In computer vision, measurement of image properties such as color or texture is essential. In this paper, we propose a solid framework for the local measurement of texture in color images. We give a physical basis for the integration of the well-known Gabor filters with the measurement of color. Our
Snyder, Jennifer
2011-01-01
Color wheels are a traditional project for many teachers. The author has used them in art appreciation classes for many years, but one problem she found when her pre-service art education students created colored wheels was that they were boring: simple circles, with pie-shaped pieces, which students either painted or colored in. This article…
Menke, Jan; Helms, Gunther; Larsen, Jörg
2010-01-01
The purpose of this experimental study was to evaluate whether the effective k-space coverage of MR images can in principle be viewed after multidimensional Fourier transform back to k-space. A water-soaked sponge phantom providing homogeneous k-space pattern was imaged with different standard MR sequences, utilizing elliptic acquisitions, partial-Fourier acquisitions and elliptic filtering as imaging examples. The resulting MR images were Fourier-transformed to the spatial frequency domain (the k-space) to visualize their effective k-space coverage. These frequency domain images are named "backtransformed k-space images." For a quantitative assessment, the sponge phantom was imaged with three-dimensional partial-Fourier sequences while varying the partial acquisition parameters in slice and phase direction. By linear regression analysis, the k-space coverage as expected from the sequence menu parameters was compared to the effective k-space coverage as observed in the backtransformed k-space images. The k-space coverage of elliptic and partial-Fourier acquisitions became visible in the backtransformed k-space images, as well as the effect of elliptic filtering. The expected and the observed k-space coverage showed a highly significant correlation (r=.99, PFourier-transforming MR images of a sponge phantom back to k-space. This method could be used for several purposes including sequence parameter optimization, basic imaging research, and to enhance a visual understanding of k-space, especially in three-dimensional MR imaging.
A DISTRIBUTION SPACE FOR FOURIER TRANSFORM
Institute of Scientific and Technical Information of China (English)
Zhou Chaoying; Yang Lihua; Huang Daren
2007-01-01
A space DF is constructed and some characterizations of space DF are given. Itis shown that the classical Fourier transform is extended to the distribution space D'F, whichcan be embedded into the Schwartz distribution space D' continuously. It is also shown thatD'F is the biggest embedded subspace of D' on which the extended Fourier transform, F, is ahomeomorphism of D'F onto itself.
Shift sampling theory of Fourier transform computation
Institute of Scientific and Technical Information of China (English)
柴玉璞
1997-01-01
The DFT transform us extended to DFTξη transform and the relationship between FT and DFTξη is given by the Fourier transform discretization theorem. Based on the theorem, the DFTξη algorithm-error equation (DFTξη A-E equation) is established, and the minimization property of discrete effect and the oscillation property of truncation effect are demonstrated. All these construct the shift sampling theory——a new theory about Fourier transform computation.
Fractional Fourier transform of Lorentz beams
Institute of Scientific and Technical Information of China (English)
Zhou Guo-Quan
2009-01-01
This paper introduces Lorentz beams to describe certain laser sources that produce highly divergent fields. The fractional Fourier transform (FRFT) is applied to treat the propagation of Lorentz beams. Based on the definition of convolution and the convolution theorem of the Fourier transform, an analytical expression for a Lorentz beam passing through a FRFT system has been derived. By using the derived formula, the properties of a Lorentz beam in the FRFT plane are illustrated numerically.
Bead-Fourier path integral molecular dynamics
Ivanov, Sergei D.; Lyubartsev, Alexander P.; Laaksonen, Aatto
2003-06-01
Molecular dynamics formulation of Bead-Fourier path integral method for simulation of quantum systems at finite temperatures is presented. Within this scheme, both the bead coordinates and Fourier coefficients, defining the path representing the quantum particle, are treated as generalized coordinates with corresponding generalized momenta and masses. Introduction of the Fourier harmonics together with the center-of-mass thermostating scheme is shown to remove the ergodicity problem, known to pose serious difficulties in standard path integral molecular dynamics simulations. The method is tested for quantum harmonic oscillator and hydrogen atom (Coulombic potential). The simulation results are compared with the exact analytical solutions available for both these systems. Convergence of the results with respect to the number of beads and Fourier harmonics is analyzed. It was shown that addition of a few Fourier harmonics already improves the simulation results substantially, even for a relatively small number of beads. The proposed Bead-Fourier path integral molecular dynamics is a reliable and efficient alternative to simulations of quantum systems.
Institute of Scientific and Technical Information of China (English)
华焱军; 黄锦海; 潘超; 王勤美
2013-01-01
膜地形图仪略大；RTVue FD-OCT获得的Rposterior/Ranterior比Gullstrand模型眼小,可能为建立更准确的标准化模型眼提供依据.%Background Corneal parameters (such as curvature,thickness,etc) are essential to the diagnosis of corneal related diseases,contact lenses fitting and corneal refractive surgery.Objective The aim of this study was to assess the repeatability and accuracy of corneal parameters obtained by RTVue Fourier-domain optical coherence topography (FD-OCT).Methods In this prospective study,77 eyes of 43 subjects with the refraction from-1.25 D to-10.00 D and astigmatism ＜2 D were enrolled in keratorefractive surgery center,Eye Hospital of Wenzhou Medical College.The anterior and posterior corneal curvature in 3 mm central zone (Ranterior and Rposterior),the ratio of posterior and anterior curvature (Rposterior/Ranterior),corneal central thickness (CCT),total corneal power(Knet),the simulated corneal power (Sim K),the anterior and posterior corneal power (Kanterior,Kposterior)were measured by FD-OCT.Corneal power (Km) was obtained by Topolyzer topography based on Placido ring.Three consecutive scans were acquired in every tested eye.Repeatability of FD-OCT measurement was assessed using the coefficient of variation CV),Cronbach Alpha and intra-class correlation coefficient (ICC).Repeated measure ANOVA was used to analyze the differences among SimK,Knet and Km.Pearson correlation analysis was used to analysis the correlation between SimK and K Knet and Km,SimK and Km.The agreement between Sim K and K Knet and Km,SimK and Km was assessed by Bland-Altman plots analysis.All the subjects understood the purpose of this investigation and written informed consent was obtained prior to the medical examination.Results The Ranterior,Rposterior,Rposterior/Ranterior,Kanterior,Kposterior,Sim K,Knet and CCT were (7.691 ±0.302) mm,(6.532±0.276) mm,0.849±0.014,(48.97±1.92)D,(-6.13±0.26)D,(43.95±1.72) D,(42.95±1.68) D and (545.20± 35.04) μm,respectively.The CV of all
Noise Tracking Using DFT Domain Subspace Decompositions
Hendriks, R.C.; Jensen, J.; Heusdens, R.
2008-01-01
All discrete Fourier transform (DFT) domain-based speech enhancement gain functions rely on knowledge of the noise power spectral density (PSD). Since the noise PSD is unknown in advance, estimation from the noisy speech signal is necessary. An overestimation of the noise PSD will lead to a loss in
Noise Tracking Using DFT Domain Subspace Decompositions
Hendriks, R.C.; Jensen, J.; Heusdens, R.
