Simulation of Zernike Polynomial Coefficients and Phase Screens with Arbitrary Orders

This program facilitates the simulation of Zernike polynomial coefficients and phase screens for any specified order. For coefficient simulation, it generates Zernike polynomial coefficients across various orders and presents them as either numerical data or graphical visualizations. The phase screen simulation component produces Zernike polynomial-based phase screens of different orders, displaying results through both numerical outputs and graphical representations. The implementation utilizes recursive algorithms for efficient polynomial generation and employs Fourier transform methods for phase screen construction. Key functions include order validation, coefficient normalization, and wavefront reconstruction algorithms. Additionally, the program supports user customization of simulation parameters, such as polynomial order selection, amplitude scaling, and spatial resolution adjustments, to generate more precise simulation outcomes. Users can modify boundary conditions and sampling intervals to optimize accuracy for specific applications.