Adaptive optics technology has been successfully applied to many research fields. For astronomical applications, Adaptive optics systems require artificial beacon for providing wave-front measurements, due to the very dark object. Laser Guide Star(LGS) is widely used as an artificial beacon, but the tip-tilt of the wave-front is not measurable with a LGS, as a consequence of the round trip of the light. Thus only natural star near the observed object can be used to measure the wave-front tilt, which limits the sky coverage due to the probability to find star within the isoplastic patch of the object. This dissertation focuses on the problems of tip-tilt determination for LGS. At first, the tilt anisoplanatism of laser beacons caused by atmospheric turbulence is studied in theory. Secondly, the experiment scheme for tip-tilt measurement using auxiliary telescopes based on the 1.2m and 25cm telescope systems is designed and verified. In the end, a new tip-tilt determination technique with a laser guide star on large telescopes is proposed based on the idea of cross-shaped sub-apertures. This dissertation aims at exploring a practical way to solve the problem of tip-tilt determination with a LGS. In the aspect of the theoretical research, the Zernike coefficient correlations between two spherical waves coming from the LGS strip are derived. Effect of the atmospherical turbulence, difference of the altitude of LGS and size of the receiving telescope on the anisoplanatism of the LGS strip are analyzed, which is a theoretical foundation for the experiment design to measure a LGS's tip-tilt. In addition, a general geometrical model of laser transceiver system is established. Correlation between upward and downward optical path is analyzed with the model. It shows that the disturbances by the turbulence in the upward laser path is the key problem of tip-tilt determination in LGS system, which provides a technical principle for tip-tilt measurement with a LGS. In the aspect of measurement technology, a method of tip-tilt measurement with a LGS using auxiliary telescopes is systematically analyzes, based on the principle of statistical technique proposed by Belen’Kii. A transfer function is proposed first in the dissertation, which shows the relationship between the different tip-tilt from LGS and auxiliary telescopes. It proves that the sky coverage is close to 100%, when two auxiliary telescopes are used. In the aspect of experimental research, a verification experiment is accomplished at the site of Yunnan Observatories. This experiment arranged a 1.2m telescope to shoot laser and to detect a star at the same time. A 25cm telescope is arranged to detect the laser strip from 45m away as an auxiliary telescope. The jitter of star is corrected by the tilt signal from auxiliary telescope by post processing. An image processing method is reported to improve the signal to noise ratio(SNR) to a low-contrast laser beacon image. A calculation method of pointing a LGS with the auxiliary telescope is first presented in this dissertation. In the end of this dissertation, a new tip-tilt determination technique of laser guide star is proposed for a large telescope, based on both of the theoretical and experimental research. This dissertation revealed the nature of the tip-tilt determination problem in LGS system, and the feasibility of the tip-tilt determination for the LGS is verified with experimental research. The theoretical results provide support for further research about tip-tilt measurement for LGS. And the experimental results verified the feasibility of the new tip-tilt measurement method for LGS.
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