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Tensor decomposition-based sparsity divergenceindex for hyperspectral anomaly detection

Lili Zhang and Chunhui Zhao

Doc ID: 290777 Received 15 Mar 2017; Accepted 23 Jul 2017; Posted 24 Jul 2017  View: PDF

Abstract: Recently, some methods exploiting both the spatial and spectral features have drawn increasing attention inhyperspectral anomaly detection (AD) and they perform well. In addition, a tensor decomposition-based (TenB)algorithm treating the hyperspecral dataset as a three-order tensor (two modes for space and one mode forspectra) has been proposed to further improve the performance for AD. In this paper, a method using sparsitydivergence index (SDI) based on tensor decomposition (SDI-TD) is proposed. First, three modes of thehyperspectral dataset are obtained by tensor decomposition. Then, low-rank and sparse matrix decomposition(LRASMD) is employed separately along the three modes and three sparse matrixes are acquired. Finally, SDIsbased on the three sparse matrixes along the three modes are obtained, and the final result is generated by usingthe joint SDI. Experiments tested on the real and synthetic hyperspectral dataset reveal that the proposed SDI-TDperforms better than the comparison algorithms.

A new data-driven linearizing approach in inverse scattering

Edwin Marengo, Raffaele Solimene, and Edson Galagarza

Doc ID: 290362 Received 09 Mar 2017; Accepted 22 Jul 2017; Posted 24 Jul 2017  View: PDF

Abstract: Direct or forward wave scattering admits three classical regimes in which the map from scatterer properties or scattering potential to the data is linear, namely, the Born, Rytov, and physical optics approximations. In this paper we derive a new decomposition of the forward scattering map which reveals a previously unknown approximate bilinear forward scattering relation. The latter is data-driven, i.e., it involves exact scattering data, and has the useful property that the dependence on the data and the potential is bilinear. This fundamental result naturally leads to a new linear inverse scattering approach that generalizes and is more broadly applicable than the classical Born-approximation-based imaging. The developed scattering and inverse scattering theory is presented in both plane wave and multipole expansion representations, and the possibility of exploiting support information is also formally addressed in the multipole domain. The paper includes computer simulations illustrating the derived theory and algorithms.

Propagation of uncertainties and applications innumerical modeling: tutorial

Dominique Barchiesi and Thomas Grosges

Doc ID: 280863 Received 15 Nov 2016; Accepted 21 Jul 2017; Posted 24 Jul 2017  View: PDF

Abstract: Some inputs of computational models are commonly retrievedfrom external sources (handbooks, articles, dedicatedmeasurements) and therefore are subject to uncertainties.The known experimental dispersion of theinputs can be propagated through the numerical modelsto produce samples of outputs. The stemming propagationof uncertainties is already significant in metrologybut has also applications in optimization and inverseproblems resolution of the modeled physical system.Moreover, the information on uncertainties canbe used to characterize and compare models, and to deducebehavior laws. This tutorial gives tools and applicationsof the propagation of experimental uncertaintiesthrough models. To illustrate the method and itsapplications, we propose to investigate the scatteringof light by gold nanoparticles that also enables the comparisonof the full Mie theory and of the dipole approximation.The position of the localized surface plasmonresonance and the corresponding value of the scatteringefficiency are more specifically studied.

Multi-focus autofocusing Airy beam

Tong li, Fei Zi, Kaikai Huag, and Xuanhui Lu

Doc ID: 295002 Received 02 May 2017; Accepted 21 Jul 2017; Posted 21 Jul 2017  View: PDF

Abstract: We propose a kind of multi-focus autofocusing Airy beam (MAAB) by modifying the frequency spectrum of symmetric Airy beam (SAB) with Gaussian band elimination filter. Unlike the original SAB, there are four off-axis foci at the autofocusing plane of the MAAB. The MAAB has better abruptly autofocusing property than original SAB. In addition, with the increase of the normalized intensity at the first peak, the focal position (second peak) of the MAAB almost remains the same, while the position of the first peak shifts along the propagation direction gradually. The characteristics of MAAB indicate potential applications in various fields.

