Accuracy and Computational Efficiency of Various Methods for Atmospheric Turbulence Structure Function Computation

Structure functions are used to characterise spatial variations in turbulent quantities such as air temperature, density, refractive index and wavefront phase. They are often used to verify numerically generated phase screens for use in numerical simulations or with, for example, spatial light modulators. The usual method of calculating the structure function of such a screen in principle requires the comparison of each pixel with every other pixel, a computationally complex and time-consuming process. This paper will compare alternative methods for calculating the structure function of numerically generated atmospheric turbulence. Specifically, it evaluates the efficiency and accuracy of the methods and highlights the strengths and limitations of each. The study aims to help researchers select the appropriate method for their specific needs, choosing between faster computation, or higher accuracy.