2008-01-01
All discrete Fourier transform (DFT) domain-based speech enhancement gain functions rely on knowledge of the noise power spectral density (PSD). Since the noise PSD is unknown in advance, estimation from the noisy speech signal is necessary. An overestimation of the noise PSD will lead to a loss in
Institute of Scientific and Technical Information of China (English)
徐丹
2009-01-01
Being a minor part in the translation field,the translation of color words is far more complex than people may have imagined.Apart from the literal meaning of color words in the target language,there are other factors that affect the understanding.This paper mainly focuses on three main characteristics of color words that make the translation work difficult-color words'variations and combinations,rich symbolic meanings and culture differences.It also provides possible ways to deal with the prickly problem of finding equivalents,the complexity of transferring symbolic meanings and the subtle problem of crossing culture boundaries in translation of color words.
... or freezer, color changes are normal for fresh meat and poultry. 2. Does a change in color indicate spoilage? Change in color alone does not mean the product is spoiled. Color changes are normal for fresh ...
Domain Decomposition Solvers for Frequency-Domain Finite Element Equations
Copeland, Dylan
2010-10-05
The paper is devoted to fast iterative solvers for frequency-domain finite element equations approximating linear and nonlinear parabolic initial boundary value problems with time-harmonic excitations. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple linear elliptic system for the amplitudes belonging to the sine- and to the cosine-excitation or a large nonlinear elliptic system for the Fourier coefficients in the linear and nonlinear case, respectively. The fast solution of the corresponding linear and nonlinear system of finite element equations is crucial for the competitiveness of this method. © 2011 Springer-Verlag Berlin Heidelberg.
Generalized Fourier-grid R-matrix theory: a discrete Fourier-Riccati-Bessel transform approach
Energy Technology Data Exchange (ETDEWEB)
Layton, E.G. (Joint Inst. for Lab. Astrophysics, Boulder, CO (United States)); Stade, E. (Colorado Univ., Boulder, CO (United States). Dept. of Mathematics)
1993-08-28
We present the latest developments in the Fourier-grid R-matrix theory of scattering. These developments are based on the generalized Fourier-grid formalism and use a new type of extended discrete Fourier transform: the discrete Fourier-Riccati-Bessel transform. We apply this new R-matrix approach to problems of potential scattering, to demonstrate how this method reduces computational effort by incorporating centrifugal effects into the representation. As this technique is quite new, we have hopes to broaden the formalism to many types of problems. (author).
Acquired color vision deficiency.
Simunovic, Matthew P
2016-01-01
Acquired color vision deficiency occurs as the result of ocular, neurologic, or systemic disease. A wide array of conditions may affect color vision, ranging from diseases of the ocular media through to pathology of the visual cortex. Traditionally, acquired color vision deficiency is considered a separate entity from congenital color vision deficiency, although emerging clinical and molecular genetic data would suggest a degree of overlap. We review the pathophysiology of acquired color vision deficiency, the data on its prevalence, theories for the preponderance of acquired S-mechanism (or tritan) deficiency, and discuss tests of color vision. We also briefly review the types of color vision deficiencies encountered in ocular disease, with an emphasis placed on larger or more detailed clinical investigations.
Colors, colored overlays, and reading skills
Directory of Open Access Journals (Sweden)
Arcangelo eUccula
2014-07-01
Full Text Available In this article, we are concerned with the role of colors in reading written texts. It has been argued that colored overlays applied above written texts positively influence both reading fluency and reading speed. These effects would be particularly evident for those individuals affected by the so called Meares-Irlen syndrome, i.e. who experience eyestrain and/or visual distortions – e.g. color, shape or movement illusions – while reading. This condition would interest the 12-14% of the general population and up to the 46% of the dyslexic population. Thus, colored overlays have been largely employed as a remedy for some aspects of the difficulties in reading experienced by dyslexic individuals, as fluency and speed. Despite the wide use of colored overlays, how they exert their effects has not been made clear yet. Also, according to some researchers, the results supporting the efficacy of colored overlays as a tool for helping readers are at least controversial. Furthermore, the very nature of the Meares-Irlen syndrome has been questioned. Here we provide a concise, critical review of the literature.
Color Reproduction with a Smartphone
Thoms, Lars-Jochen; Colicchia, Giuseppe; Girwidz, Raimund
2013-01-01
The world is full of colors. Most of the colors we see around us can be created on common digital displays simply by superposing light with three different wavelengths. However, no mixture of colors can produce a fully pure color identical to a spectral color. Using a smartphone, students can investigate the main features of primary color addition…
Color Reproduction with a Smartphone
Thoms, Lars-Jochen; Colicchia, Giuseppe; Girwidz, Raimund
2013-01-01
The world is full of colors. Most of the colors we see around us can be created on common digital displays simply by superposing light with three different wavelengths. However, no mixture of colors can produce a fully pure color identical to a spectral color. Using a smartphone, students can investigate the main features of primary color addition…
Women of Color in Experiential Education: Crossing Cultural Boundaries.
Roberts, Nina
Outdoor adventure is stereotyped as a White, male activity. Women who participate are going against the stereotype of outdoor activities as a male domain, but women of color additionally confront the domain of race. Constraints on women generally include socialization into an ethic of care, concern for physical and psychological safety, and lack…
Solving forward and inverse seismic problems by boundary-element method in frequency domain
Energy Technology Data Exchange (ETDEWEB)
Xianxi, J.
1988-01-01
Solving the boundary value problem of wave equation by boundary element method in frequency domain involves these steps: 1. ID Fourier transform of time variable is made to convert the wave equation into Helmholtz equation; 2. this equation is then solved using boundary-element method in frequency domain; 3. the result is returned to time domain by making inverse Fourier transform. Compared with other formulas, the formula in this paper brings higher accuracy but less computation.
Institute of Scientific and Technical Information of China (English)
Xiao-Hui Wang; Jia Jia; Han-Yu Liao; Lian-Hong Cai
2012-01-01
Colorization of gray-scale images has attracted many attentions for a long time.An important role of image color is the conveyer of emotions (through color themes).The colorization with an undesired color theme is less useful,even it is semantically correct.However this has been rarely considered.Automatic colorization respecting both the semantics and the emotions is undoubtedly a challenge.In this paper,we propose a complete system for affective image colorization.We only need the user to assist object segmentation along with text labels and an affective word.First,the text labels along with other object characters are jointly used to filter the internet images to give each object a set of semantically correct reference images.Second,we select a set of color themes according to the affective word based on art theories.With these themes,a generic algorithm is used to select the best reference for each object,balancing various requirements.Finally,we propose a hybrid texture synthesis approach for colorization.To the best of our knowledge,it is the first system which is able to efficiently colorize a gray-scale image semantically by an emotionally controllable fashion.Our experiments show the effectiveness of our system,especially the benefit compared with the previous Markov random field (MRF) based method.
da Pos, Osvaldo
2002-06-01
Color is a visible aspect of objects and lights, and as such is an objective characteristic of our phenomenal world. Correspondingly also objects and lights are objective, although their subjectivity cannot be disregarded since they belong to our phenomenal world. The distinction between perception and sensation deals with colors seen either in complex displays or in isolation. Reality of colors is apparently challenged by virtual reality, while virtual reality is a good example of what colors are. It seems difficult to combine that aspect of reality colors have in our experience and the concept that colors represent something in the external environment: the distinction between stimulation and perceived object is crucial for understanding the relationships between phenomenal world and physical reality. A modern concept of isomorphism seems useful in interpreting the role of colors. The relationship between the psychological structure of colors and the physical stimulation is enlightened by the analysis of pseudocolors. The perceptual, subjective characteristics of colors go along with the subjectivity of scientific concepts. Colors, emotions, and concepts are all in some people's mind: none of them is independent of the subject mind. Nevertheless they can be communicated from person to person by an appropriate scientific terminology.
