Access to eBooks is limited to institutions that have purchased or currently subscribe to the SPIE eBooks program. eBooks are not available via an individual subscription. SPIE books (print and digital) may be purchased individually on SPIE.Org.

Contact your librarian to recommend SPIE eBooks for your organization.
Chapter 6:
Spherical Aberration

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).

Online access to SPIE eBooks is limited to subscribing institutions.

Back to Top