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Accepted papers to appear in an upcoming issue

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Structured Decomposition Design of Partial Mueller Matrix Polarimeters

Andrey Alenin and J. Scott Tyo

Doc ID: 233285 Received 26 Jan 2015; Accepted 19 May 2015; Posted 19 May 2015  View: PDF

Abstract: Partial Mueller matrix polarimeters (pMMPs) are active sensing instruments that probe a scattering process with a set of polarization states and analyze the scattered light with a second set of polarization states. Unlike conventional Mueller matrix polarimeters, pMMPs do not attempt to reconstruct the entire Mueller matrix. With proper choice of generator and analyzer states, a subset of the Mueller matrix space can be reconstructed with fewer measurements than that of the full Mueller matrix polarimeter. In this paper we consider the structure of the Mueller matrix and our ability to probe it using a reduced numbers of measurements. We develop analysis tools that allow us to relate the particular choice of generator and analyzer polarization states to the portion of Mueller matrix space that the instrument measures, as well as develop an optimization method that is based on balancing the signal-to-noise-ratio of the resulting instrument with the ability of that instrument to accurately measure a particular set of desired polarization components. In the process, we identify ten classes of pMMP systems, the space coverage of which is immediately known. We demonstrate the theory with a numerical example that designs partial polarimeters for the task of monitoring the damage state of a material as presented earlier by Hoover and Tyo. We show that we can reduce the polarimeter to making eight measurements while still covering the Mueller matrix subspace spanned by the objects.

Synchronous position two-photon interference of random-phase grating

Peilong Hong and Guoquan Zhang

Doc ID: 233933 Received 05 Feb 2015; Accepted 18 May 2015; Posted 18 May 2015  View: PDF

Abstract: By generalizing the phase structure of the random-phase grating we recently designed [Opt. Express 21, 14056 (2013)], we show non-HBT type (synchronous position) two-photon grating interference can be obtained, which physically relies on groups of multiple indistinguishable two-photon paths modulated by the spatial distributions of phase modes. By properly selecting the random-phase structures, synchronous position subwavelength interference can be obtained, the period of which, in the two-photon interference domain, is decreased by a factor N (= 3, 4, 5, 6, · · · ) depending on the slit number and random-phase structure, and the visibility of N-fold subwavelength interference fringes could be improved by increasing the slit number of the grating. The results show that modulation on two-photon paths via spatial arrangements of the phase modes offers the possibility to actively control the optical high-order coherence in the same optical scheme.

Strehl ratio, a tool for optimizing optical nulls and singularities

Francois Henault

Doc ID: 234926 Received 20 Feb 2015; Accepted 18 May 2015; Posted 18 May 2015  View: PDF

Abstract: In this paper are reviewed a set of radial and azimuthal phase functions having a null Strehl ratio, that is equivalent to generating a central extinction in the image plane of an optical system. The study is conducted in the frame of Fraunhofer scalar diffraction, and oriented towards practical cases where optical nulls or singularities are produced by deformable mirrors or phase plates. The identified solutions reveal unexpected links with the zeros of type-J Bessel functions of integer order. They include linear azimuthal phase ramps giving birth to an optical vortex, azimuthally modulated phase functions and circular phase gratings (CPG). It is found in particular that the CPG radiometric efficiency could be significantly improved by the null Strehl ratio condition. Simple design rules for rescaling and combining the different phase functions are also defined. Finally, the described analytical solutions could also serve as starting points for an automated searching software tool.

TD-UAPO Diffracted Field Evaluation for Penetrable Wedges with Acute Apex Angle

Giovanni Riccio, Marcello Frongillo, and Gianluca Gennarelli

Doc ID: 235053 Received 20 Feb 2015; Accepted 18 May 2015; Posted 18 May 2015  View: PDF

Abstract: This study deals with the time domain diffraction phenomenon related to a penetrable acute-angled dielectric wedge. The transient diffracted field originated by an arbitrary function plane wave is evaluated via a convolution integral involving the time domain diffraction coefficients, which are determined here in closed form starting from the knowledge of the frequency domain counterparts. In particular, the inverse Laplace transform is applied to the Uniform Asymptotic Physical Optics diffraction coefficients valid for the internal region of the wedge and the surrounding space. Diffraction by penetrable wedges in the time domain framework is a challenging problem from the analytical point of view, and no other expressions are available in closed form for the diffraction coefficients associated to the considered problem.

