### Early Posting

#### Accepted papers to appear in an upcoming issue

OSA now posts prepublication articles as soon as they are accepted and cleared for production. See the FAQ for additional information.

**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.

**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.

**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.

**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.

**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.

**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.

**Difference between the Brewster angle and angle of minimum reflectance for incident unpolarized or circularly polarized light at interfaces between transparent media**

Rasheed Azzam

**Doc ID: 236808** Received 25 Mar 2015; Accepted 06 May 2015; Posted 06 May 2015 **View: PDF**

**Abstract: **For reflection at interfaces between transparent optically isotropic media, the difference between the Brewster angle φB of zero reflectance for incident p-polarized light and the angle φumin of minimum reflectance for incident unpolarized or circularly polarized is considered for all values of the relative refractive n in external and internal reflection. We determine that: (i) φumin < φB for all values of n; (ii) the maximum differences φB - φumin = 75° and 15° in external and internal reflection at n = 2±3^½ ; (iii) in internal reflection φumin exhibits an unexpected maximum = 12.30° at n = 4.1211; (iv) φumin = 0 if the normal-incidence intensity reflectance R0 is in the range 0 < R0 <1/3; and (v) Rumin at φumin is limited to 1/3 < Rumin <1/2.

**Low-quality Fingerprint Recognition Using a limited ellipse-band-based Matching Method**

Xinyue Zhao, Zaixing He, and Shuyou Zhang

**Doc ID: 231854** Received 07 Jan 2015; Accepted 05 May 2015; Posted 06 May 2015 **View: PDF**

**Abstract: **Recent fingerprint recognition technologies are mostly based on the minutia algorithms, which could not recognize fingerprint images in low-quality conditions. This paper proposes a novel recognition algorithm using a limited ellipse-band-based matching method. It uses the Fourier-Mellin Transformation method to improve the limitation of the original algorithm which could not resist rotation changes. Furthermore, an ellipse-band on the frequency amplitude is used to suppress noises which are brought in by the high-frequency part of images. Finally, the recognition result is obtained by considering both the contrast and position correlation peaks. The experimental results showed that the proposed algorithm can increase the recognition accuracy, especially of images in lowquality condition.

**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.

**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.

**Modal-based phase retrieval for adaptive optics**

Jacopo Antonello and Michel Verhaegen

**Doc ID: 236413** Received 18 Mar 2015; Accepted 25 Apr 2015; Posted 27 Apr 2015 **View: PDF**

**Abstract: **We consider using phase retrieval (PR) to correct phase aberrations in an optical system. Three measurements of the point-spread function (PSF) are collected to estimate an aberration. For each measurement, a different defocus aberration is applied with a deformable mirror (DM). Once the aberration is estimated using a PR algorithm, we apply the aberration correction with the DM, and measure the residual aberration using a Shack-Hartmann wavefront sensor. The extended Nijboer-Zernike theory is used for modelling the PSF. The PR problem is solved using both an algorithm called PhaseLift, which is based on matrix rank minimisation, and another algorithm based on alternating projections. For comparison, we include the results achieved using a classical PR algorithm, which is based on alternating projections and uses the fast Fourier transform.

**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.

**Electromagnetic Wave Transmission Through a Subwavelength Nano-hole in a Two-dimensional Plasmonic Layer**

Norman Horing, DESIRE MIESSEIN, and Godfrey Gumbs

**Doc ID: 226040** Received 30 Oct 2014; Accepted 22 Jan 2015; Posted 25 Feb 2015 **View: PDF**

**Abstract: **An integral equation is formulated to describe electromagnetic wave transmission through a subwavelength nano-hole in a thin plasmonic sheet in terms of the dyadic Green's function for the associated Helmholtz problem. Taking the subwavelength radius of the nano-hole to be the smallest length of the system, we have obtained an exact solution of the integral equation for the dyadic Green's function analytically and in closed form. This dyadic Green's function is then employed in the numerical analysis of electromagnetic wave transmission through the nano-hole for normal incidence of the incoming wave train. The electromagnetic transmission involves two distinct contributions, one emanating from the nano-hole and the other is directly transmitted through the thin plasmonic layer itself (which would not occur in the case of a perfect metal screen). The transmitted radiation exhibits interference fringes in the vicinity of the nano-hole, and they tend to flatten as a function of increasing lateral separation from the hole, reaching the uniform value of transmission through the sheet alone at large separations.

**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.