Three-dimensional imaging: a space invariant model for space variant systems

Streibl [Optik 66, 341-354 (1984)] has shown that afocal telecentric imaging systems are shift invariant in three dimensions. We show that afocal telecentric imaging systems are the only imaging systems that are shift invariant in three dimensions. In addition, we present a model that allows any imaging system to be modeled as an afocal telecentric imaging system preceded and succeeded by simple coordinate transformation operators. The model is derived for diffraction-limited imaging systems where the Fresnel approximation is valid. It is assumed that the object distribution is incoherently radiating and that multiple scattering and absorption within the object distribution are negligible. A physical analogy is given that provides insight into the mathematical model. Finally, a comparison with the work of Frieden is given.