Wavefront propagation based on the ray transfer matrix and numerical orthogonal Zernike gradient polynomials

Area of Science:

• Optics and Photonics
• Wavefront Sensing and Aberration Analysis

Background:

• Wavefronts change shape and size during propagation.
• Representing wavefronts using Zernike coefficients and feature rays is common.
• Existing methods may lack flexibility in analyzing propagated wavefronts.

Purpose of the Study:

• To develop a numerical method for reconstructing aberrated wavefronts after propagation.
• To introduce a ray transfer matrix for tracking feature rays.
• To validate the accuracy and flexibility of the proposed reconstruction technique.

Main Methods:

• Wavefronts represented by Zernike coefficients and feature rays.
• A ray transfer matrix parameterized by pupil radius and propagation distance used to transfer feature rays.
• Numerical orthogonal Zernike gradient polynomials derived for wavefront reconstruction from discrete data.

Main Results:

• The proposed method accurately obtains slope and position data of propagated feature rays.
• Numerical orthogonal Zernike gradient polynomials enable wavefront reconstruction.
• Validation with two aberrated wavefront examples demonstrates accuracy and flexibility.

Conclusions:

• The developed numerical method provides an accurate and flexible approach for reconstructing aberrated wavefronts.
• The ray transfer matrix and Zernike gradient polynomials are effective tools for wavefront analysis.
• This method has potential applications in optical system design and testing.