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Evaluating rms spot radii by ray tracing.

|April 15, 2010

Summary

Accurate computation of root mean square (RMS) spot radii requires careful consideration of ray tracing methods. Simple averaging formulas can lead to significant errors (15-20%) unless a square ray grid distribution is used; a fourth-order quadrature method offers superior accuracy with fewer rays.

Area of Science:

Optics
Computational Physics
Image Science

Background:

Accurate computation of root mean square (RMS) spot radii is crucial in optical system analysis.
Traditional ray tracing methods often rely on simple averaging formulas for calculating these radii.
The accuracy of these computations can be significantly influenced by the distribution of rays used in the tracing process.

Purpose of the Study:

To investigate the relationship between the number of rays traced and the accuracy of computed RMS spot radii.
To evaluate the impact of different ray grid distributions on the accuracy of standard averaging formulas.
To propose a more accurate and efficient computational method for determining RMS spot radii.

Main Methods:

Analysis of RMS spot radii computation using ray tracing.

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Comparison of results obtained with simple averaging formulas and a proposed fourth-order quadrature method.

Investigation of various ray grid point distributions (e.g., square grid) and their effect on accuracy.

Main Results:

Simple averaging formulas require a square ray grid distribution to converge to the correct center of mass and gyration radius.
Deviations of 15-20% in computed image radii can occur due to variations in grid point distributions with simple averaging.
A fourth-order quadrature formula achieves 1% accuracy with approximately 20 rays and 0.01% accuracy with 40-50 rays.

Conclusions:

The choice of ray distribution significantly impacts the accuracy of RMS spot radii computed via simple averaging.
A fourth-order quadrature method provides a highly accurate and computationally efficient alternative for RMS spot radii calculation.
This improved method reduces the number of rays needed for precise optical system analysis.