提出快速计算光学系统点扩散函数的新方法，速度提升4倍且精度高。
Fast PSF Synthesis with Defocused and Spherical Aberration
- 用分段贝塞尔加高斯积分近似推导出离焦与球差下的闭式解
- 线性复杂度下实现速度比汉克尔积分快2倍、比FFT快4倍
- 适合需要高效大范围景深合成的光学成像应用
精确估计光学系统的点扩散函数（PSF）需要求解自由空间波传播问题，涉及无法解析求解的衍射积分。我们发现，在离焦和球差条件下，通过结合分段贝塞尔近似与高斯型积分，该衍射积分可获得近似闭式解。基于此，我们开发了一种波基快速PSF模拟器，其复杂度在径向分辨率上呈线性关系。未优化版本的模拟器相比汉克尔积分实现最高2倍加速，相比FFT实现最高4倍加速，同时与波光学真实PSF高度一致，支持高效的大型景深合成。
原文摘要 · Abstract (English)
Accurately estimating the point spread function (PSF) of an optical system requires solving free-space wave propagation, which entails evaluating a diffraction integral. This integral is traditionally computed numerically using Fast Fourier Transform (FFT) or Hankel Transform, as it lacks a closed-form solution. We show that, under defocus and spherical aberration, the diffraction integral admits an approximate closed-form solution by combining a piecewise Bessel approximation with Gaussian-type integrals. Based on this result, we develop a fast wave-based PSF simulator with linear complexity in the radial resolution. The proposed, un-optimized simulator achieves up to a 2x speedup over Hankel-based integration and a 4x speedup over FFT while closely matching wave-optical PSFs, enabling efficient large-scale depth-of-field synthesis.
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