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Riemann Problem for a Geometrical Optics System

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Acta Mathematica Sinica,English Series 2014年第11期30卷 1846-1860页

作者： Han Chun YANG Hong Jun CHENG Department of Mathematics Yunnan University

The paper solves analytically the Riemann problem for a nonstrictly hyperbolic system of conservation laws arising in Geometrical Optics,in which the flux contains the nonconvex function possessing an infinite number of inflection points.Firstly,the generalized Rankine–Hugoniot relations and entropy condition of delta shock waves and left（right）-contact delta shock waves are proposed and clarified.Secondly,with the help of the convex hull,seven kinds of structures of Riemann solutions are obtained.The solutions fall into three broad categories with a series of geometric structures involving simultaneously contact discontinuities,vacuums and delta shock waves.Finally,numerical experiments confirm the theoretical analysis.

关键词： Geometrical Optics Riemann problem delta shock wave vacuum convex hull

Case study:A simple optical inverse problem from a Geometrical Optics point of view

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Journal of Advanced Dielectrics 2019年第2期9卷 56-62页

作者： Anshi Yan Yangjie Liu Wenfeng Wang School of Physics and Electronic Science Physics Building Hubei University Wuhan 430062P.R.China

In this paper,we revisit the simple problem of reflection from a dielectric sphere for light rays and define a form of optical inverse problem in the sense of Geometrical Optics(GO).A general analytic formula is derived to obtain the refraction index of the sphere for any incidence light to emerge in a deflected angle.Numerical wave simulation and ray tracing are performed to verify the inverse formulae derived.

关键词： Inverse problem Geometrical Optics metamaterials

Linking Diffractive and Geometrical Optics Surface Scattering at a Fundamental Level

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optics and Photonics Journal 2022年第1期12卷 1-17页

作者： Christi Kay Madsen Department of Electrical and Computer Engineering Texas A&M University College Station TX USA

Optical surface scattering analyses based on diffractive optics (DO) are typically applied to one surface;however, there is a need for simulating surface scattering losses for devices having many surface interactions such as light pipes. Light pipes are often simulated with geometric optics (GO) using ray tracing, where surface scattering is driven by the surface slope distribution. In the DO case, surface scattering analyses depend on the spatial frequency distribution and amplitude as well as wavelength, with the sinusoidal grating as a fundamental basis. A better understanding of the link, or transition, between DO and GO scattering domains would be helpful for efficiently incorporating scattering loss analyses into ray trace simulations. A formula for the root-mean-square (rms) scattered angle width of a sinusoidal reflection grating that depends only on the surface rms slope is derived from the nonparaxial scalar diffraction theory, thereby linking it to GO. The scatter angle’s mean and rms width are evaluated over a range of grating amplitudes and periods using scalar theory and full vector simulations from the COMSOL® wave optic module for a sinusoidal reflection grating. The conditions under which the diffraction-based solution closely approximates the GO solution, as predicted by the rms slope, are identified. Close agreement is shown between the DO and GO solutions for the same surface rms slope scattering loss due to angular filtering near the critical angle of a total internal reflection (TIR) glass-to-air interface.

关键词： Diffractive optics Geometrical Optics Diffraction Gratings Surface Scattering Light Pipes

HMO in Geometrical Optics

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Chinese Journal of Lasers 1994年第4期3卷 347-350页

作者： GUO Hong LIN Tao WANG Gang ZHANG Yuansheng DENG Ximing (1. Nafional Laboratory on High Power Laser and Physics,Shanghai Institute of optics & Fine Mechanics,P. O. Box 800-211,Shanghai 201800,China)(2. Department of Physics, University of Science & Technol Shanghai Inst of optics and Fine Mechanics Acad Sinica Shanghai China

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关键词： Geometrical Optics hydrodynamical model of optics nonlinear medium

Design of a dynamic refocus system based on the Seidel aberration theory

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Chinese optics Letters 2016年第4期14卷 64-68页

作者：邵丽娜曹召良穆全全胡立发王玉坤王少鑫宣丽 State Key Laboratory of Applied optics Changchun Institute of Optics Fine Mechanics and Physics Chinese Academy of Sciences Changchun 130033 China University of Chinese Academy of Sciences Beijing 100049 China

