Evaluating rms spot radii by ray tracing.

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.
• 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.