Summation formulas are derived for the precise calculation of certain quality parameters of the image space: (a) radius of gyration of the point spread function, (b) O’Neill’s sharpness criterion, and (c) the Linfoot quality parameters. These formulas are applicable to any optical system that exists either as a design or as a fabricated object. Also, in the case of a bandwidth-limited object spectrum it is shown that the image may be exactly represented by a summation—in place of the usual convolution integral—over the object space. All derivations employ the sampling theorem.
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