Gram-Schmidt Orthogonalization Method for Zernike Polynomial Wavefront Fitting
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Resource Overview
MATLAB implementation of Gram-Schmidt orthogonalization method with secondary equation approach for solving wavefront fitting coefficients of Zernike polynomials, featuring built-in computational functions and practical algorithm applications.
Detailed Documentation
In MATLAB, we can implement the Gram-Schmidt orthogonalization method combined with the secondary equation approach to calculate wavefront fitting coefficients for Zernike polynomials. The implementation leverages MATLAB's built-in functions for matrix operations and numerical computations to streamline the orthogonalization process. This program demonstrates how to construct an orthonormal basis set from linearly independent Zernike polynomials using iterative projection and normalization operations. Through this implementation, users can gain deeper understanding of wavefront fitting techniques using Zernike polynomials and apply them more flexibly in practical applications such as optical system analysis and wavefront reconstruction. Key computational steps include vector normalization, orthogonal projection subtraction, and coefficient solving through linear algebra operations.
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