Low-complexity Digital Filter Geometry for Spherical Coded Imaging Systems

Recent research in the area of electro-optical system design identified the benefits of spherical aberration for extending the depth-of-field of electro-optical imaging systems. In such imaging systems, spherical aberration is deliberately introduced by the optical system lowering system modulation transfer function (MTF) and then subsequently corrected using digital processing. Previous research, however, requires complex digital postprocessing algorithms severely limiting its applicability to only expensive systems. In this paper, we examine the ability of low-cost spatially invariant finite impulse response (FIR) digital filters to restore system MTF degraded by spherical aberration. We introduce an analytical model for choosing the minimum, and hence cheapest, FIR filter size capable of providing the critical level sharpening to render artifact-free images. We identify a robust quality criterion based on the post-processed MTF for developing this model. We demonstrate the reliability of the estimated model by showing simulated spherical coded imaging results. We also evaluate the hardware complexity of the FIR filters implemented for various spherical aberrations on a low-end Field-Programmable Gate Array (FPGA) platform.