Spatial incoherence in phase retrieval based on focus variation

We investigate the effect of spatial incoherence on two methods of phase retrieval based on focus variation: the transport of intensity equation and iterative wave function reconstruction. Spatial incoherence provides an upper bound on the defocus step size which should be used in each case. The requirement that phase information manifests itself in sufficient variation in the defocused images provides a lower bound on the defocus step size which should be used in each case. The scaling of these upper and lower bounds with object size and imaging resolution differs in such a way that, given the spatial incoherence properties of the source, for sufficiently low resolutions neither technique can retrieve phase information. The regions of applicability of the two techniques are discussed.