It is known that if the mutual intensity is sampled on an array of spacings, such samples can be Fourier transformed to yield images of incoherently radiating objects. In this paper, this result is extended to the imaging of partially coherent and coherent objects. An analysis of partially coherent imaging is first developed using a rather new approach, and the role of the complex ambiguity function in such imaging is emphasized. Next, using sampling theory, it is shown that in order to reconstruct images of partially coherent objects it is necessary to sample the mutual intensity on a discrete array of translations as well as on a discrete array of spacings. The required spacing and translation increments are shown to be inversely proportional to the object size and coherence extent, respectively. These requirements are stated in the form of a sampling theorem. Based on these results, an image synthesis procedure is outlined, and the capability of such a procedure for removing misfocus and other imaging aberrations is discussed. Lastly, experimental results are presented that demonstrate the aberration removal capability of this technique, using a coherent imaging system with defocus error.
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