Showing papers in "Journal of The Optical Society of America A-optics Image Science and Vision in 2016"

Introduction to the Maxwell Garnett approximation: tutorial.

Abstract: This tutorial is devoted to the Maxwell Garnett approximation and related theories. Topics covered in this first, introductory part of the tutorial include the Lorentz local field correction, the Clausius–Mossotti relation and its role in the modern numerical technique known as the discrete dipole approximation, the Maxwell Garnett mixing formula for isotropic and anisotropic media, multicomponent mixtures and the Bruggeman equation, the concept of smooth field, and Wiener and Bergman–Milton bounds.

Stokes-vector and Mueller-matrix polarimetry [Invited].

Abstract: This paper reviews the current status of instruments for measuring the full 4×1 Stokes vector S, which describes the state of polarization (SOP) of totally or partially polarized light, and the 4×4 Mueller matrix M, which determines how the SOP is transformed as light interacts with a material sample or an optical element or system. The principle of operation of each instrument is briefly explained by using the Stokes-Mueller calculus. The development of fast, automated, imaging, and spectroscopic instruments over the last 50 years has greatly expanded the range of applications of optical polarimetry and ellipsometry in almost every branch of science and technology. Current challenges and future directions of this important branch of optics are also discussed.

Fisher information theory for parameter estimation in single molecule microscopy: tutorial.

Abstract: Estimation of a parameter of interest from image data represents a task that is commonly carried out in single molecule microscopy data analysis. The determination of the positional coordinates of a molecule from its image, for example, forms the basis of standard applications such as single molecule tracking and localization-based super-resolution image reconstruction. Assuming that the estimator used recovers, on average, the true value of the parameter, its accuracy, or standard deviation, is then at best equal to the square root of the Cramer-Rao lower bound. The Cramer-Rao lower bound can therefore be used as a benchmark in the evaluation of the accuracy of an estimator. Additionally, as its value can be computed and assessed for different experimental settings, it is useful as an experimental design tool. This tutorial demonstrates a mathematical framework that has been specifically developed to calculate the Cramer-Rao lower bound for estimation problems in single molecule microscopy and, more broadly, fluorescence microscopy. The material includes a presentation of the photon detection process that underlies all image data, various image data models that describe images acquired with different detector types, and Fisher information expressions that are necessary for the calculation of the lower bound. Throughout the tutorial, examples involving concrete estimation problems are used to illustrate the effects of various factors on the accuracy of parameter estimation and, more generally, to demonstrate the flexibility of the mathematical framework.

Light-field and holographic three-dimensional displays [Invited].

Abstract: A perfect three-dimensional (3D) display that satisfies all depth cues in human vision is possible if a light field can be reproduced exactly as it appeared when it emerged from a real object. The light field can be generated based on either light ray or wavefront reconstruction, with the latter known as holography. This paper first provides an overview of the advances of ray-based and wavefront-based 3D display technologies, including integral photography and holography, and the integration of those technologies with digital information systems. Hardcopy displays have already been used in some applications, whereas the electronic display of a light field is under active investigation. Next, a fundamental question in this technology field is addressed: what is the difference between ray-based and wavefront-based methods for light-field 3D displays? In considering this question, it is of particular interest to look at the technology of holographic stereograms. The phase information in holography contributes to the resolution of a reconstructed image, especially for deep 3D images. Moreover, issues facing the electronic display system of light fields are discussed, including the resolution of the spatial light modulator, the computational techniques of holography, and the speckle in holographic images.

Electromagnetic theory of optical coherence [Invited].

Abstract: The coherence theory of random, vector-valued optical fields has been of great research interest in recent years. In this work we formulate the foundations of electromagnetic coherence theory both in the space-time and space-frequency domains, with particular emphasis on various types of optical interferometry. Analyzing statistically stationary, two-component (paraxial) electric fields in the classical and quantum-optical contexts we show fundamental connections between the conventional (polarization) Stokes parameters and the associated two-point (coherence) Stokes parameters. Measurement of the coherence and polarization properties of random vector beams by nanoparticle scattering and two-photon absorption is also addressed.

Spatially resolving antenna arrays using frequency diversity.

