## Abstract

In designing lenses with automatic computing machinery it is necessary to have certain quantitative measures of lens performance which may be called performance numbers. In a perfect system all the performance numbers are zero. For practical systems it is the object of the designer to reduce the performance numbers to satisfactorily small quantities. It is the principal purpose of this paper to define a characteristic function suitable for use as a performance number, and to derive equations for computing this function and its derivatives with respect to the parameters of the system. The characteristic function *H* is defined to be the optical path difference between a principal ray and an arbitrary ray, measured on a sphere of infinite radius centered at the intersection of the principal ray and the focal plane.

In addition performance numbers are developed for the chromatic aberration, distortion, and boundary conditions. A merit function is defined which comprises the individual performance numbers.

© 1957 Optical Society of America

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