The existence of partially coherent planar sources with different states of coherence that generate identical radiant intensity distributions after light goes through a general optical system has been investigated. The relationship that must be satisfied by the cross-spectral density functions of all such sources has been derived. A general procedure for obtaining the common part of these sources from measurable radiant intensity data is presented. Also, the possibility of the existence of planar sources producing both identical optical intensity distributions at the output plane of the system and the same radiant intensity in the far zone has been analyzed. The general functional relationship among the cross-spectral density functions of all these sources has been determined.
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