Abstract: Radio imaging devices and synthetic aperture radar typically use either mechanical scanning or phased arrays to illuminate a target with spatially varying radiation patterns. Mechanical scanning is unsuitable for many high-speed imaging applications, and phased arrays contain many active components and are technologically and cost prohibitive at millimeter and terahertz frequencies. We show that antennas deliberately designed to produce many different radiation patterns as the frequency is varied can reduce the number of active components necessary while still capturing high-quality images. This approach, called frequency-diversity imaging, can capture an entire two-dimensional image using only a single transmit and receive antenna with broadband illumination. We provide simple principles that ascertain whether a design is likely to achieve particular resolution specifications, and illustrate these principles with simulations.

Spatiotemporal blue noise coded aperture design for multi-shot compressive spectral imaging.

Abstract: Multi-shot coded aperture snapshot spectral imaging (CASSI) systems capture the spectral information of a scene using a small set of coded focal plane array (FPA) compressive measurements. Compressed sensing (CS) reconstruction algorithms are then used to reconstruct the underlying spectral 3D data cube from an underdetermined system of linear equations. Multiple snapshots result in a less ill-posed inverse problem and improved reconstructions. The only varying components in CASSI are the coded apertures, whose structure is crucial inasmuch as they determine the minimum number of FPA measurements needed for correct image reconstruction and the corresponding attainable quality. Traditionally, the spatial structures of the coded aperture entries are selected at random, leading to suboptimal reconstruction solutions. This work presents an optimal structure design of a set of coded apertures by optimizing the concentration of measure of the multi-shot CASSI sensing matrix and its incoherence with respect to the sparse representation basis. First, the CASSI matrix system representation in terms of the ensemble of random projections is established. Then, the restricted isometry property (RIP) of the CASSI projections is determined as a function of the coded aperture entries. The optimal coded aperture structures are designed under the criterion of satisfying the RIP with high probability, coined spatiotemporal blue noise (BN) coded apertures. Furthermore, an algorithm that implements the BN ensembles is presented. Extensive simulations and a testbed implementation are developed to illustrate the improvements of the BN coded apertures over the traditionally used coded aperture structures, in terms of spectral image reconstruction PSNR and SSIM.

Perfect optical vortex array with controllable diffraction order and topological charge.

Abstract: We have demonstrated a holographic grating, the far-field diffraction pattern of which is a perfect optical vortex (POV) array. The diffraction order, as well as the topological charge of each spot in the array, is controllable. By setting different parameters when designing the hologram, the spot in different diffraction orders will be changed, resulting in the variance of the POV array. During the experiment, we uploaded holograms of different design on a phase-only spatial light modulator. We then observed POV arrays with different dimensions and topological charges using a CCD camera, which fit well with the simulation. This technique provides the possibility to generate multiple POVs simultaneously, and can be used in domains where multiple POVs are of high interest such as orbital angular momentum multiplexed fiber data transmission systems.

Propagation properties of an optical vortex carried by a Bessel–Gaussian beam in anisotropic turbulence

Abstract: Rytov theory was employed to establish the transmission model for the optical vortices carried by Bessel-Gaussian (BG) beams in weak anisotropic turbulence based on the generalized anisotropic von Karman spectrum. The influences of asymmetry anisotropic turbulence eddies and source parameters on the signal orbital angular momentum (OAM) mode detection probability of partially coherent BG beams in anisotropic turbulence were discussed. Anisotropic characteristics of the turbulence could enhance the OAM mode transmission performance. The spatial partially coherence of the beam source would increase turbulent aberration's effect on the optical vortices. BG beams could dampen the influences of the turbulence because of their nondiffraction and self-healing characteristics.

