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Double freeform surfaces design for laser beam shaping with Monge-Ampere equation method

OPTICS COMMUNICATIONS 2014年 331卷 297-305页

作者： Zhang, Yaqin Wu, Rengmao Liu, Peng Zheng, Zhenrong Li, Haifeng Liu, Xu Zhejiang Univ Dept Opt Engn State Key Lab Modern Opt Instrumentat Hangzhou 310027 Zhejiang Peoples R China Univ Politecn Madrid Cedint Madrid 28223 Spain

This paper presents a method for designing double freeform surfaces to simultaneously control the intensity distribution and phase profile of the laser beam. Based on Snell's law, the conservation law of energy and the constraint imposed on the optical path length between the input and output wavefronts, the double surfaces design is converted into an elliptic Monge-Ampere (MA) equation with a nonlinear boundary problem. A generalized approach is introduced to find the numerical solution of the design model. Two different layouts of the beam shaping system are introduced and detailed comparisons are also made between the two layouts. Design examples are given and the results indicate that good matching is achieved by the MA method with more than 98% of the energy efficiency. The MA method proposed in this paper provides a reasonably good means for laser beam shaping. (C) 2014 Elsevier B.V. All rights reserved.

关键词： Nonimaging optics Aspherics computation methods Laser beam shaping

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Nonlinear differential equations for the wavefront surface at arbitrary Hartmann-plane distances

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APPLIED OPTICS 2016年第9期55卷 2160-2168页

作者： Tellez-Quinones, Alejandro Malacara-Doblado, Daniel Flores-Hernandez, Ricardo Gutierrez-Hernandez, David A. Leon-Rodriguez, Miguel Ctr Invest Opt AC Loma del Bosque 115 Col Lomas del Campestre Leon Guanajuato 37150 Mexico Inst Tecnol Leon Div Estudios Posgrad & Invest Ave Tecnol S-N Col Ind J Obregon Leon Guanajuato 37290 Mexico Univ Santiago Chile Ave Lib Bdo OHiggins 3363 Santiago 917002 Chile Univ Politecn Bicentenario Carretera Silao Romita Km 2 Silao Guanajuato 36283 Mexico

In the Hartmann test, a wave aberration function W is estimated from the information of the spot diagram drawn in an observation plane. The distance from a reference plane to the observation plane, the Hartmann-plane distance, is typically chosen as z = f, where f is the radius of a reference sphere. The function W and the transversal aberrations {X, Y} calculated at the plane z = f are related by two well-known linear differential equations. Here, we propose two nonlinear differential equations to denote a more general relation between W and the transversal aberrations {U, V} calculated at any arbitrary Hartmann-plane distance z = r. We also show how to directly estimate the wavefront surface w from the information of {U, V}. The use of arbitrary r values could improve the reliability of the measurements of W, or w, when finding difficulties in adequate ray identification at z = f. (C) 2016 Optical Society of America

关键词： Numerical approximation and analysis Geometric optics Mathematical methods (general) computation methods Lenses Testing

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Three-dimensional ray tracing in spherical and elliptical generalized Luneburg lenses for application in the human eye lens

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APPLIED OPTICS 2016年第8期55卷 2002-2010页

作者： Gomez-Correa, J. E. Coello, V. Garza-Rivera, A. Puente, N. P. Chavez-Cerda, S. Ctr Invest Cient & Educ Super Ensenada Unidad Monterrey Alianza Ctr 504 Piit Apodaca 66629 Nuevo Leon Mexico Inst Nacl Astrofis Opt & Electr Luis Enrique Erro 1 Puebla 72840 Mexico Univ Autonoma Nuevo Leon Fac Ingn Mecan & Elect Ave Univ S-N San Nicolas De Los Garza 66451 Nuevo Leon Mexico Ctr Invest Opt Loma Bosque 115 Leon 37150 Gto Mexico

Ray tracing in spherical Luneburg lenses has always been represented in 2D. All propagation planes in a 3D spherical Luneburg lens generate the same ray tracing, due to its radial symmetry. A geometry without radial symmetry generates a different ray tracing. For this reason, a new ray tracing method in 3D through spherical and elliptical Luneburg lenses using 2D methods is proposed. The physics of the propagation is shown here, which allows us to make a ray tracing associated with a vortex beam. A 3D ray tracing in a composite modified Luneburg lens that represents the human eye lens is also presented. (C) 2016 Optical Society of America