Parabasal Formulas and their Applications

Sunggoo Cho

Doc ID: 294615 Received 02 May 2017; Accepted 20 Jul 2017; Posted 20 Jul 2017  View: PDF

Abstract: Parabasal theory is a technique in geometrical optics that describes the behaviour of light rayslocated near some defined base ray rather than the optical axis. In this work, we are concerned with parabasal rays which lie in a sufficiently small neighborhood of a chief ray and develop some formulas for parabasal quantities of the chief ray.Parabasal quantities of a chief ray are shown to be intimately related to the coefficients of first order differential equations of the chief ray. Using the relations, we derive parabasal formulas containing parabasal refractive indices and parabasal powers etc.from the first order differential equations. These parabasal formulas turn out to bedecoupled differential equations of the first order differential equations so that highly coupled differential equations for a chief ray can be solved systematically. In addition, we apply parabasal formulas to paraxial region by taking the limits of the formulas. These limits give necessary conditions expressed in terms of Gaussian brackets for various initial design requirements of optical lens systems. Those necessary conditions do not seem to be derivable by using only paraxial theory without parabasal approaches developed in this work.

Single freeform surface design for prescribed input wavefront and target irradiance

Christoph Bösel and Herbert Gross

Doc ID: 296186 Received 17 May 2017; Accepted 20 Jul 2017; Posted 20 Jul 2017  View: PDF

Abstract: In beam shaping applications, the minimization of the number of necessary optical elements for the beam shaping process can benefit the compactness of the optical system and reduce its cost. The single freeform surface design for input wavefronts, which are neither planar nor spherical, is therefore of interest.In this work, the design of single freeform surfaces for a given zero-étendue source and complex target irradiances is investigated. Hence, not only collimated input beams or point sources are assumed. Instead, a predefined input ray direction vector field and irradiance distribution on a source plane, which has to be redistributed by a single freeform surface to give the predefined target irradiance, is considered. To solve this design problem, a partial differential equation (PDE) or PDE system, respectively, for the unknown surface and its corresponding ray mapping is derived from energy conservation and the ray-tracing equations.In contrast to former PDE formulations of the single freeform design problem, the derived PDE of Monge-Ampère type is formulated for general zero-étendue sources in cartesian coordinates. The PDE system is discretized with finite differences and the resulting nonlinear equation system solved by a root-finding algorithm. The basis of the efficient solution of the PDE system builds the introduction of an initial iterate constuction approach for a given input direction vector field, which uses optimal mass transport with a quadratic cost function. After a detailed description of the numerical algorithm, the efficiency of the design method is demonstrated by applying it to several design examples. This includes the redistribution of a collimated input beam beyond the paraxial approximation, the shaping of point source radiation and the shaping of an astigmatic input wavefront into a complex target irradiance distribution.

Condition for far-zone spectral isotropy of light radiated from a quasi-homogeneous source scattering on a quasi-homogeneous random medium

Xinyu Peng, Dong Ye, Muchun Zhou, Yu Xin, and MinMin Song

Doc ID: 297292 Received 12 Jun 2017; Accepted 20 Jul 2017; Posted 20 Jul 2017  View: PDF

Abstract: The far-zone spectral isotropy of light radiated from a secondary planar quasi-homogeneous (QH) source scattering on a QH medium has been discussed. Without assuming specified function of incident light, a sufficient condition for the far-zone spectral isotropy has been expressed as a new scaling law, which is analogous with the scaling law for weak scattering in previous works. Special examples are discussed to validate the obtained scaling law.

Basic properties and classification of Mueller matrices derived from their statistical definition

Razvigor Ossikovski and Jose Gil

Doc ID: 297666 Received 07 Jun 2017; Accepted 20 Jul 2017; Posted 20 Jul 2017  View: PDF

Abstract: Starting from the statistical definition of the Mueller matrix we derive the relations existing between its basic properties such as the number of contact points of its characteristic ellipsoid with the Poincaré sphere and the rank of its covariance matrix. This approach allows for the comprehensive classification of any experimental depolarizing Mueller matrix into one out of six possible classes thus making possible its phenomenological interpretation in terms of a specific fluctuating Jones generator or of a finite sum of nondepolarizing Mueller matrices.

