The influence of the installation and adjustment error of gravitational wave telescopes on the TTL coupling noise of the telescopes is studied. Since the TTL coupling noise is the second largest noise source, during the actual engineering of gravitational wave telescopes, the installation and adjustment will affect the TTL coupling noise, with little correlation between the telescope's installation and adjustment and TTL coupling noise. Therefore, the research on the relationship between the telescope's installation and adjustment tolerance and TTL coupling noise is significant for the engineering of gravitational wave telescopes, and how the gravitational wave telescope's installation and adjustment tolerance will affect the TTL coupling noise determines whether the final gravitational wave telescope meets the requirements for use. The research results can guide the installation and installation and adjustment of gravitational wave telescopes.

We can judge the installation and adjustment processes of gravitational wave telescopes by simulating and designing a gravitational wave telescope that meets the requirements of the wave-front difference index, calculating the TTL coupling noise of the designed telescope, and analyzing the influence of the telescope's installation and adjustment tolerance on the TTL coupling noise. The variable of installation and adjustment tolerance is sensitive to TTL coupling noise. By controlling the variable method with other parameters unchanged, only a certain installation and adjustment tolerance is assigned in the gravitational wave telescope, and the influence of the installation and adjustment tolerance in the telescope on the change of the exit pupil position is simulated and analyzed. Then when the laser interference signal passes through the laser interferometer and finally interferes with the four-quadrant detector, the variation of TTL coupling noise due to the installation and adjustment tolerance of the telescope is calculated. The relationship between the TTL coupling noise of the intersatellite laser interferometry system and the sensitivity of the telescope's installation and adjustment tolerance is established. In addition, the requirements of the TTL coupling noise are employed as the criterion to establish the model relationship between the installation and adjustment tolerance and the change of TTL coupling noise.

Comparison shows that the distance tolerance between the primary mirror and the secondary mirror of the gravitational wave telescope exerts more influence on the TTL coupling noise of the gravitational wave telescope than the distance tolerance between other optical elements exerts on the TTL coupling noise. The change in TTL coupling noise due to the distance tolerance between the primary and secondary mirrors is opposite in sign to that due to the distance tolerance between the secondary and third mirrors and between the third and fourth mirrors. The installation and adjustment tolerance of the distance between the diaphragm and the primary mirror has little effect on the variation of the TTL coupling noise and can be ignored. The variation of the TTL coupling noise caused by the distance installation and adjustment tolerance of each optical element and the jitter angle are distributed in a parabolic law. By analyzing the installation and adjustment tolerance of the gravitational wave telescope, the relationship between the installation and adjustment tolerance of the gravitational wave telescope and the change of TTL coupling noise is established. Via the above analysis and discussion, the sensitivity of the TTL coupling noise of the gravitational wave telescope is known. The primary and secondary distance sensitivity of the mirror is the highest, which is 15.489 times the sensitivity of the secondary and third mirrors, and 9.311 times the sensitivity of the third and fourth mirrors. The TTL coupling noise caused by the position error between the primary and secondary mirrors can be reduced by the secondary and third mirrors, and that caused by the position error between the primary and secondary mirrors can be reduced by the position error between the third and fourth mirrors.

When adjusting the space gravitational wave telescope, we should focus on controlling the distance error between the primary and the secondary mirrors. The TTL coupling noise caused by the distance installation and adjustment error between the secondary and the third mirrors, and the distance installation and adjustment error between the third and fourth mirrors can be adopted to partially offset the TTL coupling caused by the distance error between the noise of the primary and secondary mirrors. During actually adjusting the gravitational wave telescope, the distance tolerances between the primary and secondary mirrors and between the third and fourth mirrors should be considered successively, and the position tolerance between the secondary and third mirrors should be guaranteed. Our study analyzes the sensitivity of the installation and adjustment tolerance of the gravitational wave telescope to the influence of the TTL coupling noise, which can guide the actual installation and adjustment of gravitational wave telescopes. At present, we only consider the influence of installation and adjustment tolerance on the TTL coupling noise of gravitational wave telescopes, and the influence of processing tolerance on TTL coupling noises will be discussed later to guide the processing and installation of gravitational wave telescopes.