Wavefront Reconstruction For Multiple Laser Guide Star Adaptive Optics

Typically more than 60% of the incident light from object is used for wavefront sensing in the adaptive optics system(AOS). In addition, the microlens array in a Shack-Hartmann wavefront sensor(SHWFS) in AOS divides the wavefront in the telescope pupil into sub-wavefronts with a diameter of about 10 cm. Then the whole aberration is reconstructed by sensing tilt and tip in every sub-aperture. Therefore, the sub-aperture size limits the received energy equal to that of a telescope with a diameter of 10 cm. Finally, the lowest magnitude of object star sensed by a traditional AOS is only 5 mag in the process of correction and imaging.Sensing atmospheric aberration by using laser guide star(LGS) can not only improve the lowest magnitude of imaging objects, but also widen the observing field of view(FOV) where many objects are distributed. However, the altitude of LGS is much lower than that of the objects. A part of turbulence information is lost and anisoplanatism error occurs. Therefore, it is important to use multi-LGSs to resolve the problem, minimize the anisoplanatism error and reconstruct the whole aberration.In the thesis, weight factors in different layers of atmosphere are defined according to the atmospheric refractive index vertical distribution function in the H-V atmospheric refractive index structure constant model. Then effective altitudes in different layers are calculated according to their moment about the origin. We found that 99.3% of atmosphere that affects the aberration and final imaging is concentrated within altitude of 15 km from the ground layer, or 96% within altitude of 8 km from the ground layer. The atmosphere within altitude of 15 km from the ground layer could be divided into 3 layers, or 2 layers within altitude of 8 km from the ground layer: The first layer is from the ground to 1.65 km with its effective altitude of 0.15 km and atmospheric weight factor of 88.2%; The second layer is from 1.65 km to 8 km with its effective altitude of 3.78 km and atmospheric weight factor of 7.1%; The third layer is from 8 km to 15 km with its effective altitude of 11.20 km and atmospheric weight factor of 4%. I developed a new method that can generate a dynamic phase variation that agrees with the atmospheric spatial and temporal statistical properties. Atmospheric turbulence simulation program was established to provide the basis of the wavefront reconstruction algorithm validation and analysis.The weighted coefficient reconstruction method is presented. The method uses the wavefront sensed from multiple rayleigh guide stars to reconstruct the whole wavefront on the telescope. Based on the phase structure function, we used the vertical projection of each guide star on the ground as their center and calculated the weight coefficients of the wavefront along radial and angular direction of telescope pupil. The final wavefront from imaging target is reconstructed with weighted combination of wavefront from multiple guide stars. For a 1.25 m telescope, when the coherence length is 10 cm, five guide stars at an altitude of 10 km with corss arrangement whose circumcircle coincides with the telescope pupil, the sterehl ratio can reach 0.49 with the weighted coefficient reconstruction method according to the simulations of the imaging on axis without considering the correction error. Considering the unsampled error from the atmosphere above 10 km, it is 0.57 rad. Then the RMS value of total wavefront sensing error increases to 1.02 rad while the Strehl ratio can still be up to 0.35, indicating that the five rayleigh guide stars with an altitude of 10 km can meet practical requirements.An LGS AO system was constructed on the optical bench in our lab. The experimental results agreed very well with the theoretical expectations, indicating that the precision of weighted coefficient reconstruction algorithm is high enough.When the sky or space objects are imaged using multi-conjugate adaptive optics(MCAO) system on telescopes with an aperture of more than 4 m, the Sodium guide star with altitude of about 90 km is required. An algorithm of generalized Tikhonov regularized Zernike model layer tomographic wavefront reconstruction is applied to avoid large condition number of projection matrix. For a telescope with a diameter of 8 m, atmospheric turbulence coherence length of 12 cm and 3 LGSs in altitude of 90 km, the generalized Tikhonov regularized Zernike model layer tomographic wavefront reconstruction gives an average error of 0.68 rad in field of view of 1 arcmin and Strehl ratio of about 0.63 that corresponds to 1.26 times diffraction limited resolution.In layer-oriented multi-conjugate adaptive optics, the number of the sodium guide stars ranges from 3 to 5 while the number of wavefront corrector ranges from 2 to 3. Further increase in the numbers of guide stars and correctors leads to only limited improvement of the system performance. The optimal distribution of guide stars is as follows: the linear distribution for two laser guide stars with an bias angle of 15.7 "; the triangular distribution for three laser guide stars with a bias angle of 21.5"; the square distribution for four laser guide stars with a bias angle of 23.5 "; the pentagon distribution for five laser guide stars with a bias angle of 27.4". The optimum conjugate altitude depends only on the vertical distribution of atmospheric turbulence. The optimum conjugate altitudes are 0 km and 10 km for two wavefront corrector, respectively; And they are 0 km, 2 km and 11 km for three wavefront corrector, respectively.The proposed wavefront reconstruction algorithm and obtained conclusions in this thesis are useful tools in the practical applications of the multi-LGSs adaptive optics. Compared with ground layer adaptive optics(GLAO), our new algorithm improves the Strehl ratio from 0.17 to 0.26 in the average field of view, and from 0.18 to 0.45 in the center of the field of view. This research work will play a role in the advancement of laser guide star adaptive optical system in China.