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Calculation of wavefront aberration coefficients for non-circular or obscured pupils

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Optical designers sometimes find it desirable to specify the performance of an optical system or its components in terms of the specific wave aberrations. The calculations for these aberrations from interferometric data typically use the Zernike polynomials which are defined over a circular pupil with no obscurations. When confronted with a part for which the clear aperture is elliptical or rectangular or has a central obscuration, this type of specification must be examined more closely on two counts. First, what is the legitimate interpretation of such a specification when used for such a pupil? Second, when measuring the part, how is the aberration coefficient to be calculated so as to be repeatable?

© 1992 Optical Society of America

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