Structure tensor based automated detection of macular edema and central serous retinopathy using optical coherence tomography images

Abstract: Macular edema (ME) and central serous retinopathy (CSR) are two macular diseases that affect the central vision of a person if they are left untreated. Optical coherence tomography (OCT) imaging is the latest eye examination technique that shows a cross-sectional region of the retinal layers and that can be used to detect many retinal disorders in an early stage. Many researchers have done clinical studies on ME and CSR and reported significant findings in macular OCT scans. However, this paper proposes an automated method for the classification of ME and CSR from OCT images using a support vector machine (SVM) classifier. Five distinct features (three based on the thickness profiles of the sub-retinal layers and two based on cyst fluids within the sub-retinal layers) are extracted from 30 labeled images (10 ME, 10 CSR, and 10 healthy), and SVM is trained on these. We applied our proposed algorithm on 90 time-domain OCT (TD-OCT) images (30 ME, 30 CSR, 30 healthy) of 73 patients. Our algorithm correctly classified 88 out of 90 subjects with accuracy, sensitivity, and specificity of 97.77%, 100%, and 93.33%, respectively.

Evaluating color texture descriptors under large variations of controlled lighting conditions.

Abstract: The recognition of color texture under varying lighting conditions remains an open issue. Several features have been proposed for this purpose, ranging from traditional statistical descriptors to features extracted with neural networks. Still, it is not completely clear under what circumstances a feature performs better than others. In this paper, we report an extensive comparison of old and new texture features, with and without a color normalization step, with a particular focus on how these features are affected by small and large variations in the lighting conditions. The evaluation is performed on a new texture database, which includes 68 samples of raw food acquired under 46 conditions that present single and combined variations of light color, direction, and intensity. The database allows us to systematically investigate the robustness of texture descriptors across large variations of imaging conditions.

Maxwell Garnett approximation (advanced topics): tutorial

Abstract: In the second part of this tutorial, we consider several advanced topics related to the Maxwell Garnett approximation

Deconvolution methods for structured illumination microscopy

Abstract: We compare two recently developed multiple-frame deconvolution approaches for the reconstruction of structured illumination microscopy (SIM) data: the pattern-illuminated Fourier ptychography algorithm (piFP) and the joint Richardson–Lucy deconvolution (jRL). The quality of the images reconstructed by these methods is compared in terms of the achieved resolution improvement, noise enhancement, and inherent artifacts. Furthermore, we study the issue of object-dependent resolution improvement by considering the modulation transfer functions derived from different types of objects. The performance of the considered methods is tested in experiments and benchmarked with a commercial SIM microscope. We find that the piFP method resolves periodic and isolated structures equally well, whereas the jRL method provides significantly higher resolution for isolated objects compared to periodic ones. Images reconstructed by the piFP and jRL algorithms are comparable to the images reconstructed using the generalized Wiener filter applied in most commercial SIM microscopes. An advantage of the discussed algorithms is that they allow the reconstruction of SIM images acquired under different types of illumination, such as multi-spot or random illumination.

Symmetric form-invariant dual Pearcey beams.

Abstract: We introduce another type of Pearcey beam, namely, dual Pearcey (DP) beams, based on the Pearcey function of catastrophe theory. DP beams are experimentally generated by applying Fresnel diffraction of bright elliptic rings. Form-invariant Bessel distribution beams can be regarded as a special case of DP beams. Subsequently, the basic propagation characteristics of DP beams are identified. DP beams are the result of the interference of two half DP beams instead of two classical Pearcey beams. Moreover, we also verified that half DP beams (including special-case parabolic-like beams) generated by half elliptical rings (circular rings) are a new member of the family of form-invariant beams.

Optimal phase element for generating a perfect optical vortex.

Abstract: We derived exact analytical relationships to describe the complex amplitude of a perfect optical vortex generated by means of three different optical elements, namely, (i) an amplitude-phase element with a transmission function proportional to a Bessel function, (ii) an optimal phase element with a transmission equal to the sign function of a Bessel function, and (iii) a spiral axicon. The doughnut intensity was shown to be highest when using an optimal phase element. The spiral-axicon-aided diffraction ring was found to be twice as wide as when generated using two other elements. Thus, the optimal filter was shown to be best suited for generating a perfect optical vortex. The simulation results were shown to corroborate theoretical predictions, with the experiment being in agreement with theory and simulation.

Invariant quantities of a Mueller matrix under rotation and retarder transformations.

