Edge-ringing in Partially Coherent Imaging

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Abstract
A simple condition is shown to be necessary and sufficient to suppress edge-ringing in optical imaging. This criterion is valid in the presence of aberrations and apodization, and for all cases of (spatially stationary) partially coherent illumination. The edge-ringing tendencies of an optical system may be assessed through the use of two new performance functions which form a Fourier-transform pair. One of these performance functions is related to the ‘transmission cross-coefficient’ which appears in the theory of partially coherent imaging. In the coherent limit this performance function reduces to the amplitude transfer function (pupil function), and in the incoherent limit it reduces to the Optical Transfer Function (OTF). The use of this performance function for the general assessment of partially coherent imaging systems is suggested.

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