Selection of small color palette for color image quantization
Chau, Wing K.; Wong, S. K. M.; Yang, Xuedong; Wan, Shijie J.
1992-05-01
Two issues are involved in color image quantization: color palette selection and color mapping. A common practice for color palette selection is to minimize the color distortion for each pixel (the median-cut, the variance-based and the k-means algorithms). After the color palette has been chosen, a quantized image may be generated by mapping the original color of each pixel onto its nearest color in the color palette. Such an approach can usually produce quantized images of high quality with 128 or more colors. For 32 - 64 colors, the quality of the quantized images is often acceptable with the aid of dithering techniques in the color mapping process. For 8 - 16 color, however, the above statistical method for color selection becomes no longer suitable because of the great reduction of color gamut. In order to preserve the color gamut of the original image, one may want to select the colors in such a way that the convex hull formed by these colors in the RGB color space encloses most colors of the original image. Quantized images generated in such a geometrical way usually preserve a lot of image details, but may contain too much high frequency noises. This paper presents an effective algorithm for the selection of very small color palette by combining the strengths of the above statistical and geometrical approaches. We demonstrate that with the new method images of high quality can be produced by using only 4 to 8 colors.
Glasser, L.
1987-01-01
This paper explores how Fourier Transform (FT) mimics spectral transformation, how this property can be exploited to advantage in spectroscopy, and how the FT can be used in data treatment. A table displays a number of important FT serial/spectral pairs related by Fourier Transformations. A bibliography and listing of computer software related to…
An individuality model for online signatures using global Fourier descriptors
Kholmatov, Alisher; Yanikoglu, Berrin
2008-03-01
The discriminative capability of a biometric is based on its individuality/uniqueness and is an important factor in choosing a biometric for a large-scale deployment. Individuality studies have been carried out rigorously for only certain biometrics, in particular fingerprint and iris, while work on establishing handwriting and signature individuality has been mainly on feature level. In this study, we present a preliminary individuality model for online signatures using the Fourier domain representation of the signature. Using the normalized Fourier coefficients as global features describing the signature, we derive a formula for the probability of coincidentally matching a given signature. Estimating model parameters from a large database and making certain simplifying assumptions, the probability of two arbitrary signatures to match in 13 of the coefficients is calculated as 4.7x10 -4. When compared with the results of a verification algorithm that parallels the theoretical model, the results show that the theoretical model fits the random forgery test results fairly well. While online signatures are sometimes dismissed as not very secure, our results show that the probability of successfully guessing an online signature is very low. Combined with the fact that signature is a behavioral biometric with adjustable complexity, these results support the use of online signatures for biometric authentication.
Fourier-Transform Ghost Imaging with Hard X Rays
Yu, Hong; Lu, Ronghua; Han, Shensheng; Xie, Honglan; Du, Guohao; Xiao, Tiqiao; Zhu, Daming
2016-09-01
Knowledge gained through x-ray crystallography fostered structural determination of materials and greatly facilitated the development of modern science and technology in the past century. However, it is only applied to crystalline structures and cannot resolve noncrystalline materials. Here we demonstrate a novel lensless Fourier-transform ghost imaging method with pseudothermal hard x rays that extends x-ray crystallography to noncrystalline samples. By measuring the second-order intensity correlation function of the light, Fourier-transform diffraction pattern of a complex amplitude sample is achieved at the Fresnel region in our experiment and the amplitude and phase distributions of the sample in the spatial domain are retrieved successfully. For the first time, ghost imaging is experimentally realized with x rays. Since a highly coherent x-ray source is not required, the method can be implemented with laboratory x-ray sources and it also provides a potential solution for lensless diffraction imaging with fermions, such as neutrons and electrons where intensive coherent sources usually are not available.
High Performance GPU-Based Fourier Volume Rendering.
Abdellah, Marwan; Eldeib, Ayman; Sharawi, Amr
2015-01-01
Fourier volume rendering (FVR) is a significant visualization technique that has been used widely in digital radiography. As a result of its (N (2)logN) time complexity, it provides a faster alternative to spatial domain volume rendering algorithms that are (N (3)) computationally complex. Relying on the Fourier projection-slice theorem, this technique operates on the spectral representation of a 3D volume instead of processing its spatial representation to generate attenuation-only projections that look like X-ray radiographs. Due to the rapid evolution of its underlying architecture, the graphics processing unit (GPU) became an attractive competent platform that can deliver giant computational raw power compared to the central processing unit (CPU) on a per-dollar-basis. The introduction of the compute unified device architecture (CUDA) technology enables embarrassingly-parallel algorithms to run efficiently on CUDA-capable GPU architectures. In this work, a high performance GPU-accelerated implementation of the FVR pipeline on CUDA-enabled GPUs is presented. This proposed implementation can achieve a speed-up of 117x compared to a single-threaded hybrid implementation that uses the CPU and GPU together by taking advantage of executing the rendering pipeline entirely on recent GPU architectures.
High Performance GPU-Based Fourier Volume Rendering
Directory of Open Access Journals (Sweden)
Marwan Abdellah
2015-01-01
Full Text Available Fourier volume rendering (FVR is a significant visualization technique that has been used widely in digital radiography. As a result of its O(N2logN time complexity, it provides a faster alternative to spatial domain volume rendering algorithms that are O(N3 computationally complex. Relying on the Fourier projection-slice theorem, this technique operates on the spectral representation of a 3D volume instead of processing its spatial representation to generate attenuation-only projections that look like X-ray radiographs. Due to the rapid evolution of its underlying architecture, the graphics processing unit (GPU became an attractive competent platform that can deliver giant computational raw power compared to the central processing unit (CPU on a per-dollar-basis. The introduction of the compute unified device architecture (CUDA technology enables embarrassingly-parallel algorithms to run efficiently on CUDA-capable GPU architectures. In this work, a high performance GPU-accelerated implementation of the FVR pipeline on CUDA-enabled GPUs is presented. This proposed implementation can achieve a speed-up of 117x compared to a single-threaded hybrid implementation that uses the CPU and GPU together by taking advantage of executing the rendering pipeline entirely on recent GPU architectures.
Trahtman, A N
2007-01-01
The synchronizing word of deterministic automaton is a word in the alphabet of colors (considered as letters) of its edges that maps the automaton to a single state. A coloring of edges of a directed graph is synchronizing if the coloring turns the graph into deterministic finite automaton possessing a synchronizing word. The road coloring problem is a problem of synchronizing coloring of directed finite strongly connected graph with constant outdegree of all its vertices if the greatest common divisor of lengths of all its cycles is one. The problem was posed by Adler, Goodwyn and Weiss over 30 years ago and evoked a noticeable interest among the specialists in theory of graphs, deterministic automata and symbolic dynamics. The problem is described even in "Vikipedia" - the popular Internet Encyclopedia. The positive solution of the road coloring problem is presented.
