This approach can be extended to consider the partial coherence of the image itself. In particular, we can consider the mutual intensity, WDF or ambiguity function of the image. It is important to note that the spatial convolution of the object WDF with the PSI-kernel is not a WDF, and not the WDF of the image. The phase space representations of the image have relevance to phase reconstruction methods such as phase space tomography, or the transport of intensity equation approach, and to the three-dimensional image properties.
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Colin J. R. Sheppard, Shalin B. Mehta, "Phase microscope imaging in phase space," Proc. SPIE 9718, Quantitative Phase Imaging II, 97180A (9 March 2016);