The analysis tools of traditional optical systems, such as modulation transfer functions, point spread functions, resolution test charts etc. are often not sufficient when analyzing computational imaging systems. Computational imaging systems benefit from the combined use of optics and electronics for accomplishing a given imaging or system task. In traditional optical systems the goal is essentially to form images that precisely depict a given object. Electronics are not required to form clear images, but could be required to analyze the images. In computational imaging systems specialized images are formed by generalized aspheric optical elements that are jointly optimized with the electronic processing. The specialized images formed at a detector are not necessarily clear images. Electronic processing is used to remove the image blur or otherwise form a final image. Computational imaging systems offer the advantage of increased performance and decreased size, weight, and cost over traditional optical systems.
The Ambiguity Function (AF), traditionally used for the design of radar waveforms, plays an important role in computational imaging systems. The AF provides a concise analysis of the optical transfer functions of imaging systems over defocus. The Wigner Distribution (WD), traditionally used for the design of time-varying systems, is related to the AF and provides a concise analysis of the point spread functions (PSF) of imaging systems over defocus. We will describe the relationships and utility of these functions to computational imaging systems.