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Focus-error operator and related special functions

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Abstract

The effect of focus error in image formation under coherent illumination is described in terms of a differential operator of exponential type. Fourier or Talbot images of periodic objects are described in terms of the eigenfunctions and the eigenvalues of this operator. The approach is also employed to generate special functions that indicate the influence of focus error on the point-spread function, the line-spread function, and the edge response. One set of functions is identified with Boivin’s functions; the other seems to be new. Several properties of these functions (e.g., recurrence relations, power series, and differential equations) are given.

© 1983 Optical Society of America

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