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Accepted papers to appear in an upcoming issue

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Invariant quantities of a nondepolarizing Mueller matrix

Jose Gil and Ignacio San José

Doc ID: 263134 Received 13 Apr 2016; Accepted 23 May 2016; Posted 24 May 2016  View: PDF

Abstract: Orthogonal Mueller matrices can be considered either as corresponding to retarders or to generalized transformations of the polarization basis for the representation of Stokes vectors, so that they constitute the only type of Mueller matrices that preserve the degree of polarization and the intensity of any partially-polarized input Stokes vector. The physical quantities which remain invariant when a nondepolarizing Mueller matrix is transformed through its product by different types of orthogonal Mueller matrices are identified and interpreted, providing a better knowledge of the information contained in a nondepolarizing Mueller matrix.

Retinal Image Registration via Feature Guided Gaussian Mixture Model

Jiayi Ma, Chengyin Liu, Ma Yong, and Jun Huang

Doc ID: 263566 Received 19 Apr 2016; Accepted 22 May 2016; Posted 24 May 2016  View: PDF

Abstract: Registration of retinal images taken at different times, from different perspectives or with different modalities is a critical prerequisite for the diagnoses and treatments of various eye diseases. This problem can be formulated as registration of two sets of sparse feature points extracted from the given images, and it is typically solved by first creating a set of putative correspondences and then removing the false matches as well as estimating the spatial transformation between the image pairs, or solved by estimating the correspondence and transformation jointly involving an iteration process. However, the former strategy suffers from missing true correspondences and the latter strategy does not make full use of local appearance information, which may be problematic for low-quality retinal images due to lack of reliable features. In this paper, we propose a novel feature guided Gaussian mixture model (GMM) to address these issues. We formulate point registration as the estimation of a feature guided mixture of densities: a GMM is fitted to one point set, such that both the centers and local features of the Gaussian densities are constrained to coincide with the other point set. The problem is solved under a unified maximum-likelihood framework together with an iterative EM algorithm initialized by the confident feature correspondences, where the image transformation is modeled by an affine function. Extensive experiments on various retinal images show the robustness of our approach, which consistently outperforms other state-of-the-art methods, especially when the data is badly degraded.

Holographic imaging through a scattering medium by diffuser-aided statistical averaging

Manish Kumar, Michael Purcell, Stephen Rand, and Vasudevan Lakshminarayanan

Doc ID: 261278 Received 16 Mar 2016; Accepted 18 May 2016; Posted 19 May 2016  View: PDF

Abstract: We introduce a practical digital holographic method capable of imaging through a diffusive or scattering medium. The method relies on statistical averaging from a rotating ground glass diffuser to negate the adverse effects caused by speckle introduced by a first, static diffuser or scattering medium. In particular, a setup based on Fourier transform holography is used to show that an image can be recovered after scattering by introducing an additional diffuser in the optical setup. This method is capable of recovering object information from behind a scattering layer in biomedical or military imaging applications.

Enhancement of Rayleigh scattering in atwo-dimensional Fabry-Perot resonator loaded withimpurities

Almas Sadreev

Doc ID: 259273 Received 11 Feb 2016; Accepted 17 May 2016; Posted 19 May 2016  View: PDF

Abstract: We study wave transmission through a Fabry-Perot resonator (FPR) loaded with point-like impurities. Weshow both analytically in the framework of the coupled mode theory and numerically that there are twodifferent regimes for transmission as dependent on the quality of the FPR mirrors. For low quality weobtain the transmittance very similar to the clean FPR with slightly shifted Lorentz peaks. However for agood quality the transmittance peaks are strongly reduced and substituted with Gaussian peaks becauseof multiple scattering of waves by each impurity. As a side effect we observe the angular (channel) conversionin the disordered FPR. We demonstrate that the resonant peaks are dependent on the concentrationof impurities to pave a way for resonant measurement of the concentration.

Multi-fluorophore localization as a percolation problem:Limits to density and precision

Alexander Small

Doc ID: 260293 Received 02 Mar 2016; Accepted 13 May 2016; Posted 17 May 2016  View: PDF

Abstract: We show that the maximum desirable density of activated fluorophores in a superresolution experimentcan be determined by treating the overlapping point spread functions (PSFs) as a problem in percolationtheory. We derive a bound on the density of activated fluorophores, taking into account the desiredlocalization accuracy and precision, as well as the number of photons emitted. Our bound on densityis close to that reported in experimental work, suggesting that further increases in the density of imagedfluorophores will come at the expense of localization accuracy and precision.

