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--------------------- Ray Tracing and Index of Refraction Precision

--------------------------------------------------------- By Bill Claff

When I enter an optical prescription, typically from a patent, into the Optical Bench for 2D ray tracing I don't normally think about the precision of the values. I recently entered some optical prescriptions that didn't trace well and realized that the values for index of refraction were only provided to two decimal places. This article explores the sensitivity of ray tracing to index of refraction precision using one optical prescription as a case study.

Case Study

As a subject for the case study I chose the optical prescription of a the Nikon Nikkor Z 50mm f/1.2 S.
Like many well formed optical prescriptions the measured focal length agrees with the specified focal length to a hundredth of a millimeter. The index of refraction values are specified to 5 decimal places.

In this simple study I reduced the precision of the index of refraction values by 1 decimal place from 5 decimal places to 2 decimal places while observing the measured focal length and the rays as they arrive at the focal point from infinity. Here are the results shown in decreasing precision order.

Note how measured focal length starts to deviate from the correct value and how the rays do not converge well as index of refraction precision is decreased.

Conclusion

Excellent results are achieved when the index of refraction is provided to 4 or more decimal places.
Results at 3 decimal places are acceptable but those at 2 decimal places are quite poor.