Nonlinear Spline Wavefront Reconstruction fromShack-Hartmann Intensity Measurements through Small Aberration Approximations

Elisabeth Brunner, Cornelis De Visser, and Michel Verhaegen

Doc ID: 295597 Received 09 May 2017; Accepted 19 Jul 2017; Posted 20 Jul 2017  View: PDF

Abstract: We propose an extension of the Spline ABerration Reconstruction (SABRE) method to Shack-Hartmann (SH) intensity measurements, through small aberration approximations of the focal spot models. The original SABRE for SH slope measurements is restricted to the use of linear spline polynomials, due to the limited amount of data, and the resolution of its reconstruction is determined by the number of lenslets. In this work, a fast algorithm is presented that directly processes the pixel information of the focal spots allowing the employment of nonlinear polynomials for high accuracy reconstruction. In order to guarantee the validity of the small aberration approximations, the method is applied in two correction steps, with a first compensation of large, low order aberrations through the gradient based linear SABRE followed by compensation of the remaining high order aberrations with the intensity based nonlinear SABRE.

On the van Cittert - Zernike theorem for intensity correlations and its applications

Timur Gureyev, Alexander Kozlov, David Paganin, Yakov Nesterets, Frank de Hoog, and Harry Quiney

Doc ID: 297789 Received 09 Jun 2017; Accepted 19 Jul 2017; Posted 24 Jul 2017  View: PDF

Abstract: A reciprocal relationship between the autocovariance of the light intensity in the source plane and in the far-field detector plane is presented in a form analogous to the classical van Cittert - Zernike theorem, but involving intensity correlation functions. A "classical" version of the reciprocity relationship is considered first, based on the assumption of circular Gaussian statistics of the complex amplitudes in the source plane. The result is consistent with the theory of Hanbury Brown - Twiss interferometry, but it is shown to be also applicable to estimation of the source size or the spatial resolution of the detector from the noise power spectrum of flat-field images. An alternative version of the van Cittert - Zernike theorem for intensity correlations is then derived for a quantized electromagnetic beam in a coherent state, which leads to Poisson statistics for the intrinsic intensity of the beam.

A Fixed-Pattern Noise Correction Method Based on Improved Moment matching for TDI CMOS Image Sensor

Jiangtao Xu, Huafeng Nie, Kaiming Nie, and Weimin Jin

Doc ID: 281162 Received 18 Nov 2016; Accepted 16 Jul 2017; Posted 17 Jul 2017  View: PDF

Abstract: In this paper, an improved moment matching method based on spatial correlation filter (SCF) and bilateral filter (BF) is proposed to correct the fixed-pattern noise (FPN) of time-delay-integration CMOSimage sensor (TDI-CIS). Firstly, the values of row FPN (RFPN) and column FPN (CFPN) are estimatedand added to the original imagethro-ugh SCF and BF, respectively. Then the filtered image will be processed by an improved moment matching method with a moving window. Experimental results basedon a 128-stage TDI-CIS show that, after correcting the FPN in th-e image captured under uniform illumination, the standard-deviation of row-mean vector (SDRMV) decreases from 5.6761 LSB to 0.1948 LSB,while the standard-deviation of column-mean vector (SDCMV) decreases from 15.2005 LSB to 13.1949LSB. In addition, for different images captured by different TDI-CISs, the average decrease of SDRMVand SDCMV is 5.4922/2.0357 LSB respectively. Comparative experimental results indicate that the pro-posed met-hod can correct the FPNs of different TDI-CISs effectively while maintaining image detailswithout any auxiliary equipment.

A simple approach to the generalized Minkwitz theorem

Ralf Blendowske

Doc ID: 288052 Received 14 Mar 2017; Accepted 16 Jul 2017; Posted 18 Jul 2017  View: PDF

Abstract: The Minkwitz theorem plays an important role in the design of progressive addition lenses. Recently, this theorem has been generalized by Esser et al. to non-umbilic lines under the assumption of a symmetric surface. We present a simplified derivation and generalize their findings to arbitrary but sufficient smooth surfaces.

Automatic identification of fungi in microscopicleucorrhea images

Jing Zhang, Songhan Lu, Xiangzhou Wang, Xiaohui Du, NI ming, Juanxiu Liu, Lin Liu, and Yong Liu

Doc ID: 293423 Received 28 Apr 2017; Accepted 14 Jul 2017; Posted 17 Jul 2017  View: PDF

Abstract: Identifying fungi in microscopic leucorrhea images provides important information for evaluating gynecologicaldiseases. Subjective judgment and fatigue can greatly affect the recognition accuracy. This paper proposes anautomatic identification system to detect fungi in leucorrhea images that incorporates a convolutional neuralnetwork, the histogram of oriented gradients algorithm, and a binary support vector machine. In experiments, thedetection rate of the positive samples was as high as 99.8%. The experimental results demonstrate theeffectiveness of the proposed method and its potential as a primary software component of a completelyautomated system.

