An indirect algorithm of Fresnel diffraction

Li, Junchang; Wu, Yanmei

doi:10.1016/j.optcom.2008.10.060

Cited by 17 publications

(13 citation statements)

References 5 publications

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“…(4) and then in the second line expand each quadratic term. (This trick, common to "single FFT" methods, 11,13,23 is similar to, but essentially the reverse of, that in the Bluestein method. 40 ) This gives E Q -T A R G E T ; t e m p : i n t r a l i n k -; e 0 0 7 ; 1 1 6 ; 4 9 9…”

Section: Fast Algorithm For Diffraction To Arbitrary Target Pointsmentioning

confidence: 94%

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Efficient high-order accurate Fresnel diffraction via areal quadrature and the nonuniform fast Fourier transform

Barnett

2021

J. Astron. Telesc. Instrum. Syst.

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We present a fast algorithm for computing the diffracted field from arbitrary binary (sharp-edged) planar apertures and occulters in the scalar Fresnel approximation for up to moderately high Fresnel numbers (≲10 3). It uses a high-order areal quadrature over the aperture and then exploits a single 2D nonuniform fast Fourier transform to evaluate rapidly at target points (on the order of 10 7 such points per second, independent of aperture complexity). It thus combines the high accuracy of edge integral methods with the high speed of Fourier methods. Its cost is Oðn 2 log nÞ, where n is the linear resolution required in the source and target planes, to be compared with Oðn 3 Þ for edge integral methods. In tests with several aperture shapes, this translates to between two and five orders of magnitude acceleration. In starshade modeling for exoplanet astronomy, we find that it is roughly 10 4 × faster than the state-of-the art in accurately computing the set of telescope pupil wavefronts. We provide a documented, tested MATLAB/ Octave implementation. An appendix shows the mathematical equivalence of the boundary diffraction wave, angular integration, and line integral formulas and then the analysis of a new nonsingular reformulation that eliminates their common difficulties near the geometric shadow edge. This supplies a robust edge integral reference against which to validate the main proposal. © The Authors. Published by SPIE under a Creative Commons Attribution 4.0 Unported License. Distribution or reproduction of this work in whole or in part requires full attribution of the original publication, including its DOI.

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Section: Fast Algorithm For Diffraction To Arbitrary Target Pointsmentioning

confidence: 94%

“…There are two types: (i) methods implementing the convolution theorem (forward then backward FFTs), useful only for large f (nearfield), or (ii) methods exploiting the quadratic form in Eq. (1) via a single FFT, 11,13,23 useful from zero to moderate f. See Ref. 24 for a review, in which fractional FFTs are also considered.…”

Section: Introductionmentioning

confidence: 99%

Efficient high-order accurate Fresnel diffraction via areal quadrature and the nonuniform fast Fourier transform

Barnett

2021

J. Astron. Telesc. Instrum. Syst.

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“…A very simple way of obtaining MMW beam images in the visible region is based on the utilization of thermal papers. However, only rough time-integrated images of the field profiles of high-energy MMW beams can be obtained by using thermal paper [19]. In another variant of the thermographic technique, a flat sheet of dielectric material (e.g., paper, polyvinylchloride) is used as an absorbing screen for MMWs [20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

A Technique for Time-Resolved Imaging of Millimeter Waves Based on Visible Continuum Radiation from a Cs-Xe DC Discharge — Fundamentals and Applications

Gitlin¹

2016

Plasma Science and Technology - Progress in Physical States and Chemical Reactions

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The chapter presents a review of a highly sensitive technique for time-resolved imaging and measurement of the 2D intensity profiles of millimeter waves (MMW) based on the use of visible continuum radiation (VCR) from the positive column (PC) of a medium pressure Cs-Xe DC discharge (VCRD technique). The review focuses on the operating principles, fundamentals, and applications of this new technique. The design of a discharge tube and an experimental setup which were used to create a wide homogeneous PC plasma slab are described. The MMW effects on the plasma slab are studied. The mechanism of microwave-induced variations in the VCR intensity and the causes of violation of the local relation between the visible continuum emissivity and the MMW intensity are discussed. The main characteristics, e.g., spatial and temporal resolution, and sensitivity of the VCRD technique have been evaluated. Experiments on imaging of the field patterns of horn antennas and quasioptical beams demonstrated that the VCRD technique can be used for a good-quality imaging of the MMW beams in the entire MMwavelength band. The VCRD technique was applied for imaging of output field patterns of the MMW electron tubes and determination of some of their characteristics, as well as for active real-time imaging and nondestructive testing using MM waves.

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“…Over the Fresnel approximation the same approaches to determine a complex amplitude of light in an output plane are used [10][11][12][13] . One of them is direct calculation of convolution form of the Fresnel-Kirchhoff diffraction integral.…”

Section: Introductionmentioning

confidence: 99%

“…One of them is direct calculation of convolution form of the Fresnel-Kirchhoff diffraction integral. In the next possible approach, instead of directly calculating of the integral, one can find the angular spectrum (Fourier transform) of input matrix of the complex numbers and the transfer function of free-space propagation and, multiplying them, perform an inverse Fourier transform to obtain the final result [10][11][12][13] .…”

Section: Introductionmentioning

confidence: 99%

Computer simulation of the speckle field propagation

Hamarová

Horváth

Šmı́d

et al. 2010

17th Slovak-Czech-Polish Optical Conference on Wave and Quantum Aspects of Contemporary Optics

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There is presented a simulation of the speckle propagation by means of a computer in this paper. The model is designed for in-plane translation of an object generating speckle field. There is used the Fresnel-Kirchhof diffraction theory for description of the speckle field propagation. The presented numerical model involves detection of speckle pattern at any observation angles. The model is verified through a method of correlation of speckle fields which results are compared to ones provided by theoretical relations.

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An indirect algorithm of Fresnel diffraction

Cited by 17 publications

References 5 publications

Efficient high-order accurate Fresnel diffraction via areal quadrature and the nonuniform fast Fourier transform

Efficient high-order accurate Fresnel diffraction via areal quadrature and the nonuniform fast Fourier transform

A Technique for Time-Resolved Imaging of Millimeter Waves Based on Visible Continuum Radiation from a Cs-Xe DC Discharge — Fundamentals and Applications

Computer simulation of the speckle field propagation

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