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Chapter 7:
Merit Functions and Aberration Balancing
In Chapter 6 merit functions are discussed as a means of optimizing the design of an optical system. During the long history of optical design, perhaps the most familiar approach to utilizing merit functions has been to reduce the classical Seidel aberration coefficiencts to a common scale and then minimize a function of the mean square (possibly weighted) of the aberrations. This procedure is described in some detail in Chapter 6. Other merit functions based on ray optics in the vicinity of the image plane have also proved effective. Two that correlate well with each other are the size of the ray-trace spot diagram and the optical path difference (OPD). In the first, the design program aims to reduce the area on the image plane covered by the rays coming from a common point object. In the second, the objective is to make the optical path length for all rays the same from the point object to the image plane. A perfectly spherical wave front at the exit pupil leads geometrically to a zero OPD, both conditions indicating the absence of aberrations.
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