Conditions for space-invariant 3-D imaging

Abstract

Many schemes for the restoration of 3-D imagery assume that the imaging system is shift invariant in three dimensions. Unfortunately, most conventional imaging systems, although space invariant in two dimensions, exhibit moderate to strong space variance for 3-D imaging. Two key conditions must be met for space invariance to hold for 3-D imaging: (1) image magnification must be constant throughout the image space, and (2) the exit pupil of the imaging system must be at infinity. These two conditions imply that only afocal-tele-centric (doubly afocal) systems, such as the 4-f system common for coherent spatial filtering, can perform space-invariant 3-D imaging over large volumes. Even then, the effects of vignetting by finite-diameter lenses must be carefully considered. We use geometrical optics arguments to show that the regions of space for which shift-invariant imaging holds are given by the intersection of two truncated cones aligned in opposite directions along the optic axis.