Pincushion point-spread function for computer-generated holography

Abstract

Point-spread functions (PSFs) are non-stationary signals whose spatial frequency increases with the radius. These signals are only meaningful over a small spatial region when being propagated over short distances and sampled with regular sampling pitch. Otherwise, aliasing at steep incidence angles leads to the computation of spurious frequencies. This is generally addressed by evaluating the PSF in a bounded disk-shaped region, which has the added benefit that it reduces the required number of coefficient updates. This significantly accelerates numerical diffraction calculations in, e.g., wavefront recording planes for high-resolution holograms. However, the use of a disk-shaped PSF is too conservative since it only utilizes about 78.5% of the total bandwidth of the hologram. We therefore derive a novel, to the best of our knowledge, optimally shaped PSF fully utilizing the bandwidth formed by two bounding hyperbola. A number of numerical experiments with the newly proposed pincushion PSF were performed, reporting over three-fold reductions of the signal error and significant improvements to the visual quality of computer-generated holograms at high viewing angles.