Once upon a time, the evaluation of an optical design required a great deal of ingenuity. With no high-speed computers to aid them, designers were forced to find shortcuts and clever approximations to assess the performance of a lens. They developed analytical tools to provide insight from a limited amount of input data in the shortest computational time. A paraxial ray trace, accurate for a small area about the optical axis, was used as a baseline measure of a perfect image. If the lens provided a perfect image, the areas on the object that were farther from the axis would also be imaged exactly with the correct magnification. To the extent that a lens fails to do this, the differences between the rays of a perfectly imaged object and those directed by the actual lens are a measure of the optical errors, or aberrations, in the lens.

6.1 Propagating Real Rays

Figure 6.1 illustrates the propagation of a ray through an optical system. It compares two rays. One ray is propagated by a lens with no aberrations (a "perfect" lens); the other is an aberrated skew ray propagated by a real lens. To keep things as general as possible, all quantities in the figure are normalized to their maximum value. Thus, at a point in the object plane, the fraction of the field between the full field and the axis is designated as h, a proper fraction between one and zero (1 ≥ h ≥ 0).