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Apodization of annular apertures: Strehl ratio

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Abstract

We show that for any rotationally symmetric apodizer on the full aperture, there is a family of apodizers on the annular aperture with the same functional Strehl ratio vs defocus (W20) and vs spherical aberration (W40). However, in the latter case, the coefficients W20 and W40 are reduced by the factors (1 − ɛ2) and (1 − ɛ2)2, respectively, where ɛ is the central obscuration ratio. We indicate that the best focal plane is shifted from W20 = −W40 to W20 = −(1 + ɛ2)W40. These general results allow us to design and to compare novel apodizers on annular apertures which reduce the influence of W20 and W40. The Strehl ratios of a novel family of apodizers are discussed to illustrate our general results.

© 1988 Optical Society of America

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