Modern Optical Engineering: The Design of Optical Systems, Fourth Edition

Appendix A: Raytracing and Aberration Calculation

A.1 Introduction

The importance of a knowledge and understanding of raytracing techniques has been significantly reduced by the near ubiquitous use of personal computers for the design and analysis of optical systems. It is now more important to understand how to effectively use an optical software program (such as OSLO, ZEMAX, or CodeV) than it is to understand exactly how the raytracing is done. Nonetheless, it is occasionally of value to access the raytracing equations. To that end we present here the equations for raytracing meridional rays, i.e., those which lie in the y-z plane, for the benefit of those who may need to calculate one or two rays using a pocket calculator. These equations are designed for this usage, and are not suited for automatic computer use. We also present equations which are designed for computer use (i.e., which do not "blow up" unless the ray can not be calculated (a) because it never intersects the surface, or (b) because it encounters total internal reflection (TIR) at the surface. The equations for tracing paraxial rays are given in Chap. 3, Eqs. 3.16 and 3.17 (as are a set of equations suitable for tracing meridional rays using an electro-mechanical desk calculator, Eqs. 3.1 through 3.7).

This appendix also contains Coddington's equations, which trace paraxial type rays about a meridional principal ray (sometimes called para-principal rays), and allow the calculation of sagittal and tangential field curvature. Several aspects of the calculation of the other specific aberrations are also discussed...

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