Two-point Resolution in Partially Coherent Light

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Abstract
The classical approach to the study of two-point resolution has considered the case of two infinitesimal pinholes in an opaque screen. Since partially coherent imagery is non-linear with respect to either intensity or amplitude, the question of resolution needs to be re-examined for a pair or point-like particles embedded in a medium of finite but different transmission. This paper deals with this situation in ordinary microscopy. It has been found that the limit of resolution may be expressed as 0 + j , where 0 is the limit obtainable on the basis of the Sparrow criterion, and is seen to be independent of the original object contrast. The second term j is an incremental term that depends on the object contrast and the final required image contrast. Both terms, however, depend on the degree of coherence between the object particles. A simple semi-empirical expression K s = 0 sin f / u = 0·475 + 0·26 o gives the Sparrow limit of resolution, where o is the coherence between the pair of points. Curves have been given for j for different object contrast, image contrast and coherence.

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