Solving Zernike Polynomial Coefficients with MATLAB Implementation

Using MATLAB to compute Zernike polynomial coefficients significantly enhances calculation efficiency while eliminating the tediousness and complexity of manual computation. Supported by modern computing technology, this approach has become a crucial method for solving complex problems. The implementation typically involves constructing Zernike basis functions using polar coordinates, performing numerical integration through matrix operations, and solving coefficient equations using least-squares methods or singular value decomposition (SVD). Beyond the core algorithm, this technique finds applications in medical image analysis for wavefront aberration correction, computer vision for shape characterization, and precision manufacturing for surface metrology, demonstrating broad application prospects and development potential. Key MATLAB functions employed may include zernike.m for basis generation, integral2 for double integration, and pinv() for robust coefficient estimation.