Evaluating rms spot radii by ray tracing.
The computation of rms spot radii from ray trace calculations is investigated in relation to the number of rays to be traced to achieve a prescribed accuracy. It is shown that the usual simple averaging formulas will only have as limits for infinitely many rays the correct center of mass and gyration radius if a square ray grid point distribution is used throughout the limiting process. For other ray distributions the ray trace data are given weight according to the local grid point density. Using the simple averaging formulas deviations in computed image radii of 15-20% may be encountered due solely to variations in grid point distributions. A computing method is suggested using a fourth-order quadrature formula giving 1% accuracy with ~20 rays and 0.01% accuracy with ~40-50 rays.
Andersen
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