Zernike polynomials constitute an essential mathematical basis for representing functions defined over the unit disk. They are widely used in a diverse range of scientific and engineering disciplines, including adaptive optics for characterizing atmospheric distortions, ophthalmology for quantifying ocular aberrations, microscopy for instrument characterization and aberration correction, and optical metrology for surface profiling. This paper introduces ZernikeViewer, a software framework developed for the rapid calculation and visualization of fringe, phase, and point spread function (PSF) maps from Zernike coefficients. The framework leverages CPU multicore and multithreading capabilities through the .NET Task Parallel Library (TPL), augmented by codebase optimizations and the preloading of precomputed Zernike polynomial matrices. These optimizations reduce computation time by a factor of 7 to 10 compared to a conventional approach; for instance, from 1 ms to 0.1 ms for a radial order of n = 10 and from 700 ms to 80 ms for n = 100. Numerical error analysis confirms the accuracy of the computation, with an average root-mean-square (RMS) error of 0.11 ms observed in the timing measurements. Furthermore, it is demonstrated that implementing Jacobi recursion relations could potentially reduce the numerical calculation error by up to 5 orders of magnitude.
Ilya Galaktionov (Thu,) studied this question.