A multi-phase screen transmission model is usually applied to the simulation of an optical propagation process in atmospheric turbulence. The phase of an optical wave will be modulated by the phase screens, which function as atmospheric turbulence. This paper first analyzes the relationship between fractal Brownian motion and atmospheric turbulence as well as the relationship between a fractal Brownian surface and random phase screen. Then a phase screen generation algorithm based on fractal theory is proposed, which combines the random midpoint displacement principle with the successive random additions technique. Simulation results such as the phase structure function, power spectrum, and scintillation index conform more closely to the theoretical values compared with the traditional spectral inversion algorithm and Zernike polynomial method. Furthermore, it has better performance in both low- and high-frequency parts without increasing the algorithm complexity.
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