Turbulent phase derivative screens and verification of their statistics

Turbulent phase screens are commonly used in split-step, wave-optics simulations of light propagation through long atmospheric paths. Here, we describe the generation of turbulent phase gradient and Laplacian screens, as a complement to phase screens. These have applications in split-step, ray-trace simulations through turbulence, and the study of various wavefront sensors. Our method is based on a simple modification of the corresponding phase screens’ Fourier coefficients. Second-order statistics of the synthesized gradient screens are verified using a recently published method to estimate Zernike mode coefficients from a grid of phase derivative values. To perform a similar verification of the Laplacian screens, we derive a set of polynomials for estimating Zernike mode coefficients from a grid of phase Laplacian values.