The Effect of the Imaginary Part of the Refractive Index on Light Scattering by Spheres

Christopher Sorensen, Amit Chakrabarti, and George Wang

Doc ID: 237626 Received 08 Apr 2015; Accepted 18 May 2015; Posted 18 May 2015  View: PDF

Abstract: For spheres of arbitrary radius R and complex index of refraction n + iκ, we identify a new parameter that indicates when the imaginary part κ seriously affects the scattering by a sphere. The parameter is κkR, where k is the wave vector magnitude, such that when κkR grows larger than one, the scattering is affected, and when κkR > 3 the effects saturate. The effects are uncovered and demonstrated with Q-space analysis. The physical basis for κkR lies in the fact that it is the ratio of the radius to the optical skin depth.

Optimization of LED light spectrum to enhance colorfulness of illuminated objects with white light constraints

Jianfei Dong, haining wu, G.Q. Zhang, and gaojin qi

Doc ID: 226380 Received 15 Dec 2014; Accepted 17 May 2015; Posted 18 May 2015  View: PDF

Abstract: Enhancing the colorfulness of illuminated objects is a promising application of LED lighting for commercial, exhibiting and scientific purposes. This paper proposes a method to enhance the color of illuminated objects for a given polychromatic lamp. Meanwhile, the light color is restricted to white. We further relax the white light constraints by introducing soft margins. Based on the spectral and electrical characteristics of LEDs and object surface properties, we determine the optimal mixing of LED light spectrum by solving a numerical optimization problem, which is a Quadratic Fractional Programming (QFP) problem by formulation. Simulation studies show that the trade-off between the white light constraint and the level of the color enhancement can be adjusted by tuning an upper limit value of the soft margin. Furthermore, visual evaluation experiments are performed to evaluate human perception of the color enhancement. The experiments have verified the effectiveness of the proposed method.

A computational method for transmission eigenvalues for spherically stratified medium

Jing Yang and Xiaoliang Cheng

Doc ID: 236555 Received 20 Mar 2015; Accepted 17 May 2015; Posted 18 May 2015  View: PDF

Abstract: We consider the computational method for the interior transmission eigenvalue problem that arising in acoustic and electromagnetic scattering. The transmission eigenvalues contain useful information of some physical properties, such as the index of refraction. Instead of the existence and estimation of the spectral property of the transmission eigenvalues, we focus on the numerical calculation, especially for spherically stratified media. Due to the nonlinearity and the special structure of the interior transmission eigenvalue problem, there are not many numerical methods so far. Firstly, we reduce it into a second-order ordinary differential equation, then apply the Hermite finite element to the weak formulation of the equation. With proper rewriting of the matrix-vector form, we change the original nonlinear eigenvalue problem into a quadratic eigenvalue problem, which can be written as a linear system and solved by eigs in Matlab. This numerical method is fast, effective and can calculate as many transmission eigenvalues as needed at a time.

High-resolution interference with programmable classical incoherent light

erfeng zhang, WeiTao Liu, and Ping-Xing Chen

Doc ID: 234300 Received 09 Feb 2015; Accepted 17 May 2015; Posted 18 May 2015  View: PDF

Abstract: A scheme of high-resolution interference with classical incoherent light is proposed. In this scheme, the classical incoherent light is programmable in the amplitude distribution and wavefront, and with the programmable classical incoherent light we improve the resolution of the interference pattern by a factor of two comparing with the scheme by Erkmen [J. Opt. Soc. Am. A 29, 782-789 (2012)]. Compared with other schemes to observing the interference patterns, a single-pixel detection is only needed in our proposal. Moreover, the high-resolution interference pattern can be inverted to obtain an image with better resolution comparing with that of the scheme proposed by Erkmen [J. Opt. Soc. Am. A 29, 782-789 (2012)]. Furthermore, this scheme of high-resolution interference is verified in detail by theoretical analysis and numerical simulations.

Shannon Information and ROC Analysis in Imaging

Johnathan Cushing and Eric Clarkson

Doc ID: 232443 Received 14 Jan 2015; Accepted 13 May 2015; Posted 13 May 2015  View: PDF

Abstract: Shannon Information (SI) and the ideal-observer Receiver Operating Characteristic (ROC) curve are two different methods for analyzing the performance of of an imaging system for a binary classification task, such as the detection of a variable signal imbedded within a random background. In this work we describe a new ROC curve, the SIROC curve, that is derived from the SI expression for a binary classification task. We then show that the ideal-observer ROC curve and the SIROC curve have many properties in common, and are equivalent descriptions of the optimal performance of an observer on the task. This equivalence is mathematically described by an integral transform that maps the ideal-observer ROC curve onto the SIROC curve. This then leads to an integral transform relating the minimum probability of error, as a function of the odds against a signal, to the conditional entropy, as a function of the same variable. This last relation then gives us the complete mathematical equivalence between ideal-observer ROC analysis and SI analysis of the classification task for a given imaging system. We also find that there is a close relationship between the area under the ideal-observer ROC curve, which is often used as a figure of merit for imaging systems, and the area under the SIROC curve. Finally we show that the relationships between the two curves result in new inequalities relating SI to ROC quantities for the ideal observer.

