| In this dissertation, the performance of Common Path/Common Mode Adaptive Optics is studied theoretically and experimentally. Key elements, data fusion, close loop working and error analyses are under research. At the same time, the possibility of using nonlinear optics in widening the detecting wave band of Hartmann-Shack wavefront sensor is exploringly discussed.Adaptive Optics guarantees the beam quality of laser projecting system. Beam cleanup, atmospheric turbulence compensation and correction of any disturbance and fabrication error in the light way are required to promise a near diffraction beam, but normal Adaptive Optics system can only correction one of them. Common Path/Common Mode Adaptive Optics is the new way to fulfill the correction of them all.Four kinds of CP/CM derivative systems are presented. Feasibility and how to realize all the function of CP/CM Adaptive Optics are analyzed in detail. Retroreflector array is used as pseudo phase conjugator in the system. The fidelity of the conjugate wave and matching problem of the retroreflector array and Hartmann-Shack wavefront sensor is discussed. Several data fusion methods are presented in order to having two Hartmann-Shack wavefront sensors control one set of wavefront corrector. The misalignment errors of Hartmann-Shack wavefront sensor and arrangement errors of wavefront sensor and deformable mirror are analyzed. At the same time, numerical work based on the data of practically system, such as 61 element AO system, are done corresponding to the problem respectively and the results are given.The system of CP/CM AO is setup to fulfill all the functions. Through the data fusion of two Hartmann-Shack wavefront sensors, the system runs successfully and realizes the close loop. It lays a good foundation for the application of CP/CM AO.Another aspect of this paper is to expand the working band of Hartmann-Shack wavefront sensor through Frequency Transfer of Nonlinear Optics. The first problem is whether we can get the wavefront of the pump wave through the harmonic wave or not and what is the relationship of them. This problem is also important and valuable in Nonlinear Optics. It will be very helpful to understand how the aberrations affect the course of three- wave mixing, such as the change of conversion efficiency, the distribution of intensity and phase.Small signal solution of aberrated second harmonic generation is deduced from three-dimension three wave coupling functions. The numerical work gives out lot of results of different aberrations. The effects of the fundamental wave's aberrations, which will change the conversion efficiency, distribution of intensity and phase in the frequency conversion, is analyzed. It shows that when walk-off and diffraction effects could be ignored approximately estimation of the phase distribution of second-harmonic wave could be done. The far field divergent angle and second moment radius of harmonic wave will vary with the aberration of fundamental wave, but the far field divergent angle will be obviously smaller than that of fundamental wave. The phase distribution of both fundamental and harmonic wave is measured using Hartmann-Shack wave front sensor in the experiment with 1064nm and 790nm lasers, respectively. Results are given.Actually, the walk-off, diffraction effects, the roughness of the crystal surface and matching, group velocity are the factors affecting harmonic wave. It is very difficult to realize expanding the working band of Hartmann-Shack wavefront sensor through Frequency Transfer of Nonlinear Optics. Usually three wave-mixing researches are based on plane wave or Gauss wave, so study of aberrated second harmonic generation is new and important. It could be very helpful to understand and make good use of the Frequency Transfer of Nonlinear Optics.
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