Jung, E.
1984-05-01
A color recording unit was designed for output and control of digitized picture data within computer controlled reproduction and picture processing systems. In order to get a color proof picture of high quality similar to a color print, together with reduced time and material consumption, a photographic color film material was exposed pixelwise by modulated laser beams of three wavelengths for red, green and blue light. Components of different manufacturers for lasers, acousto-optic modulators and polygon mirrors were tested, also different recording methods as (continuous tone mode or screened mode and with a drum or flatbed recording principle). Besides the application for the graphic arts - the proof recorder CPR 403 with continuous tone color recording with a drum scanner - such a color hardcopy peripheral unit with large picture formats and high resolution can be used in medicine, communication, and satellite picture processing.
A resource-efficient adaptive Fourier analyzer
Hajdu, C. F.; Zamantzas, C.; Dabóczi, T.
2016-10-01
We present a resource-efficient frequency adaptation method to complement the Fourier analyzer proposed by Péceli. The novel frequency adaptation scheme is based on the adaptive Fourier analyzer suggested by Nagy. The frequency adaptation method was elaborated with a view to realizing a detector connectivity check on an FPGA in a new beam loss monitoring (BLM) system, currently being developed for beam setup and machine protection of the particle accelerators at the European Organisation for Nuclear Research (CERN). The paper summarizes the Fourier analyzer to the extent relevant to this work and the basic principle of the related frequency adaptation methods. It then outlines the suggested new scheme, presents practical considerations for implementing it and underpins it with an example and the corresponding operational experience.
Practical Fourier analysis for multigrid methods
Wienands, Roman
2004-01-01
Before applying multigrid methods to a project, mathematicians, scientists, and engineers need to answer questions related to the quality of convergence, whether a development will pay out, whether multigrid will work for a particular application, and what the numerical properties are. Practical Fourier Analysis for Multigrid Methods uses a detailed and systematic description of local Fourier k-grid (k=1,2,3) analysis for general systems of partial differential equations to provide a framework that answers these questions.This volume contains software that confirms written statements about convergence and efficiency of algorithms and is easily adapted to new applications. Providing theoretical background and the linkage between theory and practice, the text and software quickly combine learning by reading and learning by doing. The book enables understanding of basic principles of multigrid and local Fourier analysis, and also describes the theory important to those who need to delve deeper into the detai...
Fourier analysis and boundary value problems
Gonzalez-Velasco, Enrique A
1996-01-01
Fourier Analysis and Boundary Value Problems provides a thorough examination of both the theory and applications of partial differential equations and the Fourier and Laplace methods for their solutions. Boundary value problems, including the heat and wave equations, are integrated throughout the book. Written from a historical perspective with extensive biographical coverage of pioneers in the field, the book emphasizes the important role played by partial differential equations in engineering and physics. In addition, the author demonstrates how efforts to deal with these problems have lead to wonderfully significant developments in mathematics.A clear and complete text with more than 500 exercises, Fourier Analysis and Boundary Value Problems is a good introduction and a valuable resource for those in the field.Key Features* Topics are covered from a historical perspective with biographical information on key contributors to the field* The text contains more than 500 exercises* Includes practical applicati...
Replica Fourier Transform: Properties and applications
Directory of Open Access Journals (Sweden)
A. Crisanti
2015-02-01
Full Text Available The Replica Fourier Transform is the generalization of the discrete Fourier Transform to quantities defined on an ultrametric tree. It finds use in conjunction of the replica method used to study thermodynamics properties of disordered systems such as spin glasses. Its definition is presented in a systematic and simple form and its use illustrated with some representative examples. In particular we give a detailed discussion of the diagonalization in the Replica Fourier Space of the Hessian matrix of the Gaussian fluctuations about the mean field saddle point of spin glass theory. The general results are finally discussed for a generic spherical spin glass model, where the Hessian can be computed analytically.
Methods of Fourier analysis and approximation theory
Tikhonov, Sergey
2016-01-01
Different facets of interplay between harmonic analysis and approximation theory are covered in this volume. The topics included are Fourier analysis, function spaces, optimization theory, partial differential equations, and their links to modern developments in the approximation theory. The articles of this collection were originated from two events. The first event took place during the 9th ISAAC Congress in Krakow, Poland, 5th-9th August 2013, at the section “Approximation Theory and Fourier Analysis”. The second event was the conference on Fourier Analysis and Approximation Theory in the Centre de Recerca Matemàtica (CRM), Barcelona, during 4th-8th November 2013, organized by the editors of this volume. All articles selected to be part of this collection were carefully reviewed.
Projective Fourier duality and Weyl quantization
Energy Technology Data Exchange (ETDEWEB)
Aldrovandi, R.; Saeger, L.A.
1996-08-01
The Weyl-Wigner correspondence prescription, which makes large use of Fourier duality, is reexamined from the point of view of Kac algebras, the most general background for non-commutative Fourier analysis allowing for that property. It is shown how the standard Kac structure has to be extended in order to accommodate the physical requirements. An Abelian and a symmetric projective Kac algebras are shown to provide, in close parallel to the standard case, a new dual framework and a well-defined notion of projective Fourier duality for the group of translations on the plane. The Weyl formula arises naturally as an irreducible component of the duality mapping between these projective algebras. (author). 29 refs.
Color Image Enhancement Based on Maximum Fuzzy Entropy
Institute of Scientific and Technical Information of China (English)
QU Yi; XU Li-hong; KANG Qi
2004-01-01
A color image enhancement approach based on maximum fuzzy entropy and genetic algorithm is proposed in this paper. It enhances color images by stretching the contrast of S and I components respectively in the HSI color representation. The image is transformed from the property domain to the fuzzy domain with S-function. To preserve as much information as possible in the fuzzy the domain, the fuzzy entropy function is used as objective function in a genetic algorithm to optimize three parameters of the S-function. The Sigmoid function is applied to intensify the membership values and the results are transformed back to the property domain to produce the enhanced image. Experiments show the effectiveness of the approach.
Fractional Fourier Transform for Ultrasonic Chirplet Signal Decomposition
Directory of Open Access Journals (Sweden)
Yufeng Lu
2012-01-01
Full Text Available A fractional fourier transform (FrFT based chirplet signal decomposition (FrFT-CSD algorithm is proposed to analyze ultrasonic signals for NDE applications. Particularly, this method is utilized to isolate dominant chirplet echoes for successive steps in signal decomposition and parameter estimation. FrFT rotates the signal with an optimal transform order. The search of optimal transform order is conducted by determining the highest kurtosis value of the signal in the transformed domain. A simulation study reveals the relationship among the kurtosis, the transform order of FrFT, and the chirp rate parameter in the simulated ultrasonic echoes. Benchmark and ultrasonic experimental data are used to evaluate the FrFT-CSD algorithm. Signal processing results show that FrFT-CSD not only reconstructs signal successfully, but also characterizes echoes and estimates echo parameters accurately. This study has a broad range of applications of importance in signal detection, estimation, and pattern recognition.
