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Refracting the k-function: Stavroudis's solution to the eikonal equation for multielement optical systems.

John A Hoffnagle¹, David L Shealy

¹Picarro, Inc., 3105 Patrick Henry Drive, Santa Clara, California 95054, USA.

Journal of the Optical Society of America. A, Optics, Image Science, and Vision

|June 7, 2011

Summary

This study introduces a method to extend the Stavroudis k-function, enabling optical field calculations in complex systems. The technique allows for repeated application, enhancing its utility for multielement optical designs.

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Area of Science:

Optics
Mathematical Physics

Background:

The k-function provides solutions to the eikonal equation in homogeneous optical media.
Existing methods are limited in handling complex optical systems with multiple elements.

Purpose of the Study:

To extend the Stavroudis k-function formalism for analyzing complex optical systems.
To develop a method for calculating optical fields after refraction or reflection at boundaries.

Main Methods:

Introducing a procedure termed 'refracting the k-function'.
Applying the k-function to model optical fields interacting with refractive or reflective boundaries.
Iteratively applying the k-function for multielement systems.

Main Results:

An analytic solution for the k-function, wavefronts, and caustics for a biconvex thick lens with axial plane wave illumination.
Numerical results for off-axis plane wave illumination of a two-mirror telescope.

Conclusions:

The 'refracting the k-function' method effectively extends the k-function's applicability to complex, multielement optical systems.
This approach provides a powerful tool for analyzing optical field propagation and aberrations.