Atmospheric Turbulence Random Phase Screen with Harmonic Compensation Algorithm

In atmospheric turbulence research, the simulation of random phase screens is crucial for optical propagation modeling. Traditional methods based on Fourier transforms generate high-frequency turbulence structures effectively but suffer from missing low-frequency components. The improved approach compensates for this deficiency by superimposing sub-harmonic components to restore low spatial frequencies.

The core methodology involves: First generating a base phase screen using power spectrum inversion, which captures high-frequency turbulence characteristics well but lacks large-scale fluctuations. Then through hierarchical sub-harmonic superposition, low-frequency perturbations are injected across multiple scales. The resulting composite phase screen more accurately represents the continuous turbulence spectrum from micro-scale to macro-scale variations.

This method significantly enhances the spatial structural completeness of phase screens, particularly beneficial for long-distance light propagation or large-aperture optical system simulations. MATLAB's implementation advantages lie in its built-in FFT operations and matrix manipulations, which efficiently handle iterative computations for spectrum generation and spatial domain reconstruction. Key functions include fft2/ifft2 for Fourier transforms, meshgrid for coordinate system setup, and sophisticated random number generation for creating atmospheric phase distortions that obey Kolmogorov turbulence statistics.