Criteria for Selection of Point-Ahead Angle Compensation Strategy in Intersatellite Laser Ranging Interferometry of TianQin Based on Research of Tilt-to-Length Coupling Noise

TianQin is expected to deploy three spacecraft in Earth orbit at the altitude of about 1 × 108 m to form an equilateral triangular constellation with arm lengths of about 1.7 × 108 m. It is aimed at detecting gravitational waves in the frequency range from 0.1 mHz to 1 Hz by means of high sensitive laser ranging interferometry with pathlength measurement noise below 1 pm/Hz1/2. The long-range propagation of beam in the intersatellite laser ranging interferometry between the three spacecraft results in a non-negligible time delay of 0.58 s. Therefore, there is an angular difference between the optimal outgoing and incoming laser beam of laser ranging interferometry on each spacecraft, which is denoted as the point-ahead angle. Due to the relative motion between the three spacecraft, the point-ahead angle of TianQin constellation is approximately 22.96 μrad with a dynamic variation range of ±24.71 nrad. Point-ahead-angle mechanism is a fine steering mirror used for point-ahead angle compensation to diminish the beam pointing error, thus to maintain the intersatellite laser link as well as to diminish the tilt-to-length coupling noise, which are vital to the gravitational wave detection. Both the static and dynamic point-ahead angle compensation strategies can be used in TianQin and the selection of the two is based on minimizing the total point-ahead-angle-related tilt-to-length coupling noise. In this paper, a criteria for selection of the two strategies are proposed by establishing a model of point-ahead-angle-related tilt-to-length coupling noise as well as a corresponding evaluation function for calculation and comparison. The results indicate that the dynamic compensation strategy is the optimal choice only when the first-order tilt-to-length coupling coefficient of point-ahead-angle mechanism is less than 6.4 × 10−9 m/rad, otherwise the static compensation strategy should be used. The proposed criteria, as well as the model and the requirement for point-ahead-angle mechanism, can serve as a common theoretical basis in laser ranging interferometry applications.