Abstract: Mueller matrices are defined with respect to appropriate Cartesian reference frames for the representation of the states of polarization of the input and output electromagnetic probe beams. The polarimetric quantities that are invariant under rotations of the said reference frames about the respective directions of propagation (rotation transformations) provide particularly interesting physical information. Moreover, certain properties are also invariant with respect to the action of birefringent devices located on both sides of the medium under consideration (retarder transformations). The polarimetric properties that remain invariant under rotation and retarder transformations are calculated from any given Mueller matrix and are then analyzed and interpreted, providing significant parameterizations of Mueller matrices in terms of meaningful physical quantities.

Interactive Removal and Ground Truth for Difficult Shadow Scenes

Abstract: A user-centric method for fast, interactive, robust, and high-quality shadow removal is presented. Our algorithm can perform detection and removal in a range of difficult cases, such as highly textured and colored shadows. To perform detection, an on-the-fly learning approach is adopted guided by two rough user inputs for the pixels of the shadow and the lit area. After detection, shadow removal is performed by registering the penumbra to a normalized frame, which allows us efficient estimation of nonuniform shadow illumination changes, resulting in accurate and robust removal. Another major contribution of this work is the first validated and multiscene category ground truth for shadow removal algorithms. This data set containing 186 images eliminates inconsistencies between shadow and shadow-free images and provides a range of different shadow types such as soft, textured, colored, and broken shadow. Using this data, the most thorough comparison of state-of-the-art shadow removal methods to date is performed, showing our proposed algorithm to outperform the state of the art across several measures and shadow categories. To complement our data set, an online shadow removal benchmark website is also presented to encourage future open comparisons in this challenging field of research.

Extremum-seeking control of the beam pattern of a reconfigurable holographic metamaterial antenna.

Abstract: Robust, continuous, and software-defined beam pattern control of holographic metamaterial antennas is necessary to realize the potential of these low-power-consumption, thin, lightweight, inexpensive antennas for consumer usage of satellite communication. We present a complete feedback control approach that enables adaptive control of the radiation pattern for the electronically scanned metamaterial antenna that is robust to measurement noise and is able to continuously optimize performance throughout changing environmental conditions and antenna characteristics. The physical size, weight, and cost advantages of the metamaterial antenna make it an attractive technology when paired with robust and adaptive on-board software strategies to optimize antenna performance and self-tune for various environmental conditions.

Scanning Fourier transform spectrometer in the visible range based on birefringent wedges.

Abstract: We introduce a spectrometer capable of measuring sample absorption spectra in the visible regime, based on a time-domain scanning Fourier transform (FT) approach. While infrared FT spectrometers typically employ a Michelson interferometer to create the two delayed light replicas, the proposed apparatus exploits a compact common-mode passive interferometer that relies on the use of birefringent wedges. This ensures excellent path-length stability (∼λ/300) and accuracy, with no need for active feedback or beam tracking. We demonstrate the robustness of the technique measuring the transmission spectrum of a colored bandpass filter over one octave of bandwidth and compare the results with those obtained with a commercial spectrophotometer.

Optical Hall effect—model description: tutorial

Abstract: The optical Hall effect is a physical phenomenon that describes the occurrence of magnetic-field-induced dielectric displacement at optical wavelengths, transverse and longitudinal to the incident electric field, and analogous to the static electrical Hall effect. The electrical Hall effect and certain cases of the optical Hall effect observations can be explained by extensions of the classic Drude model for the transport of electrons in metals. The optical Hall effect is most useful for characterization of electrical properties in semiconductors. Among many advantages, while the optical Hall effect dispenses with the need of electrical contacts, electrical material properties such as effective mass and mobility parameters, including their anisotropy as well as carrier type and density, can be determined from the optical Hall effect. Measurement of the optical Hall effect can be performed within the concept of generalized ellipsometry at an oblique angle of incidence. In this paper, we review and discuss physical model equations, which can be used to calculate the optical Hall effect in single- and multiple-layered structures of semiconductor materials. We define the optical Hall effect dielectric function tensor, demonstrate diagonalization approaches, and show requirements for the optical Hall effect tensor from energy conservation. We discuss both continuum and quantum approaches, and we provide a brief description of the generalized ellipsometry concept, the Mueller matrix calculus, and a 4×4 matrix algebra to calculate data accessible by experiment. In a follow-up paper, we will discuss strategies and approaches for experimental data acquisition and analysis.

