On the degrees of freedom of the phase retrieval problem in phase space

Phase-space tomography describes the recovery of signals from a tomographic reconstruction of the generalized radiance distribution with measurements being interpreted as projections of phase space. For coherent signals the phase space of the Wigner distribution function is a highly redundant signal representation. For efficient signal recovery based on phase-space information, it is necessary to address these redundancies. To understand the number of independent measurements necessary for the recovery of the WDF, Talbot self-imaging is used to derive a formalism for discrete phase-space tomography and signal recovery.