Independent Sampling and Padding for Rayleigh–Sommerfeld Diffraction: A Scaled Convolution Approach

We propose a novel fast numerical calculation method for the Rayleigh–Sommerfeld diffraction integral, which is developed based on the existing scaled convolution method. This approach enables fast calculations for general cases of off-axis scenarios where the sampling intervals and numbers of the input and observation planes are unequal. Additionally, it allows for arbitrary adjustment of the sampling interval of the impulse response function, facilitating a manual trade-off between computational load and accuracy. The errors associated with this method, which is equivalent to interpolation, primarily arise from the discontinuities of the sampling matrix of the impulse response function on its boundaries of periodic extension. To address this issue, we propose the concept of the padding function and its construction method, and we evaluate its effectiveness in enhancing computational accuracy.