Dodecagonal photonic quasi-crystal fiber with high birefringence

Abstract: A photonic quasi-crystal fiber (PQF) with high birefringence is proposed. A dodecagonal Stampfli quasi-periodic lattice of air holes constitutes the cladding of the PQF. The PQF maintains the properties of high birefringence and single-mode operation regime in a wide wavelength range from 1.2 to 2.0 μm by optimizing the size of the air holes around the core of the PQF. A birefringence with 3.86×10−2 can be obtained at 1.31 and 1.55 μm optical telecommunication windows. The birefringence is of the order of 10−2, which is two orders of magnitude larger than that of the conventional polarization-maintaining fibers and hardly affected by the incident wavelength. The proposed PQF also maintains a high nonlinear coefficient and low confinement loss. Our structure and simulation results are expected to provide a valuable reference and basic data to relative fabrication and experiments.

Statistics of colors in paintings and natural scenes

Abstract: Painters reproduce some spatial statistical regularities of natural scenes. To what extent they replicate their color statistics is an open question. We investigated this question by analyzing the colors of 50 natural scenes of rural and urban environments and 44 paintings with abstract and figurative compositions. The analysis was carried out using hyperspectral imaging data from both sets and focused on the gamut and distribution of colors in the CIELAB space. The results showed that paintings, like natural scenes, have gamuts with elongated shapes in the yellow–blue direction but more tilted to the red direction. It was also found that the fraction of discernible colors, expressed as a function of the number of occurrences in the scene or painting, is well described by power laws. These have similar distribution of slopes in a log–log scale for paintings and natural scenes. These features are observed in both abstract and figurative compositions. These results suggest that the underlying chromatic structure of artistic compositions generally follows the main statistical features of the natural environment.

Propagation of the OAM mode carried by partially coherent modified Bessel-Gaussian beams in an anisotropic non-Kolmogorov marine atmosphere.

Abstract: This study investigates the effect of the anisotropic non-Kolmogorov turbulence of the marine atmosphere on propagation of orbital angular momentum (OAM) modes carried by partially coherent modified Bessel–Gaussian (PCMBG) beams. The analytic formula of the probability density of OAM modes is derived and used to explore the evolution of the received power of the OAM mode. PCMBG beams with long wavelength, low quantum number of the OAM mode, and a high spectral degree of coherence of the source are robust for the OAM mode propagation in turbulence. The influences of the source characteristics and turbulent properties on the received power of the OAM mode are also analyzed in depth.

Closed-form impulse response model of non-line-of-sight single-scatter propagation.

Abstract: For optical scattering communication, a closed-form expression of channel impulse response (CIR) is favorable for further system design and channel capacity analysis. Combining the mean value theorem of integrals and L'Hopital's rule, the exact non-line-of-sight (NLOS) single-scatter propagation model is simplified to a closed-form CIR model for a laser source with a narrow beam. Based on this model, by joint geometrical and empirical approaches, a piecewise CIR expression is presented under certain system NLOS geometries. Through numerical results on CIR for various NLOS geometries, the proposed model is verified with the exact NLOS single-scatter propagation model and the previous Gamma fitting model, showing that our model agrees better with the former than the latter.

Propagation properties of Airy-Gaussian vortex beams through the gradient-index medium.

Abstract: Propagation of Airy-Gaussian vortex (AiGV) beams through the gradient-index medium is investigated analytically and numerically with the transfer matrix method. Deriving the analytic expression of the AiGV beams based on the Huygens diffraction integral formula, we obtain the propagate path, intensity and phase distributions, and the Poynting vector of the first- and second-order AiGV beams, which propagate through the paraxial ABCD system. The ballistic trajectory is no longer conventional parabolic but trigonometric shapes in the gradient-index medium. Especially, the AiGV beams represent the singular behavior at the propagation path and the light intensity distribution. The phase distribution and the Poynting vector exhibit in reverse when the AiGV beams through the singularity. As the order increases, the main lobe of the AiGV beams is gradually overlapped by the vortex core. Further, the sidelobe weakens when the AiGV beams propagate nearly to the singularity. Additionally, the figure of the Poynting vector of the AiGV beams proves the direction of energy flow corresponding to the intensity distribution. The vortex of the second-order AiGV beams is larger, and the propagation velocity is faster than that of the first order.

