Effect of the Focusing System on Measurements in Gravitational Wave Detection Telescope

Telescopes primarily transmit and receive laser beams over long distances as part of a gravitational wave interferometric measurement system. Due to factors such as optical design, fabrication, and alignment, the wavefront at the exit pupil of the telescope inevitably experiences distortion, resulting in wavefront aberrations that couple with pointing jitter to generate tilt-to-length (TTL) coupling noise. During the process of gravitational wave detection, the large distance between the primary and secondary mirrors and temperature fluctuations in space can cause significant axial misalignment between them. This results in a substantial displacement of the primary-secondary mirror system's primary focus along the axial direction, further degrading the wavefront at the exit pupil of the telescope. The TTL coupling noise caused in this scenario will affect the detection of gravitational waves, thus requiring the adjustment of the position of the three-four mirror system through the focusing system to minimize TTL coupling noise. In this paper, the model for TTL coupling noise was established using the first 36 orders of Zernike polynomials. The misalignment model of the primary-secondary mirror system was derived using geometric optics theory. The study investigates the influence of the telescope focusing system before and after focusing on the wavefront aberrations and TTL coupling noise at the exit pupil of the telescope. The analysis indicates that with a misalignment of 7.56 mu m in the axial distance between the primary and secondary mirrors, the addition of a focusing system reduces the wavefront error at the exit pupil of the telescope from 0.0328 lambda to 0.0046 lambda. Furthermore, the maximum coupling noise between wavefront distortion and pointing jitter is reduced from 4 pm Hz-1/2 to 0.4 pm Hz-1/2. This provides valuable insights for the design of gravitational wave detection telescopes and the study of focusing systems.