Bandwidth Correction in the Spectral Measurement ofLight Emitting Diodes

Shiqun Jin, Chan Huang, Guo Xia, Mingyong Hu, and Zhijian Liu

Doc ID: 296145 Received 17 May 2017; Accepted 14 Jul 2017; Posted 17 Jul 2017  View: PDF

Abstract: Light emitting diodes (LEDs) is widely employed in industrial applications and scientific researches. However,spectral distortions will occur due to the broadening effects of the spectrometer when LED spectrum is obtainedwith a spectrometer. In this paper, a novel approach is put forward to correct bandwidth for LED spectrum basedon Levenberg-Marquardt algorithm and He-Zheng model. We compare estimation errors of different LED spectraby using the proposed method and also the Richardson-Lucy method and differential operator approach. Theexperimental results show that the effect of the proposed approach is better than that of other two methods.

Improving Color Constancy by Discounting the Variation of Camera Spectral Sensitivity

Shao-Bing Gao, Ming Zhang, Chao-Yi Li, and Yong-Jie Li

Doc ID: 297212 Received 08 Jun 2017; Accepted 11 Jul 2017; Posted 11 Jul 2017  View: PDF

Abstract: It is an ill-posed problem to recover the true scene colors from a color biased image by discounting the effects of scene illuminant and camera spectral sensitivity (CSS) at the same time. Most color constancy (CC) models have been designed to first estimate the illuminant color, which is then removed from the color biased image to obtain an image taken under white light, without the explicit consideration of CSS effect on CC. This paper first studies the CSS effect on illuminant estimation arising in the inter-dataset-based CC (inter-CC), i.e., training a CC model on one dataset and then testing on another dataset captured by a distinct CSS. We show the clear degradation of existing CC models for inter-CC application. Then a simple way is proposed to overcome such degradation by first learning quickly a transform matrix between the two distinct CSSs (CSS-1 and CSS-2). The learned matrix is then used to convert the data (including the illuminant ground truth and the color biased images) rendered under CSS-1 into CSS-2, and then train and apply the CC model on the color biased images under CSS-2, without the need of burdensome acquiring of training set under CSS-2. Extensive experiments on synthetic and real images show that our method can clearly improve the inter-CC performance for traditional CC algorithms. We suggest that by taking the CSS effect into account, it is more likely to obtain the truly color constant images invariant to the changes of both illuminant and camera sensors.

Far-zone behaviors of light waves on scattering fromanisotropic quasi-homogeneous media with semisoftboundary

Zhenfei Jiang, Li Zhu, Xiaoling Ji, Ke Cheng, and Tao Wang

Doc ID: 297849 Received 13 Jun 2017; Accepted 11 Jul 2017; Posted 12 Jul 2017  View: PDF

Abstract: A model of anisotropic quasi-homogeneous media with adjustable boundary has been presented with the help ofthree-dimensional multi-Gaussian function. After that, the behaviors of far-zone field of light waves on scatteringfrom an anisotropic semisoft-boundary quasi-homogeneous medium are illustrated. It is shown that the spectraldensity of the scattered field is flatten-Gaussian-centered owing to the semisoft boundary of the scatterer, while thespectral degree of coherence is Gaussian-centered which is independent of the boundary of scatterer. It is alsoshown that both the spectral density and the spectral degree of coherence are anisotropic because of theanisotropy of the scattering medium.