Properties of laser speckle images produced from narrow elliptical illumination regions

Hisashi Togashi

Doc ID: 260358 Received 02 Mar 2016; Accepted 11 May 2016; Posted 17 May 2016  View: PDF

Abstract: The properties of laser speckles formed by laser light scattered from narrow elliptical illumination regions on a rough surface are investigated. Analytical expressions are derived for the correlation between one-dimensional pixel data arrays in single speckle images and between averaged pixel data arrays of speckle images from different illumination regions. In deriving the formulae, the phase shift of the scattered light is expressed by a function that approximates the roughness of the illuminated surface. Experimental results are interpreted by the formulae and the parameters of the formulae are evaluated.

Mie scattering of highly focused, scalar fields: an analytic approach

Nicole Moore and Miguel Alonso

Doc ID: 259708 Received 22 Feb 2016; Accepted 09 May 2016; Posted 09 May 2016  View: PDF

Abstract: We present a method for modeling the scattering of a focused scalar field incident on a spherical particle. This approach involves the expansion of the incident field in an orthonormal basis of closed-form solutions of the Helmholtz equation which are nonparaxial counterparts of Laguerre-Gaussian beams. This method also allows for the analytic calculation of the forces and torques exerted on a particle at any position with respect to the beam's focus.

Optimal Channels for Channelized Quadratic Estimators

MEREDITH KUPINSKI and Eric Clarkson

Doc ID: 254964 Received 05 Jan 2016; Accepted 07 May 2016; Posted 09 May 2016  View: PDF

Abstract: We present a new method for computing optimized channels for estimation tasks that is feasible for highdimensionalimage data. Maximum-likelihood (ML) parameter estimates are challenging to computefrom high-dimensional likelihoods. The dimensionality reduction from M measurements to L channelsis a critical advantage of channelized quadratic estimators (CQE) since estimating likelihood momentsfrom channelized data requires smaller sample sizes and inverting a smaller covariance matrix is easier.The channelized likelihood is then used to form ML estimates of the parameter(s). In this work we choosean imaging example where the second-order statistics of the image data depend upon the parameter ofinterest: the correlation length. Correlation lengths are used to approximate background textures in manyimaging applications and in these cases an estimate of the correlation length is useful for pre-whitening.In a simulation study we compare the estimation performance, as measured by the root mean-squarederror (RMSE), of correlation length estimates from CQE and power spectral density (PSD) distributionfitting. To abide by the assumptions of the PSD method we simulate an ergodic, isotropic, stationary, andzero-mean random process. These assumptions are not part of the CQE formalism. The CQE methodassumes a Gaussian channelized likelihood which can be a valid for non-Gaussian image data since thechannel outputs are formed from weighted sums of the image elements. We have shown that for 3 or morechannels the RMSE of CQE estimates of correlation length is lower than conventional PSD estimates.We also show that computing CQE using a standard non-linear optimization method produces channelswhich yield RMSE within 2% of the analytic optimum. CQE estimates of anisotropic correlation length estimation are reported to a demonstrate this technique on a two-parameter estimation problem.

Sufficient Conditions for the Avoidance of Spectral Dispersion in Optical Prisms

Psang Dain Lin

Doc ID: 259586 Received 25 Feb 2016; Accepted 06 May 2016; Posted 06 May 2016  View: PDF

Abstract: Prisms are common optical elements consisting of only flat boundary surfaces. One of the main functions of a prism is that of re-orienting the image. In a previous study by the present group (Tsai and Lin, Appl. Opt. 45, 3951 (2006)), it was shown that when the rays enter and exit a prism perpendicularly, image re-orientation is achieved without spectral dispersion. The present study derives a further sufficient condition to avoid spectral dispersion caused by refraction. The condition explains the ability of Dove prisms and solid glass corner-cubes to produce the required image orientation even when the entrance and exit rays are not normal to the respective boundary surfaces. In general, the proposed condition provides a useful analytical guideline for avoiding spectral dispersion (and hence chromatic aberration) in a wide variety of optical systems.

Contextual phase estimation from two-plane intensity measurements

Jebathilagar Ivan and JOSHUA DEEPAK VEESA

Doc ID: 259536 Received 17 Feb 2016; Accepted 05 May 2016; Posted 06 May 2016  View: PDF

Abstract: In the work of Gori et al [1] it was shown that cross-spectral densities of varying degrees of coherence couldreproduce the same intensities at all points in space, and this had implications for phase estimation methodsbased on transverse plane intensity measurements, which assumed cross-spectrally purity on the measured lightfield. Here we provide a pair of examples of paraxial light fields whose intensities defined at all points in spacedoes not have a corresponding cross-spectrally pure field amplitude. The Gerchberg Saxton (GS) algorithmis applied on pairs of transverse intensities drawn from these examples. The phase as estimated by the GSalgorithm at a given transverse plane is found to be contextual, and to be intrinsically dependent on thepairing plane. This contextual phase estimation at a given transverse plane could be attributed to the lack ofa cross-spectrally pure field amplitude which is consistent with the set of transported intensities, at all pointsin space.