关键词： Inhomogeneous optical media computation methods Ray trajectories in inhomogeneous media Gradient-index lenses Vision color and visual optics Visual optics modeling

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Regularizing active set method for retrieval of the atmospheric aerosol particle size distribution function

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JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION 2008年第2期25卷 348-356页

作者： Wang, Yanfei Yang, Changchun Chinese Acad Sci Inst Geol & Geophys Beijing 100029 Peoples R China

The determination of the aerosol particle size distribution function by using the particle spectrum extinction equation is an ill-posed integral equation of the first kind [S. Twomey, J. Comput. Phys. 18, 188 (1975);Y. F. Wang, computational methods for Inverse Problems and Their Applications (Higher Education Press, 2007)], since we are often faced with limited or insufficient observations in remote sensing and the observations are contaminated. To overcome the ill-posed nature of the problem, regularization techniques were developed. However, most of the literature focuses on the application of Phillips-Twomey regularization and its variants, which are unstable in several cases. As is known, the particle size distribution is always nonnegative, and we are often faced with incomplete data. Therefore, we study the active set method and propose a regularizing active set algorithm for ill-posed particle size distribution function retrieval and for enforcing nonnegativity in computation. Our numerical tests are based on synthetic data for theoretical simulations and the field data obtained with a CE 318 Sun photometer for the Po Yang lake region of Jiang Xi Province, China, and are performed to show the efficiency and feasibility of the proposed algorithms. (C) 2008 Optical Society of America.

关键词： computation methods Computed tomography Extinction coefficients Inverse problems Mie theory Remote sensing

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Improved Dirichlet-to-Neumann map method for scattering by circular cylinders on a lattice

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JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION 2012年第9期29卷 1999-2004页

作者： She, Shichang Lu, Ya Yan City Univ Hong Kong Dept Math Kowloon Hong Kong Peoples R China

A simple model for two-dimensional photonic crystal devices consists of a finite number of possibly different circular cylinders centered on lattice points of a square or triangular lattice and surrounded by a homogeneous or layered background medium. The Dirichlet-to-Neumann (DtN) map method is a special method for analyzing the scattering of an incident wave by such a structure. It is more efficient than existing numerical or semianalytic methods, such as the finite element method and the multipole method, since it takes advantage of the underlying lattice structure and the simple geometry of the unit cells. The DtN map of a unit cell is a relation between a wave field component and its normal derivative on the cell boundary, and it can be used to avoid further computation inside the unit cell. In this paper, an improved DtN map method is developed by constructing special DtN maps for boundary and corner unit cells using the method of fictitious sources. (C) 2012 Optical Society of America

关键词： computation methods Finite difference time domain Numerical simulation Photonic crystals Refractive index Scattering

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computation theory of partially coherent imaging by stacked pupil shift matrix

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JOURNAL OF THE OPTICAL SOCIETY OF AMERICA A-OPTICS IMAGE SCIENCE AND VISION 2008年第12期25卷 3111-3119页

作者： Yamazoe, Kenji Canon Inc Utsunomiya Tochigi 3213298 Japan

A theory of partially coherent imaging is presented. In this theory, a singular matrix P is introduced in a spatial frequency domain. The matrix P can be obtained by stacking pupil functions that are shifted according to the illumination condition. Applying singular-value decomposition to the matrix P generates eigenvalues and eigenfunctions. Using eigenvalues and eigenfunctions, the aerial image can be computed without the transmission cross coefficient (TCC). A notable feature of the matrix P is that the relationship between the matrix P and the TCC matrix T isT=P(dagger)P, where dagger represents the Hermitian conjugate. This suggests that the matrix P can be regarded as a fundamental operator in partially coherent imaging. (C) 2008 Optical Society of America

关键词： computation methods Light intensity Matrix methods Pupil Spatial frequency Transmission coefficient

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Application of T-matrix method in solving mixed boundary separable obstacle problem

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OPTICS EXPRESS 2014年第13期22卷 16273-16281页

作者： Ye, Xiuzhu Song, Rencheng Chen, Xudong Beihang Univ Dept Elect & Comp Engn Beijing 100191 Peoples R China Natl Univ Singapore Dept Elect & Comp Engn Singapore 117576 Singapore