Phase retrieval for multiple objects from their averaged diffraction

Rick Millane and Joe Chen

Doc ID: 232902 Received 20 Jan 2015; Accepted 12 May 2015; Posted 12 May 2015  View: PDF

Abstract: The problem of reconstructing multiple objects from the average of their diffracted intensities is investigated. Reconstruction feasibility (uniqueness) depends on the number of objects, and their supports and dimensionality, and is characterised by an appropriately calculated constraint ratio. For objects with sufficiently different supports, and a favorable constraint ratio, the reconstruction problem has a unique solution. For objects with identical supports there can be multiple solutions, even with a favorable constraint ratio. However, positivity of the objects and noncentrosymmetry of the support reduces the degree of nonuniqueness, and a unique solution may exist with a favorable constraint ratio. An iterative projection based algorithm to reconstruct the multiple objects is described. The efficacy of the reconstruction algorithm and the uniqueness results are demonstrated by simulation.

Angular spectral framework to test full corrections of paraxial solutions

María-Jesús González-Morales and Raúl Mahillo-Isla

Doc ID: 234048 Received 06 Feb 2015; Accepted 08 May 2015; Posted 12 May 2015  View: PDF

Abstract: Different correction methods for paraxial solutions have been used when such solutions extend out of the paraxial regime. Researchers have used correction methods guided by either their experience or some educated hypothesis pertinent in the particular problem that they were tackling. This article provides a framework to classify full wave correction schemes. For a given solution of the paraxial wave equation, we can select the best correction scheme of those available. Some common correction methods are considered and evaluated under the proposed scope. The conditions that a couple of solutions of the Helmholtz equation must accomplish to accept a common paraxial approximation of both solutions are given.

Analysis of temporal power spectra for optical waves propagating through weak anisotropic non-Kolmogorov turbulence

Linyan Cui

Doc ID: 233322 Received 26 Jan 2015; Accepted 02 May 2015; Posted 04 May 2015  View: PDF

Abstract: Analytic expressions for the temporal power spectra of irradiance fluctuations and angle of arrival (AOA) fluctuations are derived for optical waves propagating through weak anisotropic non-Kolmogorov atmospheric turbulence. In the derivation, the anisotropic non-Kolmogorov spectrum is adopted, which adopts the assumption of circular symmetry in the orthogonal plane throughout the path and the same degree of anisotropy along the propagation direction for all the turbulence cells. The final expressions consider simultaneously the anisotropic factor and general spectral power law values. When the anisotropic factor equals one (corresponding to the isotropic turbulence), the derived temporal power spectral models have good consistency with the known results for the isotropic turbulence. Numerical calculations show that the increased anisotropic factor alleviates the atmospheric turbulence’s influence on the final expressions.

Extraction of all propagation constants in a specified region from the transcendental equation of a dispersion relation by using Sakurai-Sugiura projection method

Shingo Sato, Takao Shimada, and Koji Hasegawa

Doc ID: 233620 Received 04 Feb 2015; Accepted 02 May 2015; Posted 04 May 2015  View: PDF

Abstract: A transcendental equation occurs when we compute dispersion relations of an electromagnetic waveguide such as a planar multilayer waveguide. Without the initial guess, Sakurai-Sugiura projection method (SSM) can obtain solutions of the transcendental equation in a region bounded by a contour integral path in a complex plane. In this paper, a criterion employing the condition number of eigenvalues as a simple index to distinguish physical solutions from spurious solutions in SSM is presented and a transcendental equation of a multilayer waveguide obtained by the transfer matrix method is solved by SSM. Numerical results show usefulness of the index and good agreement with those of the argument principle method and Newton’s method.