This Letter presents an optical design method based on the Seidel aberration theory for dynamic refocus systems. The function of a dynamic refocus system is to increase the amount of return photons when a pulsed laser travels over an extended height range. In this study, the dynamic refocus system is a short focal image system. The aberrations of the dynamic refocus system are calculated individually. Aplanatic lenses are used to eliminate the main spherical aberration. A field lens is used to change the stop position in order to eliminate comas and astigmatism. The effectiveness of the initial design results are confirmed, and the designed dynamic refocus objective with an aperture of F-number 0.98 and a focal length of 14.325 mm is achieved. The total motion of the dynamic refocus mirror is approximately 216 pm at heights that ranged from 8 to 18 kin. The optimum result shows that the dynamic refocus system is an ideal optical image system at each conjugating height with 10 km sample thicknesses.

关键词： Geometrical Optics Optical design

Spiral spectrum of Airy-Schell beams through non-Kolmogorov turbulence

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Chinese optics Letters 2016年第4期14卷 54-58页

作者：朱云章里程张逸新 School of IoT Engineering Jiangnan University School of Science Jiangnan University

Based on the Geometrical Optics approximation, we analyze the effects of non-Kolmogorov turbulence on the spiral spectrum of the orbital angular momentum （OAM） of Airy-Schell beams. Our numerical results of Airy-Schell beams on the horizontal path show that the beam spreading due to diffraction is smaller for shorter wavelengths, a smaller OAM quantum number, a larger radius of the main ring, and a higher arbitrary trans- verse scale in weak turbulence. The oscillation frequency of the mode probability density of Airy-Schell beams in the radial direction is much lower than that of Hankel-Bessel beams. The mode probability densities of Airy-Schell and HankM-Bessel beams are remarkably dependent on the wavelength and OAM quantum num- ber. In order to improve the mode probability density, Airy-Schell beams with shorter wavelengths and lower OAM quantum numbers may be the better choice, which is diametrically opposite to Hankel-Bessel beams. Our research provides a reasonable basis for selecting light sources and precise tracking.

关键词： Bessel functions Geometrical Optics Laser beams Light sources Probability Quantum theory Spectrum analysis Turbulence Turbulence models

Demonstration of full-parallax three-dimensional holographic display on commercial 4 K flat-panel displayer

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Chinese optics Letters 2016年第1期14卷 26-30页

作者： Frank C. Fan Sam Choi C. C. Jiang AFC Technology Co. Ltd. Shenzhen 518104 China

A novel method for a full-parallax three-dimensional （3D） holographic display by means of a lens array and a holographic functional screen is proposed. The process of acquisition, coding, restoration, and display is described in detail. It provides an efficient way to transfer the two-dimensional redundant information for human vision to the identifiable 3D display for human eyes. A holo-video system based on a commercial 4 K fiat-panel displayer is demonstrated as the result.

关键词： Geometrical Optics Holography

High dense views auto-stereoscopic three-dimensional display based on frontal projection with LLA and diffused screen

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Chinese optics Letters 2015年第1期13卷 46-48页

作者：赵天奇桑新柱于迅博高鑫王鹏刘养东谢松林颜玢玢余重秀徐大雄 State Key Laboratory of Information Photonics and Optical Communications Beijing University of Posts and Telecommunications

We present a high dense views auto-stereoscopic three-dimensional display method with the projectors array and lenticular lens array （LLA） screen. The principle and configuration are demonstrated. This display method utilizes lenticular screen to modulate the information of projectors. To increase the dense of views, we propose a novel arrangement way of projectors array. In the experiment, the viewer can obtain smooth motion parallax and evident stereo feeling at optimal distance. Through analyzing and observation, the maximum display depth is found to be more than 50 cm.

关键词： Geometrical Optics

High optical-efficiency integral imaging display with a gradient-aperture parallax barrier

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Chinese optics Letters 2013年第7期11卷 34-36页

作者：吴非王琼华邓欢罗成高李大海 School of Electronics and Information Engineering Sichuan University Department of Communication Engineering Chengdu Technological University

We propose a one-dimensional integral imaging （1DII） display that consists of a display panel and a gradient-aperture parallax barrier. The gradient-aperture parallax barrier is symmetrical, and its slit widths gradually increase from both sides to the middle. The leftmost and rightmost slits are used to fix the viewing angle, whereas the other slits are used to increase the optical efficiency. A prototype of the proposed 1DII display is developed. Its optical efficiency is higher than that of the conventional display, but the viewin~ an^les are the same.

关键词： Geometrical Optics