TABLE OF CONTENTS In the preceding chapters we discussed the image-forming characteristics of optical systems, but we limited our consideration to an infinitesimal thread-like region about the optical axis called the paraxial region. In this chapter we will consider, in general terms, the behavior of lenses with finite apertures and fields of view. It has been pointed out that well-corrected optical systems behave nearly according to the rules of paraxial imagery. This is another way of stating that a lens without aberrations forms an image of the size and in the location given by the equations for the paraxial or first-order region. We shall measure the aberrations by the amount by which rays miss the paraxial image point.
It can be seen that aberrations may be determined by calculating the location of the paraxial image of an object point and then tracing a large number of rays (by the exact trigonometrical ray-tracing equations of App. A) to determine the amounts by which the rays depart from the paraxial image point. Stated this baldly, the mathematical determination of the aberrations of a lens which covered any reasonable field at a real aperture would seem a formidable task, involving an almost infinite amount of calculation. However, by classifying the various types of image faults and by understanding the behavior of each type, the work of determining the aberrations of a lens system can be simplified greatly, since only a few rays need be traced to evaluate each aberration; thus the problem assumes...
