Some Useful Correspondences In Aberration Theory

There are many correspondences between the behavior of monochromatic aberrations and chromatic aberrations. Usually the behavior of the chromatic aberrations is of a lower order than the corresponding monochromatic behavior. The cause of the 5th-order mono-chromatic astigmatism, for example, is similar in type to the cause of the chromatic variation of 3rd-order astigmatism. The stop-shift behavior of 3rd-order monochromatic coma is similar to that of first-order lateral color, and so on. These correspondences are interesting for two reasons. One is that they have not been commented on much before, despite the value of one's being aware of these relationships. Methods used to control a monochromatic aberration may also apply to the corresponding chromatic aberration, and vice-versa, for example. The other benefit to studying this topic is that the chromatic aberrations, which are of a lower order than their monochro-matic correspondences, are much easier to understand and visualize. A simple diagram can illustrate the stop-shift behavior of lateral color much more easily than trying to do the same thing with 3rd-order coma. Finally, the very important distinction between intrinsic and induced aberrations can be best illustrated with chromatic aberrations, because of their lower order.