Spatial bandwidth analysis of fast backward Fresnel diffraction for precise computer-generated hologram design.

Designing near-field computer-generated holograms (CGHs) for a spatial light modulator (SLM) requires backward diffraction calculations. However, direct implementation of the discrete computational model of the Fresnel diffraction integral often produces inaccurate reconstruction. Finite sizes of the SLM and the target image, as well as aliasing, are major sources of error. Here we present a new design prescription for precise near-field CGHs based on comprehensive analysis of the spatial bandwidth. We demonstrate that, by controlling two free variables related to the target image, the designed hologram is free from aliasing and can have minimum error. To achieve this, we analyze the geometry of the target image, hologram, and Fourier transform plane of the target image to derive conditions for minimizing reconstruction error due to truncation of spatial frequencies lying outside of the hologram. The design prescription is verified by examples showing reconstruction error versus controlled parameters. Finally, it is applied to precise three-dimensional image reconstruction.