The practical problem of imaging scatterers enclosed by separable obstacles with mixed boundary is addressed. Both the unknown scatterers and the known obstacle media can be mixture of dielectric and perfect electric conducting (PEC) materials. The scattering phenomenon of such problem is well modeled by T-matrix method. By usage of separable prior information, the obstacle media are treated as known scatterers rather than part of the background. The number of unknowns is thus reduced greatly. After recovering the profiles of scatterers by T-matrix method, a criterion is further provided to classify the PEC and dielectric scatterers. Various numerical examples are presented to show the effectiveness and good performance of the method. (C)2014 Optical Society of America

关键词： computation methods Image storage Inverse problems Medical imaging Optical fibers Remote sensing

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Fast and accurate spectral-estimation axial super-resolution optical coherence tomography

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OPTICS EXPRESS 2021年第24期29卷 39946-39966页

作者： de Wit, Jos Angelopoulos, Kostas Kalkman, Jeroen Glentis, George-Othon Delft Univ Technol Dept Imaging Phys NL-2028 CJ Delft Netherlands Univ Peloponnese Dept Informat & Telecommun Tripolis 22100 Greece

Spectral-estimation OCT (SE-OCT) is a computational method to enhance the axial resolution beyond the traditional bandwidth limit. However, it has not yet been used widely due to its high computational load, dependency on user-optimized parameters, and inaccuracy in intensity reconstruction. In this study, we implement SE-OCT using a fast implementation of the iterative adaptive approach (IAA). This non-parametric spectral estimation method is optimized for use on OCT data. Both in simulations and experiments we show an axial resolution improvement with a factor between 2 and 10 compared to standard discrete Fourier transform. Contrary to parametric methods, IAA gives consistent peak intensity and speckle statistics. Using a recursive and fast reconstruction scheme the computation time is brought to the sub-second level for a 2D scan. Our work shows that SE-OCT can be used for volumetric OCT imaging in a reasonable computation time, thus paving the way for wide-scale implementation of superresolution OCT. (C) 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

关键词： computation methods Image quality Medical imaging Phase estimation Real time imaging Spectroscopy

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Discrete linear canonical transform computation by adaptive method

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OPTICS EXPRESS 2013年第15期21卷 18138-18151页

作者： Zhang, Feng Tao, Ran Wang, Yue Beijing Inst Technol Dept Elect Engn Beijing 100081 Peoples R China

The linear canonical transform (LCT) describes the effect of quadratic phase systems on a wavefield and generalizes many optical transforms. In this paper, the computation method for the discrete LCT using the adaptive least-mean-square (LMS) algorithm is presented. The computation approaches of the block-based discrete LCT and the stream-based discrete LCT using the LMS algorithm are derived, and the implementation structures of these approaches by the adaptive filter system are considered. The proposed computation approaches have the inherent parallel structures which make them suitable for efficient VLSI implementations, and are robust to the propagation of possible errors in the computation process. (C) 2013 Optical Society of America

关键词： computation methods Fourier transforms Signal synthesis Three dimensional television Transforms Wave propagation

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Characterization of complex plasmonic modes in two-dimensional periodic arrays of metal nanospheres

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JOURNAL OF THE OPTICAL SOCIETY OF AMERICA B-OPTICAL PHYSICS 2011年第6期28卷 1446-1458页

作者： Fructos, Ana L. Campione, Salvatore Capolino, Filippo Mesa, Francisco Univ Calif Irvine Dept Elect Engn & Comp Sci Irvine CA 92697 USA Univ Seville Coll Phys Dept Elect & Electromagnetism E-41012 Seville Spain Univ Seville ETS Ingn Informat Dept Appl Phys 1 E-41012 Seville Spain

Two-dimensional periodic arrays of noble metal nanospheres support a variety of optical phenomena, including bound and leaky modes of several types. The scope of this paper is the characterization of the modal dispersion diagrams of planar arrays of silver nanospheres, with the ability to follow individual modal evolutions. The metal spherical nanoparticles are described using the single dipole approximation technique by including all the retarded dynamic field terms. Polarizability of the nanospheres is provided by the Mie theory. Dispersion diagrams for both physical and nonphysical modes are shown for a square lattice of Ag nanospheres for the case of lossless and lossy metal particles, with dipole moments polarized along the x, y, and z directions. Though an array with one set of parameters has been studied, the analysis method and classification are general. The evolution of modes through different Riemann sheets and analysis of guidance and radiation are studied in detail. (C) 2011 Optical Society of America

关键词： Analytical techniques computation methods Mie theory Modal dispersion Optical properties Raman spectroscopy

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