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. The feasibility of the proposed method is verified by numerical simulation and compared with the DI-method in a simplified scenario. It shows that the proposed method has good computational accuracy for the general case where the sampling interval of the input and observation plane is not equal under non-near-field diffraction, and when the diffraction distance is large, although the computational accuracy of the proposed method cannot exceed that of the DI-method, the computational amount can be significantly reduced with almost no effect on the computational accuracy. This method provides a general numerical calculation scheme of diffraction in the non-near field case for areas such as computational holography.