Convergence of Fourier-based time methods for turbomachinery wake passing problems
Gomar, Adrien; Bouvy, Quentin; Sicot, Frédéric; Dufour, Guillaume; Cinnella, Paola; François, Benjamin
2014-12-01
The convergence of Fourier-based time methods applied to turbomachinery flows is assessed. The focus is on the harmonic balance method, which is a time-domain Fourier-based approach standing as an efficient alternative to classical time marching schemes for periodic flows. In the literature, no consensus exists concerning the number of harmonics needed to achieve convergence for turbomachinery stage configurations. In this paper it is shown that the convergence of Fourier-based methods is closely related to the impulsive nature of the flow solution, which in turbomachines is essentially governed by the characteristics of the passing wakes between adjacent rows. As a result of the proposed analysis, a priori estimates are provided for the minimum number of harmonics required to accurately compute a given turbomachinery configuration. Their application to several contra-rotating open-rotor configurations is assessed, demonstrating the practical interest of the proposed methodology.
Inversion of Fourier Transforms by Means of Scale-Frequency Series
Directory of Open Access Journals (Sweden)
Nassar H. S. Haidar
2014-01-01
Full Text Available We report on inversion of the Fourier transform when the frequency variable can be scaled in a variety of different ways that improve the resolution of certain parts of the frequency domain. The corresponding inverse Fourier transform is shown to exist in the form of two dual scale-frequency series. Upon discretization of the continuous scale factor, this Fourier transform series inverse becomes a certain nonharmonic double series, a discretized scale-frequency (DSF series. The DSF series is also demonstrated, theoretically and practically, to be rate-optimizable with respect to its two free parameters, when it satisfies, as an entropy maximizer, a pertaining recursive nonlinear programming problem incorporating the entropy-based uncertainty principle.
Rejection of Linear FM Interference in DSSS System Based on Fractional Fourier Transform
Institute of Scientific and Technical Information of China (English)
QI Lin; TAO Ran; ZHOU Si-yong
2005-01-01
A new method for the rejection of linear frequency modulation (LFM) interference in direct sequence spread spectrum (DSSS) system based on the fractional Fourier transform is proposed, and the configuration of the receiver with an interference exciser is also presented. Based on the property that the fractional Fourier transform of a signal is equivalent to rotating the signal in the time-frequency plane, the received signal is transform into a certain fractional Fourier domain, this transform will result in the least spectrum overlap between the signal and interference. Then, a narrowband filter is exploited to extract most of the interference energy. The performance analyses show that remarkable improvements in signal-to-noise ratio (SNR) and biterror-ratio (BER) are obtained.
Building a symbolic computer algebra toolbox to compute 2D Fourier transforms in polar coordinates.
Dovlo, Edem; Baddour, Natalie
2015-01-01
The development of a symbolic computer algebra toolbox for the computation of two dimensional (2D) Fourier transforms in polar coordinates is presented. Multidimensional Fourier transforms are widely used in image processing, tomographic reconstructions and in fact any application that requires a multidimensional convolution. By examining a function in the frequency domain, additional information and insights may be obtained. The advantages of our method include: •The implementation of the 2D Fourier transform in polar coordinates within the toolbox via the combination of two significantly simpler transforms.•The modular approach along with the idea of lookup tables implemented help avoid the issue of indeterminate results which may occur when attempting to directly evaluate the transform.•The concept also helps prevent unnecessary computation of already known transforms thereby saving memory and processing time.
Energy Technology Data Exchange (ETDEWEB)
Lü, X.; Schrottke, L.; Grahn, H. T. [Paul-Drude-Institut für Festkörperelektronik, Leibniz-Institut im Forschungsverbund Berlin e. V., Hausvogteiplatz 5–7, 10117 Berlin (Germany)
2016-06-07
We present scattering rates for electrons at longitudinal optical phonons within a model completely formulated in the Fourier domain. The total intersubband scattering rates are obtained by averaging over the intrasubband electron distributions. The rates consist of the Fourier components of the electron wave functions and a contribution depending only on the intersubband energies and the intrasubband carrier distributions. The energy-dependent part can be reproduced by a rational function, which allows for the separation of the scattering rates into a dipole-like contribution, an overlap-like contribution, and a contribution which can be neglected for low and intermediate carrier densities of the initial subband. For a balance between accuracy and computation time, the number of Fourier components can be adjusted. This approach facilitates an efficient design of complex heterostructures with realistic, temperature- and carrier density-dependent rates.
Institute of Scientific and Technical Information of China (English)
王冰
2012-01-01
Different nations have different or even opposite perception of color, which results in non-equivalence of color words in mutual translation between Chinese and English. This paper is to discuss non-equivalence of color words between Chinese and English on the two aspects and emphasizes the importance of transmitting cultural message accurately in the mutual translation between Chinese and English. Studying the cultural connotations of the words is of great importance for successful communication.
Fourier transforms and convolutions for the experimentalist
Jennison, RC
1961-01-01
Fourier Transforms and Convolutions for the Experimentalist provides the experimentalist with a guide to the principles and practical uses of the Fourier transformation. It aims to bridge the gap between the more abstract account of a purely mathematical approach and the rule of thumb calculation and intuition of the practical worker. The monograph springs from a lecture course which the author has given in recent years and for which he has drawn upon a number of sources, including a set of notes compiled by the late Dr. I. C. Browne from a series of lectures given by Mr. J . A. Ratcliffe of t
Fourier analysis in several complex variables
Ehrenpreis, Leon
2006-01-01
Suitable for advanced undergraduates and graduate students, this text develops comparison theorems to establish the fundamentals of Fourier analysis and to illustrate their applications to partial differential equations.The three-part treatment begins by establishing the quotient structure theorem or fundamental principle of Fourier analysis. Topics include the geometric structure of ideals and modules, quantitative estimates, and examples in which the theory can be applied. The second part focuses on applications to partial differential equations and covers the solution of homogeneous and inh
Quantum transport efficiency and Fourier's law.
Manzano, Daniel; Tiersch, Markus; Asadian, Ali; Briegel, Hans J
2012-12-01
We analyze the steady-state energy transfer in a chain of coupled two-level systems connecting two thermal reservoirs. Through an analytic treatment we find that the energy current is independent of the system size, hence violating Fourier's law of heat conduction. The classical diffusive behavior in Fourier's law of heat conduction can be recovered by introducing decoherence to the quantum systems constituting the chain. We relate these results to recent discussions of energy transport in biological light-harvesting systems, and discuss the role of quantum coherence and entanglement.
Quantum transport efficiency and Fourier's law
Manzano, Daniel; Asadian, Ali; Briegel, Hans J
2011-01-01
We analyze the steady-state energy transfer in a chain of coupled two-level systems connecting two thermal reservoirs. Through an analytic treatment we find that the energy current is independent of the system size, hence violating Fourier's law of heat conduction. The classical diffusive behavior in Fourier's law of heat conduction can be recovered by introducing decoherence to the quantum systems constituting the chain. Implications of these results on energy transfer in biological light harvesting systems, and the role of quantum coherences and entanglement are discussed.