Modeling open nanophotonic systems using the Fourier modal method: Generalization to 3D Cartesian coordinates

Teppo Häyrynen, Andreas Osterkryger, Jakob Rosenkrantz de Lasson, and Niels Gregersen

Doc ID: 295258 Received 05 May 2017; Accepted 11 Jul 2017; Posted 21 Jul 2017  View: PDF

Abstract: Recently, an open geometry Fourier modal method based on a new combination of an open boundary condition and a non-uniform $k$-space discretization was introduced for rotationally symmetric structures providing a more efficient approach for modeling nanowires and micropillar cavities [J. Opt. Soc. Am. A 33, 1298 (2016)]. Here, we generalize the approach to three-dimensional (3D) Cartesian coordinates allowing for the modeling of rectangular geometries in open space.The open boundary condition is a consequence of having an infinite computational domain described using basis functions that expand the whole space. The strength of the method lies in discretizing the Fourier integrals using a non-uniform circular "dartboard" sampling of the Fourier $k$ space. We show that our sampling technique leads to a more accurate description of the continuum of the radiation modes that leak out from the structure. We also compare our approach to conventional discretization with direct and inverse factorization rules commonly used in established Fourier modal methods. We apply our method to a variety of optical waveguide structures and demonstrate that the method leads to a significantly improved convergence enabling more accurate and efficient modeling of open 3D nanophotonic structures.

Perceptually Optimized Image Rendering

Valero Laparra, Alex Berardino, Johannes Ballé, and Eero Simoncelli

Doc ID: 285927 Received 02 Feb 2017; Accepted 08 Jul 2017; Posted 10 Jul 2017  View: PDF

Abstract: We develop a framework for rendering photographic images by directly optimizing their perceptual similarity to the original scene. Specifically, over the set of all images that can be rendered on a given display,we minimize the Normalized Laplacian Pyramid Distance (NLPD), a measure of perceptual dissimilarity that is derived from a simple model of the early stages of the human visual system. When rendering images acquired with higher dynamic range than that of the display, we find that the optimization boosts the contrast of low-contrast features without introducing significant artifacts, yielding results of comparable visual quality to current state-of-the art methods, but without manual intervention or parameter settings. We also demonstrate the effectiveness of the framework for a variety of other display constraints, including limitations on minimum luminance (black point), mean luminance (as a proxy for energy consumption), and quantized luminance levels (halftoning). We show that the method may generally be used to enhance details and contrast, and in particular can be use on images degraded by optical scattering (e.g., fog). Finally, we demonstrate the necessity of each of the NLPD components – an initial power function, a multi-scale transform, and local contrast gain control – in achieving these results and we show that NLPD is competitive with the current state-of-the-art image quality metrics.

Self-focusing of a partially coherent beam with circular coherence

Chaoliang Ding, Liuzhan Pan, Jari Turunen, and Matias Koivurova

Doc ID: 295796 Received 11 May 2017; Accepted 07 Jul 2017; Posted 07 Jul 2017  View: PDF

Abstract: In a recent publication [Santarsiero et al., Opt. Lett. 42, 1512 (2017)], a novel class of partially coherentsources with circular coherence was introduced. In this paper we examine the propagation behaviorof the spectral density and the spectral degree of spatial coherence of a beam generated by such asource in free space and in oceanic turbulent media. It is found that the beam exhibits self-focusing,which is dependent on the initial coherence and the parameters of oceanic turbulence. The self-focusingphenomenon disappears when the initial coherence is high enough or the oceanic turbulence is strong.The area of high coherence appears in the center and along two diagonal lines. With increasing turbulence,the coherence area reduces gradually along one diagonal line, and is retained along the other one. Aphysical interpretation of the self-focusing phenomenon is presented and potential applications in opticalunderwater communication and beam shaping are considered.

Quasimonochromatic modes of quasistationary, pulsed scalar optical fields

Lutful Ahad, Ismo Vartiainen, Tero Setala, Ari Tapio Friberg, and Jari Turunen

Doc ID: 294887 Received 28 Apr 2017; Accepted 06 Jul 2017; Posted 06 Jul 2017  View: PDF

Abstract: We investigate the temporal coherence of random, pulsed, quasistationary scalar light fields and introduce a new type of expansion for the mutual coherence function in terms of fully coherent frequency-shifted quasimonochromatic modes of identical shape. The mode representation is valid provided the pulse length is shorter and the coherence time is much shorter than the width of the time window in which the field is considered. The construction of the expansion is particularly straightforward since information is required only on the average spectrum and the average temporal intensity. The method enables to assess the coherence properties of quasistationary light by analyzing the behavior of deterministic quasimonochromatic fields. The frequency-domain counterpart of the representation is also given. The method is illustrated by application to a pulsed free-electron laser source.

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