Sub-sampled single-step Fresnel diffraction for efficient computation of high-resolution holograms

The rapid increase in the size of image sensors and growing computational power have generated demand for large-scale diffraction calculations across a wide range of optical applications. For instance, synthetic-aperture digital holography requires diffraction calculations exceeding 10,000 × 10,000 pixels, whereas computer-generated holography may require more than 100,000 × 100,000 pixels. Conventional diffraction calculations generally assume equal pixel counts in the source and destination planes. However, when high-resolution diffraction results are verified on lower-resolution display devices, the resolution mismatch incurs unnecessary computational costs. Downsampling can reduce the computation cost, but it introduces aliasing artifacts. In this paper, we propose a method that combines single-step Fresnel diffraction with a subsampled fast Fourier transform. This approach enables fast and memory-efficient computation of diffraction results at the desired resolution from high-resolution data, while avoiding aliasing noise.