Fast Fourier Transform algorithm design and tradeoffs
Kamin, Ray A., III; Adams, George B., III
1988-01-01
The Fast Fourier Transform (FFT) is a mainstay of certain numerical techniques for solving fluid dynamics problems. The Connection Machine CM-2 is the target for an investigation into the design of multidimensional Single Instruction Stream/Multiple Data (SIMD) parallel FFT algorithms for high performance. Critical algorithm design issues are discussed, necessary machine performance measurements are identified and made, and the performance of the developed FFT programs are measured. Fast Fourier Transform programs are compared to the currently best Cray-2 FFT program.
Illustrative EDOF topics in Fourier optics
George, Nicholas; Chen, Xi; Chi, Wanli
2011-10-01
In this talk we present a series of illustrative topics in Fourier Optics that are proving valuable in the design of EDOF camera systems. They are at the level of final examination problems that have been made solvable by a student or professoi having studied from one of Joseph W. Goodman's books---our tribute for his 75fr year. As time permits, four illustrative topics are l) Electromagnetic waves and Fourier optics;2) The perfect lens; 3) Connection between phase delay and radially varying focal length in an asphere and 4) tailored EDOF designs.
Electro-optic imaging Fourier transform spectrometer
Chao, Tien-Hsin (Inventor); Znod, Hanying (Inventor)
2009-01-01
An Electro-Optic Imaging Fourier Transform Spectrometer (EOIFTS) for Hyperspectral Imaging is described. The EOIFTS includes an input polarizer, an output polarizer, and a plurality of birefringent phase elements. The relative orientations of the polarizers and birefringent phase elements can be changed mechanically or via a controller, using ferroelectric liquid crystals, to substantially measure the spectral Fourier components of light propagating through the EIOFTS. When achromatic switches are used as an integral part of the birefringent phase elements, the EIOFTS becomes suitable for broadband applications, with over 1 micron infrared bandwidth.
Color sensing under microwaves
Choudhury, Debesh
2013-09-01
Inspired by recent results of artificial color due to Caulfield, we carry out intuitive experimental investigations on color sensing under microwave illumination. Experiemnts have been carried out using a Gunn diode as the microwave source and a microwave diode as a detector. More precise experimental studies have also been carried out utilizing a vector network analyzer. Preliminary results of the experiments validate the feasibility of sensing and discriminating otherwise visual colors under microwave illumination. Caulfield's presumption possibly paves the way for artificial color perception using microwaves.
Phylogenetic approach to the evolution of color term systems.
Haynie, Hannah J; Bowern, Claire
2016-11-29
The naming of colors has long been a topic of interest in the study of human culture and cognition. Color term research has asked diverse questions about thought and communication, but no previous research has used an evolutionary framework. We show that there is broad support for the most influential theory of color term development (that most strongly represented by Berlin and Kay [Berlin B, Kay P (1969) (Univ of California Press, Berkeley, CA)]); however, we find extensive evidence for the loss (as well as gain) of color terms. We find alternative trajectories of color term evolution beyond those considered in the standard theories. These results not only refine our knowledge of how humans lexicalize the color space and how the systems change over time; they illustrate the promise of phylogenetic methods within the domain of cognitive science, and they show how language change interacts with human perception.
Does the Entorhinal Cortex use the Fourier Transform?
Directory of Open Access Journals (Sweden)
Jeff eOrchard
2013-12-01
Full Text Available Some neurons in the entorhinal cortex (EC fire bursts when the animal occupies locations organized in a hexagonal grid pattern in their spatial environment. Place cells have also been observed, firing bursts only when the animal occupies a particular region of the environment. Both of these types of cells exhibit theta-cycle modulation, firing bursts in the 4-12Hz range. Grid cells fire bursts of action potentials that precess with respect to the theta cycle, a phenomenon dubbed "theta precession". Various models have been proposed to explain these phenomena, and how they relate to navigation. Among the most promising are the oscillator interference models. The bank-of-oscillators model proposed by Welday et al. (2011 exhibits all these features. However, their simulations are based on theoretical oscillators, and not implemented entirely with spiking neurons. We extend their work in a number of ways. First, we place the oscillators in a frequency domain and reformulate the model in terms of Fourier theory. Second, this perspective suggests a division of labour for implementing spatial maps: position, versus map layout. The animal's position is encoded in the phases of the oscillators, while the spatial map shape is encoded implicitly in the weights of the connections between the oscillators and the read-out nodes. Third, it reveals that the oscillator phases all need to conform to a linear relationship across the frequency domain. Fourth, we implement a partial model of the EC using spiking leaky integrate-and-fire (LIF neurons. Fifth, we devise new coupling mechanisms, enlightened by the global phase constraint, and show they are capable of keeping spiking neural oscillators in consistent formation. Our model demonstrates place cells, grid cells, and phase precession. The Fourier model also gives direction for future investigations, such as integrating sensory feedback to combat drift, or explaining why grid cells exist at all.
Encyclopedia of color science and technology
2016-01-01
The Encyclopedia of Color Science and Technology provides an authoritative single source for understanding and applying the concepts of color to all fields of science and technology, including artistic and historical aspects of color. Many topics are discussed in this timely reference, including an introduction to the science of color, and entries on the physics, chemistry and perception of color. Color is described as it relates to optical phenomena of color and continues on through colorants and materials used to modulate color and also to human vision of color. The measurement of color is provided as is colorimetry, color spaces, color difference metrics, color appearance models, color order systems and cognitive color. Other topics discussed include industrial color, color imaging, capturing color, displaying color and printing color. Descriptions of color encodings, color management, processing color and applications relating to color synthesis for computer graphics are included in this work. The Encyclo...
Fourier and wavelet spectral analysis of EMG signals in supramaximal constant load dynamic exercise.
Camata, Thiago V; Dantas, Jose L; Abrao, Taufik; Brunetto, Maria A C; Moraes, Antonio C; Altimari, Leandro R
2010-01-01
Frequency domain analyses of changes in electromyographic (EMG) signals over time are frequently used to assess muscle fatigue. Fourier based approaches are typically used in these analyses, yet Fourier analysis assumes signal stationarity, which is unlikely during dynamic contractions. Wavelet based methods of signal analysis do not assume stationarity and may be more appropriate for joint time-frequency domain analysis. The purpose of this study was to compare Short-Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT) in assessing muscle fatigue in supramaximal constant load dynamic exercise (110% VO(2peak)). The results of this study indicate that CWT and STFT analyses give similar fatigue estimates (slope of median frequency) in supramaximal constant load dynamic exercise (P>0.05). However, the results of the variance was significantly lower for at least one of the muscles studied in CWT compared to STFT (P signal analysis using STFT. Thus, the stationarity assumption may not be the sole factor responsible for affecting the Fourier based estimates.
Fourier and wavelet spectral analysis of EMG signals in maximal constant load dynamic exercise.
