Semi-analytic Fresnel diffraction calculation with polynomial decomposition

Split-step wave-optical simulations are useful for studying optical propagation through random media like atmospheric turbulence. The standard method involves alternating steps of paraxial vacuum propagation and turbulent phase accumulation. We present a semi-analytic approach to evaluating the Fresnel diffraction integral with one phase screen between the source and observation planes and another screen in the observation plane. Specifically, we express the first phase screen’s transmittance as a Fourier series, which allows us to bring phase screen effects outside of the Fresnel diffraction integral, thereby reducing the numerical computations. This particular setup is useful for simulating astronomical imaging geometries and two-screen laboratory experiments that emulate real turbulence with phase wheels, spatial light modulators, etc. Further, this is a key building block in more general semi-analytic split-step simulations that have an arbitrary number of screens. Compared with the standard angular-spectrum approach using the fast Fourier transform, the semi-analytic method provides relaxed sampling constraints and an arbitrary computational grid. Also, when a limited number of observation-plane points is evaluated or when many time steps or random draws are used, the semi-analytic method can compute faster than the angular-spectrum method.

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Semi-analytic simulation of optical wave propagation through turbulence

Schmidt

Tellez

Gbur

2022

Appl. Opt.

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Technique for enhancing the accuracy of the Rayleigh–Sommerfeld convolutional diffraction through the utilization of independent spatial sampling

Zhao,

Lu,

et al. 2024

Opt. Lett.

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The Rayleigh–Sommerfeld diffraction integral (RSD) is a rigorous solution that precisely satisfies both Maxwell’s equations and Helmholtz’s equations. It seamlessly integrates Huygens’ principle, providing an accurate description of the coherent light propagation within the entire diffraction field. Therefore, the rapid and precise computation of the RSD is crucial for light transport simulation and optical technology applications based on it. However, the current FFT-based Rayleigh–Sommerfeld integral convolution algorithm (CRSD) exhibits poor performance in the near field, thereby limiting its applicability and impeding further development across various fields. The present study proposes, to our knowledge, a novel approach to enhance the accuracy of the Rayleigh–Sommerfeld convolution algorithm by employing independent sampling techniques in both spatial and frequency domains. The crux of this methodology involves segregating the spatial and frequency domains, followed by autonomous sampling within each domain. The proposed method significantly enhances the accuracy of RSD during the short distance while ensuring computational efficiency.

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Improvement of Fresnel Diffraction Convolution Algorithm

Ge,

Song,

Caiyang

et al. 2024

Applied Sciences

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With the development of digital holography, the accuracy requirements for the reconstruction phase are becoming increasingly high. The transfer function of the double fast transform (D-FFT) algorithm is distorted when the diffraction distance is larger than the criterion distance dt, which reduces the accuracy of solving the phase. In this paper, the Fresnel diffraction integration algorithm is improved by using the low-pass Tukey window to obtain more accurate reconstructed phases. The improved algorithm is called the D-FFT (Tukey) algorithm. The D-FFT (Tukey) algorithm adjusts the degree of edge smoothing of the Tukey window, using the peak signal-to-noise ratio (PSNR) and the structural similarity (SSIM) to remove the ringing effect and obtain a more accurate reconstructed phase. In a simulation of USAF1951, the longitudinal resolution of the reconstructed phase obtained by D-FFT (Tukey) reached 1.5 μm, which was lower than the 3 μm obtained by the T-FFT algorithm. The results of Fresnel holography experiments on lung cancer cell slices also demonstrated that the phase quality obtained by the D-FFT (Tukey) algorithm was superior to that of the T-FFT algorithm. D-FFT (Tukey) algorithm has potential applications in phase correction, structured illumination digital holographic microscopy, and microscopic digital holography.

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Semi-analytic Fresnel diffraction calculation with polynomial decomposition

Cited by 3 publications

References 14 publications

Semi-analytic simulation of optical wave propagation through turbulence

Semi-analytic simulation of optical wave propagation through turbulence

Technique for enhancing the accuracy of the Rayleigh–Sommerfeld convolutional diffraction through the utilization of independent spatial sampling

Improvement of Fresnel Diffraction Convolution Algorithm

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