Partially coherent microscope imaging system in phase space: effect of defocus and phase reconstruction

Explicit relationships between the defocused partially coherent cross-coefficient and phase space representations in the image plane are derived. Measurement of a phase space representation in the image plane in principle allows the complex image to be extracted. Implications for phase retrieval using the weak object transfer function or the transport of intensity equation are considered. The phase gradient transfer function, which determines the image for an object exhibiting a slowly varying phase gradient for a partially coherent microscope system, is derived. The effect of the effective source size and geometry on phase imaging with the transport of intensity equation is investigated. The primary consequence of source shape is a rescaling of the phase reconstruction. An annular source is found to give close to a linear response, while at the same time providing improved transverse resolution and an improved response to low spatial frequencies.