Costa, Marcelo V; Pereira, Lucas A; Oliveira, Ricardo S; Pedro, Rafael E; Camata, Thiago V; Abrao, Taufik; Brunetto, Maria A C; Altimari, Leandro R
2010-01-01
Frequency domain analyses of changes in electromyographic (EMG) signals over time are frequently used to assess muscle fatigue. Fourier based approaches are typically used in these analyses, yet Fourier analysis assumes signal stationarity, which is unlikely during dynamic contractions. Wavelet based methods of signal analysis do not assume stationarity and may be more appropriate for joint time-frequency domain analysis. The purpose of this study was to compare Short-Time Fourier Transform (STFT) and Continuous Wavelet Transform (CWT) in assessing muscle fatigue in maximal constant load dynamic exercise (100% W(max)). The results of this study indicate that CWT and STFT analyses give similar fatigue estimates (slope of median frequency) in maximal constant load dynamic exercise (P>0.05). However, the results of the variance was significantly lower for at least one of the muscles studied in CWT compared to STFT (P〈0.05) indicating more variability in the EMG signal analysis using STFT. Thus, the stationarity assumption may not be the sole factor responsible for affecting the Fourier based estimates.
Nonuniform fast Fourier transform method for numerical diffraction simulation on tilted planes.
Xiao, Yu; Tang, Xiahui; Qin, Yingxiong; Peng, Hao; Wang, Wei; Zhong, Lijing
2016-10-01
The method, based on the rotation of the angular spectrum in the frequency domain, is generally used for the diffraction simulation between the tilted planes. Due to the rotation of the angular spectrum, the interval between the sampling points in the Fourier domain is not even. For the conventional fast Fourier transform (FFT)-based methods, a spectrum interpolation is needed to get the approximate sampling value on the equidistant sampling points. However, due to the numerical error caused by the spectrum interpolation, the calculation accuracy degrades very quickly as the rotation angle increases. Here, the diffraction propagation between the tilted planes is transformed into a problem about the discrete Fourier transform on the uneven sampling points, which can be evaluated effectively and precisely through the nonuniform fast Fourier transform method (NUFFT). The most important advantage of this method is that the conventional spectrum interpolation is avoided and the high calculation accuracy can be guaranteed for different rotation angles, even when the rotation angle is close to π/2. Also, its calculation efficiency is comparable with that of the conventional FFT-based methods. Numerical examples as well as a discussion about the calculation accuracy and the sampling method are presented.
Color fringe projection profilometry using geometric constraints
Cheng, Teng; Du, Qingyu; Jiang, Yaxi
2017-09-01
A recently proposed phase unwrapping method using geometric constraints performs well without requiring additional camera, more patterns or global search. The major limitation of this technique is the confined measurement depth range (MDR) within 2π in phase domain. To enlarge the MDR, this paper proposes using color fringes for three-dimensional (3D) shape measurement. Each six fringe periods encoded with six different colors are treated as one group. The local order within one group can be identified with reference to the color distribution. Then the phase wrapped period-by-period is converted into the phase wrapped group-by-group. The geometric constraints of the fringe projection system are used to determine the group order. Such that the MDR is extended from 2π to 12π by six times. Experiment results demonstrate the success of the proposed method to measure two isolated objects with large MDR.
Fourier theory and C∗-algebras
Bédos, Erik; Conti, Roberto
2016-07-01
We discuss a number of results concerning the Fourier series of elements in reduced twisted group C∗-algebras of discrete groups, and, more generally, in reduced crossed products associated to twisted actions of discrete groups on unital C∗-algebras. A major part of the article gives a review of our previous work on this topic, but some new results are also included.
Ultrafast Fourier-transform parallel processor
Energy Technology Data Exchange (ETDEWEB)
Greenberg, W.L.
1980-04-01
A new, flexible, parallel-processing architecture is developed for a high-speed, high-precision Fourier transform processor. The processor is intended for use in 2-D signal processing including spatial filtering, matched filtering and image reconstruction from projections.
Euler Polynomials, Fourier Series and Zeta Numbers
DEFF Research Database (Denmark)
Scheufens, Ernst E
2012-01-01
Fourier series for Euler polynomials is used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent series....
Fourier Series Formalization in ACL2(r
Directory of Open Access Journals (Sweden)
Cuong K. Chau
2015-09-01
Full Text Available We formalize some basic properties of Fourier series in the logic of ACL2(r, which is a variant of ACL2 that supports reasoning about the real and complex numbers by way of non-standard analysis. More specifically, we extend a framework for formally evaluating definite integrals of real-valued, continuous functions using the Second Fundamental Theorem of Calculus. Our extended framework is also applied to functions containing free arguments. Using this framework, we are able to prove the orthogonality relationships between trigonometric functions, which are the essential properties in Fourier series analysis. The sum rule for definite integrals of indexed sums is also formalized by applying the extended framework along with the First Fundamental Theorem of Calculus and the sum rule for differentiation. The Fourier coefficient formulas of periodic functions are then formalized from the orthogonality relations and the sum rule for integration. Consequently, the uniqueness of Fourier sums is a straightforward corollary. We also present our formalization of the sum rule for definite integrals of infinite series in ACL2(r. Part of this task is to prove the Dini Uniform Convergence Theorem and the continuity of a limit function under certain conditions. A key technique in our proofs of these theorems is to apply the overspill principle from non-standard analysis.
Fourier inversion on a reductive symmetric space
Ban, E.P. van den
2001-01-01
Let X be a semisimple symmetric space. In previous papers, [8] and [9], we have dened an explicit Fourier transform for X and shown that this transform is injective on the space C 1 c (X) ofcompactly supported smooth functions on X. In the present paper, which is a continuation of these papers, we e
Vector valued Fourier multipliers and applications
Directory of Open Access Journals (Sweden)
Davide Guidetti
2010-12-01
Full Text Available In questo seminario sono illustrati alcuni recenti sviluppi della teoria dei moltiplicatori di Fourier negli spazi L^p a valori in spazi di Banach. Seguono alcune applicazioni a problemi al contorno di tipo ellittico e a problemi misti di tipo parabolico.
Vector valued Fourier multipliers and applications
Davide Guidetti
2010-01-01
In questo seminario sono illustrati alcuni recenti sviluppi della teoria dei moltiplicatori di Fourier negli spazi L^p a valori in spazi di Banach. Seguono alcune applicazioni a problemi al contorno di tipo ellittico e a problemi misti di tipo parabolico.
On the Scaled Fractional Fourier Transformation Operator
Institute of Scientific and Technical Information of China (English)
FAN Hong-Yi; HU Li-Yun
2008-01-01
Based on our previous study [Chin.Phys.Lett.24(2007)2238]in which the Fresnel operator corresponding to classical Fresnel transform was introduced,we derive the fractional Fourier transformation operator,and the optical operator method is then enriched.
Fourier transforms on an amalgam type space
Liflyand, E
2012-01-01
We introduce an amalgam type space, a subspace of $L^1(\\mathbb R_+).$ Integrability results for the Fourier transform of a function with the derivative from such an amalgam space are proved. As an application we obtain estimates for the integrability of trigonometric series.
Fourier Analysis with Respect to Bilinear Maps
Institute of Scientific and Technical Information of China (English)
O.BLASCO; J.M.CALABUIG
2009-01-01
Several results about convolution and about Fourier coefficients for X-valued functions defined on the torus satisfying the condition sup‖y‖=1∫π-π‖B(f(eiθ),y)‖dθ/2π＜∞ for a bounded bilinear map B:X ×Y →Z are presented and some applications are given.
Harmonic oscillator: an analysis via Fourier series
de Castro, A S
2013-01-01
The Fourier series method is used to solve the homogeneous equation governing the motion of the harmonic oscillator. It is shown that the general solution to the problem can be found in a surprisingly simple way for the case of the simple harmonic oscillator. It is also shown that the damped harmonic oscillator is susceptible to the analysis.
