Aliasing-reduced Fresnel diffraction with scale and shift operations

TL;DR

This paper investigates aliasing errors in shifted-Fresnel diffraction used in optical simulations and proposes improvements to reduce aliasing while allowing different sampling rates between planes.

Contribution

The paper analyzes aliasing conditions in shifted-Fresnel diffraction and introduces modifications to mitigate aliasing errors in numerical simulations.

Findings

Aliasing occurs under specific conditions in shifted-Fresnel diffraction.

Proposed improvements effectively reduce aliasing errors.

Enhanced shifted-Fresnel diffraction allows different sampling rates with less error.

Abstract

Numerical simulation of Fresnel diffraction with fast Fourier transform (FFT) is widely used in optics, especially computer holography. Fresnel diffraction with FFT cannot set different sampling rates between source and destination planes, while shifted-Fresnel diffraction can set different rates. However, an aliasing error may be incurred in shifted-Fresnel diffraction in a short propagation distance, and the aliasing conditions have not been investigated. In this paper, we investigate the aliasing conditions of shifted-Fresnel diffraction and improve its properties based on the conditions.