Numerical Simulation Of The Atmospheric Turbulence Phase Screen Based On Fractal

When propagating in the atmosphere, laser beam quality will be inevitably deteriorated by the turbulence, which seriously limits the performance especially for practical use of laser engineering systems. Hence theoretical research of turbulence effects on laser propagation is of great importance in wide areas of laser application.Besides traditional methods such as experiments and theoretical analysis, numerical simulation is also an effective approach, in which phase-screen ( PS) theory, as an effective approximated method of laser propagation, has been widely used to solve various kinds of practical problems. Based on the classical statistical turbulence theory, i.e., Oboukhov-Kolmogorov (O-K) theory, and with the development of the research results on turbulence and atmospheric turbulence in recent years, a fractal model is introduced and used to model the phase screen distorted by atmospheric turbulence in fractal theory.This thesis first introduces the O-K statistical theory of turbulence in Chapter two. Based on power spectrum method and Zernike polynomial method, numerical simulation of wave front phase screen distorted by Kolmogorov atmospheric turbulence is implemented and is in Chapter 3. Analysis shows that the high spatial frequency components of PS generated by power spectrum method is well fitted the theory value, the low spatial frequency part is out of the lower-bound. In the other hand, Zernike polynomial method gives a deficient result in the high spatial frequency part.Second, the shortcomings of O-K statistical laws are analyzed. Because of the intermittency of turbulence, O-K statistical law is not suited for all cases. Therefore, the intermittency of turbulence is not ignorable when studying the properties of light propagating in the atmosphere. Hence a modified power spectrum model of Komgorov turbulence is provided. In the recent decades, many experimental results show that the index of refractive structure function did not fully satisfy the O-K scaling law, and scaling invariance is still exists, which is called Non-Oboukhov-kolmogorov(N-O-K) turbulence. In this thesis, based on the relationship between atmospheric refractive index structure function and power spectrum, a generalized expression of the atmospheric turbulence power spectrum is given.Third, based on fractal theory, a formalism to model the atmospheric turbulence PS is introduced, with which the random midpoint motion(RMM) algorithm is used to simulate both the O-K and N-O-K phase screens respectively. Simulation accuracy is examined by comparing the phase structure function with the theoretical value. Results show that RMM algorithm can bring us a satisfied approximation to the theory. In the weak turbulence conditions, scintillation index of plane wave is calculated. Simulation results show that the value gets in line with the theoretical value, which verifies the reliability of the phase screen. Finally, phase screens are integrated in synthetic aperture lidar (SAL) imaging model to preliminary analyze the influence of turbulence on SAL.