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Characteristic functions and the aberrations of symmetric optical systems. I. Transverse aberrations when the eikonal is given

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Abstract

We describe the transverse aberrations of a symmetric optical system with a given eikonal (angle characteristic function). The aberrations are expressed in the coordinates of the image field and the pupil parameters according to Schwarzschild. Conditions for freedom from aberrations and for aberrations in the focal plane are considered. We show how the transverse aberrations up to the ninth order can be calculated from eikonal coefficients; we give the conditions under which the eikonal coefficients are identical to the aberration coefficients.

© 1988 Optical Society of America

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