Analytical solution for Gamo entropy under spatially partial coherent illumination.

We present a methodology for obtaining the analytical solution of the Gamo entropy, defined by the intensity matrix proposed by Gamo [J. Opt. Soc. Am.47, 976 (1957)JOSAAH0030-394110.1364/JOSA.47.000976]. The matrix, which consists of numerous image amplitudes at all the sampling points of the entire imaging plane, is generally infinite-dimensional. The essence of our theory is that the computational difficulties arising because of the infinite-dimensionality are avoided by introducing the inner products of two image amplitudes. The integral in continuous space plays the role of a buffer against the infinite-dimensionality. The validity of the approach is confirmed by comparing our analytical solution and Yamazoe's numerical simulations [J. Opt. Soc. Am. A28, 448 (2011)JOAOD60740-323210.1364/JOSAA.28.000448].