Degrees of Freedom of an Image

The maximum number of degrees of freedom of an image, which is usually derived by a rough application of the sampling theorem, has a precise mathematical meaning. This is established by applying the theory of prolate spheroidal functions, as discussed by Slepian and Pollack and other authors. Both coherent and incoherent illumination are considered. The number of degrees of freedom of the image can be substantially different in both cases. A dramatic example is represented by the thin-ring pupil, which is virtually unidimensional in the former case and two dimensional in the latter case.