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Parabasal Formulas and their Applications

Sunggoo Cho

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

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

Single freeform surface design for prescribed input wavefront and target irradiance

Christoph Bösel and Herbert Gross

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

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

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

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

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

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

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

Razvigor Ossikovski and Jose Gil

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

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

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

Elisabeth Brunner, Cornelis De Visser, and Michel Verhaegen

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

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

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

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

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

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

A simple approach to the generalized Minkwitz theorem

Ralf Blendowske

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

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

Automatic identification of fungi in microscopicleucorrhea images

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

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

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

Bandwidth Correction in the Spectral Measurement ofLight Emitting Diodes

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

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

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

Improving Color Constancy by Discounting the Variation of Camera Spectral Sensitivity

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

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

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

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

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

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

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

Perceptually Optimized Image Rendering

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

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

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

Self-focusing of a partially coherent beam with circular coherence

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

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

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

Quasimonochromatic modes of quasistationary, pulsed scalar optical fields

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

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

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

Differential Piston Phase Variance in Non-Kolmogorov Atmospheres

Jeremy Bos, Venkata Gudimetla, and Jason Schmidt

Doc ID: 291947 Received 24 Apr 2017; Accepted 25 Jun 2017; Posted 28 Jun 2017  View: PDF

Abstract: We derive a generalized expression for the differential piston phase variance in non-Kolmogorov turbulence. Specifically, our result applies in the case where index of refraction is described by a power-law medium with an exponent between 0 and 1. Kolmogorov assumptions of homogeneity and isotropy are maintained. After some development, our expression is derived using the Mellin transform techniques and may be generalized to other forms for the three-dimensional index of refraction turbulence power spectrum. This analytical result has two regions of convergence. The separation between these regions is defined by a characteristic time given as the ratio of the mean wind speed and aperture size. By evaluating this expression, we find the differential piston phase variance exhibits a power-law behavior roughly proportional to that of the medium. In addition, we find that piston phase variance decreases with increase in aperture size. We also find that the differential piston phase variance is independent of aperture size as the power-law approaches unity.

Centralized Inverse-Fano Distribution for Controlling Conversion Gain Measurement Accuracy of Detector Elements

Aaron Hendrickson

Doc ID: 285179 Received 18 Jan 2017; Accepted 13 Jun 2017; Posted 14 Jun 2017  View: PDF

Abstract: Statistical theory is applied to derive the exact distribution of the Photon Transfer conversion gain measurement for detector elements. This previously uncharacterized distribution is confirmed by experiment, thus confirming the theory and enhancing the credibility of the statistical model used. Analysis of the statistical distance between the derived functions and computationally fast approximate forms is carried out to determine the conditions when such approximations are useful. Theoretical results are then applied to develop algorithms for use in live experiments to calculate appropriate sample sizes for measuring the conversion gain given a user-specified acceptable uncertainty.

Transparency in stereopsis: parallel encoding of overlapping depth planes

Adam James Reeves and David Lynch

Doc ID: 270140 Received 27 Sep 2016; Accepted 10 Jun 2017; Posted 12 Jun 2017  View: PDF

Abstract: We report that after extensive training, expert adults can accurately report the number, up to 6, of transparent overlapping depth planes portrayed by brief (400ms or 200ms) random-element stereoscopic displays, and can well discriminate 6 from 7 planes. Naïve subjects did poorly above 3 planes. Displays contained seven rows of 12 randomly located x’s or +’s with disparities from 3’ to 214’; jittering the disparities and number in each row to remove spurious cues had little effect on accuracy. Removing the central 3o of the 10o display to eliminate foveal vision hardly reduced the number of reportable planes. Experts could report how many of 6 planes contained +’s when the remainder contained x’s, and most learnt to report up to 6 planes in reverse contrast (left eye white +’s; right eye black +’s). Long-term training allowed some experts to reach 8 depth planes. Results suggest that adult stereoscopic vision can learn to distinguish the outputs of six or more statistically independent, contrast-insensitive, narrowly-tuned, asymmetric disparity channels, in parallel.

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