Off-axis angular spectrum method with variable sampling interval

Abstract

We proposed a novel off-axis angular spectrum method (ASM) for simulating free space wave propagation with a large shifted destination plane. The off-axis numerical simulation took wave propagation between a parallel source and a destination plane, but a destination plane was shifted from a source plane. The shifted angular spectrum method was proposed for diffraction simulation with a shifted destination plane and satisfied the Nyquist condition for sampling by limiting a bandwidth of a propagation field to avoid an aliasing error due to under sampling. However, the effective sampling number of the shifted ASM decreased when the shifted distance of the destination plane was large which caused a numerical error in the diffraction simulation. To compensate for the decrease of an effective sampling number for the large shifted destination plane, we used a variable sampling interval in a Fourier space to maintain the same effective sampling number independent of the shifted distance of the destination plane. As a result, our proposed off-axis ASM with a variable sampling interval can produce simulation results with high accuracy for nearly every shifted distance of a destination plane when an off-axis angle is less than 75°. We compared the performances of the off-axis ASM using the Chirp Z transform and non-uniform FFT for implementing a variable spatial frequency in a Fourier space.