An optimal balance of spherical aberrations under partially coherent illumination is presented. The visibility of a two-point image as a merit function is used to estimate the image aberrations. Although the optimal balance of aberrations has been evaluated by Maréchal [ Rev. Opt. 2, 257 ( 1947)] and Wang [ Proc. Phys. Soc. London 53, 157 ( 1941)] for incoherent illumination, it has not been treated for partially coherent illumination. In this paper, a general relationship between the optimal balance of aberrations and the degree of mutual coherence under partially coherent illumination is discussed. The result obtained for incoherent illumination turns out to be a special case of that for partially coherent illumination. In other words, the result of optimal balance of aberrations under partially coherent illumination is a general case that includes coherent, incoherent, and partially coherent illumination.
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