Angular dependence of sampling modulation transfer function

Sampling modulation transfer function (MTF) as defined in Park et al. [Appl. Opt. 23, 2527-2582 (1984)] as an x and y sampling can be generalized for image data not along x and y directions. For a given sampling lattice (such as in a laser printer, a scene projector, or a focal-plane array), we construct a two-dimensional sampling MTF based on the distance between nearest samples in each direction. Because the intersample distance depends on direction, the sampling MTF will be best in the directions of highest spatial sampling and poorer in the directions of sparse sampling. We compare hexagonal and rectangular lattices in terms of their equivalent spatial frequency bandwidth. We filter images as a demonstration of the angular-dependent two-dimensional sampling MTF.