Abstract

A method has been described previously whereby, as a result of tracing relatively few rays through an optical system, the intersection points of a large number of rays from an object point with any assumed image plane can be found by means of an interpolation formula. When these latter rays are distributed equally over the exit pupil, the resulting spot diagram indicates the distribution of illuminance in the image of the point. The interpolation formula is of the fifth degree. In the present paper, the coefficients of this formula are grouped according to increasing powers of the aperture, thus giving a new type of image theory for large aperture and field. This new analysis of the image errors leads to simple geometrical patterns that enable the designer to ascertain the effect of changes in the constructional data on the complex spot diagrams. The analysis is applied to an actual lens, and an example of the way it is used to improve the lens is given.

© 1957 Optical Society of America

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