The previous chapters have been concerned with various aspects of geometrical optics. From this discussion, the reader should be able to see how, by ray tracing, the aberrations of a lens are calculated and spot diagrams are generated. Furthermore, the wavefront aberrations can be calculated as a part of the ray trace, and used to analyze systems whose performance is close to the diffraction limit. This information can be used to compute the MTF, which itself is a measure of closeness to diffraction-limited performance. However, ray tracing gives us virtually no diagnostic information that is helpful in understanding why a lens has the aberrations that it does. Nor does it tell us what parameters should be changed in order to reduce the aberrations.
Although this book is written on the assumption that the reader will be doing lens design with modern lens design software, and that only a very small amount of calculation will be carried out manually, it is still essential for the designer to understand the basic principles of aberration correction. This chapter and the next are concerned with the derivation and discussion of analytical formulae, derived originally by Seidel, which do help us to understand to a third-order approximation why aberrations arise, and what can be done to reduce them. This material is of great importance in understanding lens design.
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