Euler Polynomials, Fourier Series and Zeta Numbers
DEFF Research Database (Denmark)
Scheufens, Ernst E
2012-01-01
Fourier series for Euler polynomials is used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent series....
Bernoulli Polynomials, Fourier Series and Zeta Numbers
DEFF Research Database (Denmark)
Scheufens, Ernst E
2013-01-01
Fourier series for Bernoulli polynomials are used to obtain information about values of the Riemann zeta function for integer arguments greater than one. If the argument is even we recover the well-known exact values, if the argument is odd we find integral representations and rapidly convergent ...
Clifford Fourier transform on vector fields.
Ebling, Julia; Scheuermann, Gerik
2005-01-01
Image processing and computer vision have robust methods for feature extraction and the computation of derivatives of scalar fields. Furthermore, interpolation and the effects of applying a filter can be analyzed in detail and can be advantages when applying these methods to vector fields to obtain a solid theoretical basis for feature extraction. We recently introduced the Clifford convolution, which is an extension of the classical convolution on scalar fields and provides a unified notation for the convolution of scalar and vector fields. It has attractive geometric properties that allow pattern matching on vector fields. In image processing, the convolution and the Fourier transform operators are closely related by the convolution theorem and, in this paper, we extend the Fourier transform to include general elements of Clifford Algebra, called multivectors, including scalars and vectors. The resulting convolution and derivative theorems are extensions of those for convolution and the Fourier transform on scalar fields. The Clifford Fourier transform allows a frequency analysis of vector fields and the behavior of vector-valued filters. In frequency space, vectors are transformed into general multivectors of the Clifford Algebra. Many basic vector-valued patterns, such as source, sink, saddle points, and potential vortices, can be described by a few multivectors in frequency space.
Fourier transform infrared spectrometery: an undergraduate experiment
Lerner, L.
2016-11-01
Simple apparatus is developed, providing undergraduate students with a solid understanding of Fourier transform (FT) infrared (IR) spectroscopy in a hands on experiment. Apart from its application to measuring the mid-IR spectra of organic molecules, the experiment introduces several techniques with wide applicability in physics, including interferometry, the FT, digital data analysis, and control theory.
A Fourier analysis of extremal events
DEFF Research Database (Denmark)
Zhao, Yuwei
is the extremal periodogram. The extremal periodogram shares numerous asymptotic properties with the periodogram of a linear process in classical time series analysis: the asymptotic distribution of the periodogram ordinates at the Fourier frequencies have a similar form and smoothed versions of the periodogram...
A data-dependent Fourier filter based on image segmentation for random seismic noise attenuation
Zhou, JiaXiong; Lu, Wenkai; He, Jianwei; Liu, Bing; Ren, Tin
2015-03-01
In this paper, we propose a data-dependent Fourier filter (DDFF) based on image segmentation for random seismic noise attenuation. In the proposed method, the original seismic data is divided into some overlapped small blocks. For each block, a local Fourier filter is designed automatically in two steps. At first, a binary mask is obtained by segmenting the Fourier amplitude spectra (FAS) of this block. The histogram of the FAS is used to get the threshold for the FAS segmentation. Secondly, an average filter is applied on the binary mask to get the tapered Fourier filter. In the proposed method, the DDFFs for all blocks are compact and time-space variant. After all blocks are processed, they are merged together to form the filtered result. We illustrate our method by a 2D synthetic seismic data, and give a comparison with the coherent event extraction method in Fourier domain. At last, a real 3D seismic data example demonstrates that the proposed method obtains some promising results.
Wijk, Arjan van
2005-01-01
Synthesis of 13C-enriched carotenoids. Carotenoids are natural colorants, ranging in color from pale yellow to deep purple, with important biological functions. Carotenoids in the human diet have a beneficial health effect, playing a role in the prevention of cardiovascular disease and cancer. To ge
Dvořák, Zdeněk; Norin, Sergey; Postle, Luke
2016-01-01
Let G be a graph with a list assignment L. Suppose a preferred color is given for some of the vertices; how many of these preferences can be respected when L-coloring G? We explore several natural questions arising in this context, and propose directions for further research.
Hoang, M.A.; Geusebroek, J.M.; Deprettere, E.F.; Belloum, A.; Heijnsdijk, J.W.J.; van der Stappen, F.
2002-01-01
In computer vision, measurement of image properties such as color or texture is essential. However, existing methods for measuring color and texture in combination are not well-defined neither from a measurement theoretical basis nor from a physical point of view. We propose a solid framework for th
Lee, Byoungho; Yun, Hansik; Lee, Seung-Yeol; Kim, Hwi
2016-03-01
In general, color filter is an optical component to permit the transmission of a specific color in cameras, displays, and microscopes. Each filter has its own unchangeable color because it is made by chemical materials such as dyes and pigments. Therefore, in order to express various colorful images in a display, one pixel should have three sub-pixels of red, green, and blue colors. Here, we suggest new plasmonic structure and method to change the color in a single pixel. It is comprised of a cavity and a metal nanoaperture. The optical cavity generally supports standing waves inside it, and various standing waves having different wavelength can be confined together in one cavity. On the other hand, although light cannot transmit sub-wavelength sized aperture, surface plasmons can propagate through the metal nanoaperture with high intensity due to the extraordinary transmission. If we combine the two structures, we can organize the spatial distribution of amplitudes according to wavelength of various standing waves using the cavity, and we can extract a light with specific wavelength and amplitude using the nanoaperture. Therefore, this cavity-aperture structure can simultaneously tune the color and intensity of the transmitted light through the single nanoaperture. We expect that the cavity-apertures have a potential for dynamic color pixels, micro-imaging system, and multiplexed sensors.
Wijk, Arjan van
2005-01-01
Synthesis of 13C-enriched carotenoids. Carotenoids are natural colorants, ranging in color from pale yellow to deep purple, with important biological functions. Carotenoids in the human diet have a beneficial health effect, playing a role in the prevention of cardiovascular disease and cancer. To ge
DuBois, Ann
2010-01-01
The blending of information from an academic class with projects from art class can do nothing but strengthen the learning power of the student. Creating three-dimensional color wheels provides the perfect opportunity to combine basic geometry knowledge with color theory. In this article, the author describes how her seventh-grade painting…
S.M. Heditniemi (Sandra); R.C. Laskar (R.C.); H.M. Mulder (Martyn)
2012-01-01
textabstractLet $G = (V,E)$ be a graph. A partition $\\pi = \\{V_1, V_2, \\ldots, V_k \\}$ of the vertices $V$ of $G$ into $k$ {\\it color classes} $V_i$, with $1 \\leq i \\leq k$, is called a {\\it quorum coloring} if for every vertex $v \\in V$, at least half of the vertices in the closed neighborhood
DEFF Research Database (Denmark)
Bombin Palomo, Hector
2015-01-01
Color codes are topological stabilizer codes with unusual transversality properties. Here I show that their group of transversal gates is optimal and only depends on the spatial dimension, not the local geometry. I also introduce a generalized, subsystem version of color codes. In 3D they allow...