Modified scaling angular spectrum method for numerical simulation in long-distance propagation* *Project supported by the National Natural Science Foundation of China (Grant No. 61705254) and the Key Research and Development Program of Shaanxi Province of China (Grant No. 2020GY-114).

Abstract

The angular method (AS) cannot be used in long-distance propagation because it produces severe numerical errors due to the sampling problem in the transfer function. Two ways can solve this problem in AS for long-distance propagation. One is zero-padding to make sure that the calculation window is wide enough, but it leads to a huge calculation burden. The other is a method called band-limited angular spectrum (BLAS), in which the transfer function is truncated and results in that the calculation accuracy decreases as the propagation distance increases. In this paper, a new method called modified scaling angular spectrum (MSAS) to solve the problem for long-distance propagation is proposed. A scaling factor is introduced in MSAS so that the sampling interval of the input plane can be adjusted arbitrarily unlike AS whose sampling interval is restricted by the detector’s pixel size. The sampling interval of the input plane is larger than the detector’s pixel size so the size of calculation window suitable for long-distance field propagation in the input plane is smaller than the size of the calculation window required by the zero-padding. Therefore, the method reduces the calculation redundancy and improves the calculation speed. The results from simulations and experiments show that MSAS has a good signal-to-noise ratio (SNR), and the calculation accuracy of MSAS is better than BLAS.