Adequacy of rigorous coupled-wave approach for thin-film silicon solar cells with periodically corrugated metallic backreflectors: spectral analysis

Akhlesh Lakhtakia, Mikhail Shuba, Muhammad Faryad, Peter Monk, and Manuel Solano

Doc ID: 237668 Received 08 Apr 2015; Accepted 02 May 2015; Posted 06 May 2015  View: PDF

Abstract: The rigorous coupled-wave approach (RCWA) is extensively used to compute optical absorption and photon absorption in thin-film photovoltaic solar cells backed by 1D metallic gratings when the wave vector of the incident light lies wholly in the grating plane. The RCWA algorithm converges rapidly for incident s-polarized light over the entire 400-to-1100-nm solar spectrum. It also performs well for incident p-polarized light in the 400-to-650-nm spectral regime, but even with a large number of Floquet harmonics in the solution the total reflectance is underestimated in the 650-to-1100-nm spectral regime. Despite that shortcoming, the RCWA underestimates the solar-spectrum-integrated photon absorption rate only by 5-to-10% for p-polarized light. As sunlight is almost unpolarized, the RCWA should be considered adequate to design thin-film silicon solar cells with periodically corrugated metallic backreflectors.

Creation of a 50,000λ long needle-like field with 0.36λ width – reply to comment

Qing Cao, Minning Zhu, and Hua Gao

Doc ID: 232884 Received 21 Jan 2015; Accepted 24 Apr 2015; Posted 24 Apr 2015  View: PDF

Abstract: This is the reply to the comment by Chavez-Cerda and Pu [J. Opt. Soc. Am. A ××× (2015)] on our recent work about the 50,000λ long needle-like field [J. Opt. Soc. Am. A 31, 500 (2014)]. First, they employed an incorrect boundary condition as the fundament of their argument. In fact, it is not the electric field but its tangential component that must be zero at the surface of the perfect metal. Our result is completely consistent with the correct boundary condition. Second,an arbitrary constant phase factor in the incident radially polarized beam, exp(jπ/4) for instance, has no influence on the result. Accordingly, our initial condition is proper. Third, for the suggested applications of electron acceleration and of optical trapping of thin and long objects, there is no need of the longitudinal component of the energy flow density.

Origins of Radiative Transport Theory: Diagrammatic and Multiscale Approaches

John Schotland and Alexandre Caze

Doc ID: 232297 Received 16 Jan 2015; Accepted 14 Mar 2015; Posted 17 Mar 2015  View: PDF

Abstract: The radiative transport equation (RTE) is widely used to describe the propagation of multiply- scattered light in disordered media. In this tutorial, we present two derivations of the RTE for scalar wave fields. The first derivation is based on diagrammatic perturbation theory, while the second stems from an asymptotic multiscale expansion. Although the two approaches are quite distinct mathematically, some common ground can be found and is discussed.

Bit error rate of focused Gaussian beams in weak oceanic turbulence: Comment

Mikhail Charnotskii

Doc ID: 229256 Received 11 Dec 2014; Accepted 08 Jan 2015; Posted 20 Mar 2015  View: PDF

Abstract: Recent calculations [1] of the scintillation index of focused beams did not take into account the second order of the perturbation theory, and therefore led the author to erroneous conclusions regarding dependence of the scintillation index for the focused beams on the aperture size. The log-normal intensity probability distribution used for the Bit Error Rate (BER) calculations in [1] is also invalid for the wide focused beams. As a result, most of conclusions of [1] are incorrect.

Creation of a 50,000λ long needle-like field with 0.36λ width: comment

Sabino Chavez-Cerda and Jixiong Pu

Doc ID: 223032 Received 15 Sep 2014; Accepted 08 Dec 2014; Posted 09 Dec 2014  View: PDF

Abstract: In a recent paper, a method for the generation of a long, narrow needle of light was proposed [J. Opt. Soc. Am. A 31, 500 (2014)]. The authors missed some fundamental aspects of the mathematical physics of cylindrical electromagnetic waves described by Bessel functions that are essential to obtain the desired result. Also, their solution of the wave field lacks the component of longitudinal energy flow that is needed for most of the applications they suggest. We show that a minor modification solves this absence with practically negligible increase of the needle width.

(CV) Independence and interaction of luminance and chromatic contributions to spatial hyperacuity performance

Bonnie Cooper and Barry Lee

Doc ID: 198653 Received 30 Sep 2013; Accepted 02 Feb 2014; Posted 03 Feb 2014  View: PDF

Abstract: Here we test interactions of luminance and chromatic input to spatial hyperacuity mechanisms. First, we tested alignment with matching or mismatching (contrast polarity or modality) grating pairs that were adjusted to detection threshold. Thresholds with mismatched pairs were significantly elevated. Second, we determined alignment acuity as a function of luminance or chromatic contrast alone or in the presence of contrast pedestals. For in-phase pedestal conditions, performance followed the envelope of the more sensitive mechanism. However, polarity reversals revealed an asymmetric effect for luminance and chromatic conditions. This suggests that luminance can overrule chromatic mechanisms in hyperacuity; we interpret these findings in the context of spatial mechanisms.

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