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We have discussed partially coherent imaging and the effects of partial coherence on the operation of various instruments. Because of the basic nonlinearity in partially coherent imaging systems, it is only in very restrictive cases that it is possible to state with mathematical precision that partial coherence creates no problem in a particular imaging system. Through analysis of the experimental results, one can construct a nomograph describing the conditions of partial coherence under which the imaging system is linear. The effects of partial coherence on an imaging system depend on both the value of R, the ratio of the numerical aperture of the objective to the numerical aperture of the condenser, and on the extent to which the object contains frequencies beyond the cutoff of the imaging objective. The cutoff of the imaging objective depends on its numerical aperture (NA). Coherence effects thus depend on R, the spatial frequency content of the object, and the NA of the imaging objective. These variables have been combined in an empirically determined nomograph (shown in Fig. 18.1) to give the conditions under which coherence effects are essentially absent in an imaging system. In this figure, L denotes the limiting spatial frequency in the target. Two sets of values of L are shown in Fig. 18.1. One set corresponds to the choice of N = 4 in Eq. (17.2), and the other set corresponds to the more conservative choice of N = 10.
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