Zernike Polynomials for Generating Aspheric Wavefronts

Zernike polynomials are a set of orthogonal polynomials widely utilized in optical applications. These polynomials enable the representation of aspheric wavefronts as a series of simple mathematical functions. In computational implementations, Zernike coefficients are typically calculated through numerical integration or least-squares fitting to wavefront data, with algorithms often employing polar coordinate transformations for efficient evaluation. The polynomials also play a crucial role in diffraction analysis and optical transfer function generation, fundamental tasks in optical engineering. Code implementations frequently use Zernike expansions to model wavefront aberrations, where each polynomial term corresponds to specific aberration types like defocus, astigmatism, or coma. The orthogonal nature of these polynomials ensures stable numerical computations when reconstructing wavefronts from experimental measurements. Consequently, Zernike polynomials find extensive applications beyond aspheric wavefront modeling, including optical imaging systems, wavefront sensing, and optical signal processing. In modern optical applications, they have become indispensable tools for aberration correction, optical system characterization, and image quality assessment, with many optical design software packages incorporating Zernike-based analysis modules for performance optimization.