Rank-based camera spectral sensitivity estimation.

Abstract: In order to accurately predict a digital camera response to spectral stimuli, the spectral sensitivity functions of its sensor need to be known. These functions can be determined by direct measurement in the lab-a difficult and lengthy procedure-or through simple statistical inference. Statistical inference methods are based on the observation that when a camera responds linearly to spectral stimuli, the device spectral sensitivities are linearly related to the camera rgb response values, and so can be found through regression. However, for rendered images, such as the JPEG images taken by a mobile phone, this assumption of linearity is violated. Even small departures from linearity can negatively impact the accuracy of the recovered spectral sensitivities, when a regression method is used. In our work, we develop a novel camera spectral sensitivity estimation technique that can recover the linear device spectral sensitivities from linear images and the effective linear sensitivities from rendered images. According to our method, the rank order of a pair of responses imposes a constraint on the shape of the underlying spectral sensitivity curve (of the sensor). Technically, each rank-pair splits the space where the underlying sensor might lie in two parts (a feasible region and an infeasible region). By intersecting the feasible regions from all the ranked-pairs, we can find a feasible region of sensor space. Experiments demonstrate that using rank orders delivers equal estimation to the prior art. However, the Rank-based method delivers a step-change in estimation performance when the data is not linear and, for the first time, allows for the estimation of the effective sensitivities of devices that may not even have "raw mode." Experiments validate our method.

Open-geometry Fourier modal method: modeling nanophotonic structures in infinite domains.

Abstract: 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 to the continuous nature of the radiation modes are handled using a discretization based on nonuniform sampling of the k space. We apply the method to a variety of photonic structures and demonstrate that our method leads to significantly improved convergence with respect to the number of degrees of freedom, which may pave the way for more accurate and efficient modeling of open nanophotonic structures.

Increase of resolution by use of microspheres related to complex Snell's law.

Abstract: The increase of resolution by the use of microspheres is related to the use of evanescent waves satisfying complex Snell’s law with complex trigonometric functions related to the incident and refracted angles, while the refractive indices are real. The evanescent waves are obtained in addition to initial propagating waves satisfying the ordinary Snell’s law. The lateral spatial wave vectors of the evanescent waves, which include information on the object fine structures, are converted at the microsphere surface to smaller wave vectors. Due to the reduction in the magnitudes of the spatial wave vectors of the evanescent waves, they become propagating waves including the fine structures which are recovered in the image plane.

Reverse propagation and negative angular momentum density flux of an optical nondiffracting nonparaxial fractional Bessel vortex beam of progressive waves

Abstract: Energy and angular momentum flux density characteristics of an optical nondiffracting nonparaxial vector Bessel vortex beam of fractional order are examined based on the dual-field method for the generation of symmetric electric and magnetic fields. Should some conditions determined by the polarization state, the half-cone angle as well as the beam-order (or topological charge) be met, the axial energy and angular momentum flux densities vanish (representing Poynting singularities), before they become negative. These negative counterintuitive properties suggest retrograde (negative) propagation as well as a rotation reversal of the angular momentum with respect to the beam handedness. These characteristics of nondiffracting nonparaxial Bessel fractional vortex beams of progressive waves open new capabilities in optical tractor beam tweezers, optical spanners, invisibility cloaks, optically engineered metamaterials, and other applications.

Accurate rapid averaging of multihue ensembles is due to a limited capacity subsampling mechanism.

Abstract: It is claimed that the extraction of average features from rapidly presented ensembles is holistic, with attention distributed across the whole set. We investigated whether observers’ extraction of mean hue is holistic or could reflect subsampling. Analysis of selections for the mean hue revealed a distribution that peaked at the expected mean hue. However, an ideal observer simulation suggested that a subsampling mechanism incorporating just two items from each ensemble would suffice to reproduce the precision of most observers. The results imply that hue may not be averaged as holistically and efficiently as other attributes.