In precision optical instruments, it is often the case that aspects of the illumination system pupil--such as ellipticity, telecentricity, and partial coherence--relate directly to image resolution and placement accuracy. Standard design and analysis tools are often ill-suited to performing tolerance analyses on illuminators, since the figures-of-merit in terms of system performance do not reduce neatly to wavefront and distortion, as they often do for imaging optics. In order to address these deficiencies, we developed a multiparameter tolerancing method based on a probabilistic treatment of errors in an illumination system, and we will describe the work we have done in this paper.
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