Small Field Tritanopia in the Peripheral Retina

Vicki Volbrecht

Doc ID: 260040 Received 25 Feb 2016; Accepted 03 May 2016; Posted 03 May 2016  View: PDF

Abstract: If stimuli are made sufficiently small, color-normal individuals report a loss in hue perception, in particular adecrease in the perception of green, in both the fovea and peripheral retina. This effect is referred to as small fieldtritanopia. It is not clear, however, how rod input may alter the dynamics of small field tritanopia in the peripheralretina. This paper looks at peripheral hue-naming data obtained for small stimuli at mesopic and photopic retinalilluminances under conditions that minimize (bleach) and maximize (no bleach) rod contribution. The data showthat attenuation in the perception of green occurs with larger stimuli in the no-bleach condition than in the bleachcondition. As retinal illuminance increases, the stimulus size that elicits small field tritanopia decreases; but thestimulus size is still larger under the no-bleach condition. Small field tritanopia in both the bleach and no-bleachconditions may be related to short-wavelength-sensitive (S) cone activity and its potential role in the mediation of theperception of green. The differences in stimulus size for small field tritanopia may be explained by rod input into themagnocellular and koniocellular pathways, which compromises the strength of the chromatic signals and creates adifferential loss in the perception of green as compared to the other elemental hues.

A tutorial on Maxwell Garnett approximation. I. Introduction

Vadim Markel

Doc ID: 260083 Received 29 Feb 2016; Accepted 24 Apr 2016; Posted 28 Apr 2016  View: PDF

Abstract: This tutorial is devoted to the Maxwell Garnett approximation and related theories. Topics covered inthe first, introductory part of the tutorial include the Lorentz local-field correction, the Clausius-Mossottirelation and its role in the modern numerical technique known as the Discrete Dipole Approximation(DDA), the Maxwell Garnett mixing formula for isotropic and anisotropic media, multi-componentmixtures and the Bruggeman mixing formula, the concept of smooth field, and Wiener and Bergman-Milton bounds.

Propagation of polarized waves in inhomogeneous media

Mikhail Charnotskii

Doc ID: 255813 Received 15 Dec 2015; Accepted 11 Mar 2016; Posted 14 Mar 2016  View: PDF

Abstract: A parabolic equation for electromagnetic wave propagation in a random medium is extended to include the depolarization effects in the narrow-angle, forward-scattering setting. Closed-form parabolic equations for propagation of the coherence tensor are derived under a Markov approximation model. For a general partially coherent and partially polarized beam wave, this equation can be reduced to a system of ordinary differential equations allowing a simple numeric solution. An analytical solution exists for statistically homogeneous waves. Estimates based on the perturbation solution support the common knowledge that the depolarization at the optical frequencies is negligible for atmospheric turbulence propagation. These results indicate that the recently published theory (O. Korotkova, Opt. Lett., 40, 3077-3080, 2015) is not valid for atmospheric turbulence.

Enhanced manifold regularization for semi-supervisedclassification

Haitao Gan, Zhizeng Luo, Yingle Fan, and Nong Sang

Doc ID: 246705 Received 24 Jul 2015; Accepted 07 Feb 2016; Posted 11 Feb 2016  View: PDF

Abstract: Manifold regularization (MR) has become one of the most widely used approaches in the semi-supervisedlearning field. It has shown the superiority by exploiting the local manifold structure of both labeledand unlabeled data. The manifold structure is modeled by constructing a Laplacian graph and thenincorporated in learning through a smoothness regularization term. Hence the labels of labeled andunlabeled data vary smoothly along the geodesics on the manifold. However, MR has ignored the discriminativeability of the labeled and unlabeled data. To address the problem, we propose an enhancedMR framework for semi-supervised classification in which the local discriminative information of thelabeled and unlabeled data is explicitly exploited. To make full use of labeled data, we firstly employ asemi-supervised clustering method to discover the underlying data space structure of the whole dataset.Then we construct a local discrimination graph to model the discriminative information of labeled andunlabeled data according to the discovered intrinsic structure. Therefore, the data points which may befrom different clusters though similar on the manifold are enforced far away from each other. Finally, thediscrimination graph is incorporated into the MR framework. In particular, we utilize semi-supervisedfuzzy c-means (SSFCM) and Laplacian regularized Kernel Minimum Squared Error (LapKMSE) for semisupervisedclustering and classification, respectively. Experimental results on several benchmark datasetsand face recognition demonstrate the effectiveness of our proposed method.

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