Stepwise angular spectrum method for curved surface diffraction

Hwang, Chi-Young; Oh, Sangeun; Jeong, Il-Kwon; Kim, Hwi

doi:10.1364/oe.22.012659

Cited by 13 publications

(3 citation statements)

References 15 publications

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“…Electromagnetic waves that pass curved surfaces interchanging between refractive indices can be modeled using the staircase method [1], where, for example, the propagation distance is chopped into several subdistances and the x; y section is separated into some areas with refractive index n 1 and others with n 2 . By stating that we have large field extents and large distances to propagate, we like to avoid the staircase approach in order to have a fast and efficient computation algorithm.…”

Section: Literature Historymentioning

confidence: 99%

Generalized propagation of light through optical systems I Mathematical basics

Tessmer

Groß

2015

J. Opt. Soc. Am. A

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The propagation of an input field through tilted and curved surfaces is presented and applied for a field tracing routine. This routine employs a ray tracing method for optimal coordinate customization, which is done due to the strong linear phase terms that arise because of tilted coordinates on one hand and the possibility of an application of fast numerical routines on the other. Several methods are proposed on how to optimize the field sampling during the propagation process, as for the astigmatic phase front problem and the curvature of the surface itself. Two solution methods are given to propagate from the curved surface through the homogeneous space to another two-dimensional submanifold. The approach is fully vectorial, Maxwell exact excluding only surface curvature terms for the Fresnel coefficients. A simple numerical propagation example is given.

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Section: Literature Historymentioning

confidence: 99%

Generalized propagation of light through optical systems I Mathematical basics

Tessmer

Groß

2015

J. Opt. Soc. Am. A

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“…However, most of the sound field calculation methods achieving by integral or finite element analysis may encounter the problem of cumbersome calculation or singularity. Those analytic solutions involve Rayleigh-Sommerfield integral method (Song and Kim, 2002), edge element method (Rahani and Kundu, 2011), angular spectrum method (Hwang et al, 2014), and distributed point source method (Banerjee et al, 2007). By comparison, the multi-Gaussian beam (MGB) model used in this paper has certain advantages in explicit ultrasonic field evaluation because of its high computational efficiency and calculation accuracy (Huang et al, 2005).…”

Section: Introductionmentioning

confidence: 99%

Ultrasonic field analysis with local interface curvature effect based on the multi-Gaussian beam model

Lyu

Gao

et al. 2022

Journal of Vibration and Control

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In ultrasonic testing, the amplitude of echoes is determined by the sound pressure along the acoustic axis. When the workpiece has a local curved surface, the ultrasonic field redistribution has a close relationship with the curvature of the incident local region, which raises questions of testing validity and accuracy. In order to develop the curvature adaptation window for a given test condition, the influence of local curved interface on the ultrasonic transmission and reflection field is analyzed quantitatively in this paper. Based on the multi-Gaussian beam model, the distribution of transmitted and reflected sound pressure in the local curved region is calculated by using matrix transformation technique. Furthermore, the relationship between interface curvature and sound pressure along the acoustic axis is obtained. To validate the accuracy of proposed calculation model, developed relationship has been compared against a finite element method computed using COMSOL Multiphysics. It is indicated that the proposed calculation model is more efficient and the regular changes of sound pressure are basically consistent with that of finite element method.

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“…The angular spectrum representation is the most popular formula for optical wave propagation in free space and known as a perfect analytic solution of arbitrary free space optical scalar wave field. In practice, the numerical model derived from the angular spectrum representation is calculated and visualized in the discrete spatial sampling grids [10,11]. Theoretically, the angular spectrum representation is the linear and coherent superposition of infinitely extended plane wave basis with complex amplitude.…”

Section: Introductionmentioning

confidence: 99%

Numerical visualization of aperiodic scalar optical wave fields

2017

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In numerical wave optic simulations using the conventional angular spectrum method, numerical inter-periodic interference occurs as a result of the inherent periodicity of the discrete Fourier transform. In this paper, we propose an aperiodic angular spectrum representation of a scalar optical wave field without numerical inter-periodic interference in an aperiodic area. The visualization of holographic three-dimensional image light field is presented for the validity of the proposed method. It is believed that the proposed method can be broadly applied to visualization of scalar optical wave field represented by the angular spectrum plane wave bases.

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Stepwise angular spectrum method for curved surface diffraction

Cited by 13 publications

References 15 publications

Generalized propagation of light through optical systems I Mathematical basics

Generalized propagation of light through optical systems I Mathematical basics

Ultrasonic field analysis with local interface curvature effect based on the multi-Gaussian beam model

Numerical visualization of aperiodic scalar optical wave fields

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