Analysis of alignment requirements for off-axis resonant cavity based on coupling efficiency

The optical path length stability of the off-axis four-reflection telescope is one of the key technical indicators for the TianQin gravitational wave detection system. In the mHz observation band, the telescope must exhibit an optical path length stability of 0.4pm/Hz 1/2 . As a feasible solution, the optical path length stability measurement of the off-axis four-reflection telescope based on the Pound–Drever–Hall (PDH) technique imposes stringent requirements on the alignment of the off-axis resonant cavity (ORC). Taking the off-axis two-reflection prototype as the research object, we propose a Monte Carlo analysis-based method for ORC alignment precision analysis. By considering misalignment as an intermediate function, we establish a relationship between the coupling efficiency of the ORC and the wavefront aberration of the telescope. The research results show that by considering the combined effects of multiple misalignment couplings of the primary and secondary mirrors, when the detected telescope wavefront aberration is better than 0.068 λ ( λ =1064nm) with a probability of 98%, the ORC coupling efficiency can achieve greater than 40% with a probability of 97.13%, which can be used as the main reference indicator for system misalignment analysis. This method simplifies the alignment difficulty of the target under test and can provide alignment reference for subsequent resonant cavities with internal off-axis telescopes.