Images of circular phase objects in partially coherent light have been studied. It has been shown that recognizable contrast is obtained in the image of phase objects formed by an ordinary microscope even when the cone of the illuminating beam is sizable and the microscope is focused perfectly.
M. DE and S. C. SOM, "Diffraction Images of Circular Phase Objects in Partially Coherent Light," J. Opt. Soc. Am. 53, 779-784 (1963)