FFT calculation for Fresnel diffraction and energy conservation criterion of sampling quality

Li, Junchang; Fan, Zebin; Fu, Yunchang

doi:10.1117/12.482883

Cited by 6 publications

(5 citation statements)

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“…In such case, aliasing probably appears when calculating the longitudinal component. One solution of this problem is to select larger computational window, the other is to utilize FFT‐based direct integration method [1, 3] to calculate the field distributions on the target planes from temporary planes 2 and 3, and the vectorial transfer functions are given as Eqs. (23) and (24).…”

Section: Discussionmentioning

confidence: 99%

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Fast analysis of arbitrary beam through planar multilayer structures

Liang

Bai

et al. 2012

Micro & Optical Tech Letters

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In this article, a fast and accurate method is presented for analyzing the interaction between arbitrary oriented finite beams over planar multilayer structures.The method is based on Transfer Matrix algorithm and optical fast‐Fourier‐transform based angular spectrum method. Full vectorial near‐fields of electromagnetic beam refracted and reflected by the multilayer can be calculated within several seconds. A numerical simulation in FEKO and an experiment are respectively implemented, and good agreement compared with the hybrid method is obtained. The method can be used in the design process of the multilayer with big amount of parameter adjustment, and then full‐wave simulation can be adopted to get exact results. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 54:2185–2190, 2012; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27014

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Section: Discussionmentioning

confidence: 99%

“…The propagation and diffraction of light in an isotropic, homogenous linear medium has been widely discussed in many optical literatures [1–5]. The Rayleigh–Sommerfeld (RS) diffraction formula is an approach to give exact solutions of such problem without any approximations.…”

Section: Introductionmentioning

confidence: 99%

Fast analysis of arbitrary beam through planar multilayer structures

Liang

Bai

et al. 2012

Micro & Optical Tech Letters

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“…The energy of the main lobe is higher than the sidelobe in the focusing plane, and the acoustic meta-lens has a subwavelength spatial resolution beyond the diffraction limit. Based on the Rayleigh-Somerfield (RS, Rayleigh-Somerfield) theory in the optical theory system [ [33][34][35]], the formula for the diffraction sound field (z > 0) beyond the acoustic metalens structure can be expressed as…”

Section: Methodsmentioning

confidence: 99%

Helmholtz-Structured Two-Dimensional Super-Diffraction Meta-Lens

Zheng

Duan

et al. 2022

Front. Phys.

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Focusing beyond the acoustic diffraction limit has always been expected, especially in acoustic imaging and ultrasonic therapy. Manipulating the acoustic waves beyond the diffraction limit offers an alternative application potential in high-resolution imaging and medical ultrasound diagnosis and treatment. Here, a two-dimensional circular meta-lens is presented, with a sub-wavelength acoustic Helmholtz resonator array to implement the super-diffraction focusing. The proposed acoustic meta-lens consists of 28 units, which possesses the ability to yield designed arbitrary phase shifts and maintain the impedance matching to provide the high sound transmission efficiency. The simulation and experimental results show that the designed acoustic meta-lens can realize subwavelength sound focusing beyond the diffraction limit. The proposed method can greatly promote the application and development of the acoustic superfocusing technology in acoustic imaging, particle manipulation, and other fields.

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“…12 The DI method computes the diffraction integrals in the spatial domain by means of numerical integration, which can be treated as a linear convolution and can be effectively calculated by means of a FFT and an inverse FFT (IFFT). [13][14][15] Although numerical calculation of both the AS and the DI methods has been discussed extensively in the literature, 4,6,7,[12][13][14][15][16] there is still some confusion to be cleared up. First, the implementation of the diffraction integral by means of convolution and a FFT was not clearly presented.…”

Section: Introductionmentioning

confidence: 99%

“…Li et al suggested using an energy conservation criterion for validation of the sampling quality, but it is difficult to select a proper sampling interval in advance. 15 Delen and Hooker used a small sampling interval (less than half of a wavelength) for the FFT-AS method but encountered a large computational load. 16 An improper sampling interval will cause either a large aliasing error or a large computation load.…”

Section: Introductionmentioning

confidence: 99%

Fast-Fourier-transform based numerical integration method for the Rayleigh-Sommerfeld diffraction formula

2006

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The numerical calculation of the Rayleigh-Sommerfeld diffraction integral is investigated. The implementation of a fast-Fourier-transform (FFT) based direct integration (FFT-DI) method is presented, and Simpson's rule is used to improve the calculation accuracy. The sampling interval, the size of the computation window, and their influence on numerical accuracy and on computational complexity are discussed for the FFT-DI and the FFT-based angular spectrum (FFT-AS) methods. The performance of the FFT-DI method is verified by numerical simulation and compared with that of the FFT-AS method.

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FFT calculation for Fresnel diffraction and energy conservation criterion of sampling quality

Cited by 6 publications

References 0 publications

Fast analysis of arbitrary beam through planar multilayer structures

Fast analysis of arbitrary beam through planar multilayer structures

Helmholtz-Structured Two-Dimensional Super-Diffraction Meta-Lens

Fast-Fourier-transform based numerical integration method for the Rayleigh-Sommerfeld diffraction formula

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