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

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.