Research on nonlinear calibration of angular measurements for precision pointing mechanisms in space gravitational wave detection

During the detection missions, the influence of inter-satellite laser transmission time and orbital mechanics results in the generation of a leading angle. This angle is accurately adjusted through the Point Ahead Angle Mechanism (PAAM) to ensure the establishment of inter-satellite links. However, the PAAM is affected by the hysteresis nonlinearity of piezoelectric ceramics, leading to pointing jitter error in the outgoing laser path, which ultimately impacts the precision of the laser emission angle. To measure the leading angle, high-resolution capacitive displacement sensors are employed; however, the angle measurement using capacitive displacement sensors exhibits significant nonlinearity, which does not meet the high-precision measurement requirements of the beam. This paper proposes a nonlinear correction model for the angular measurement of capacitive displacement sensors using a Backpropagation Neural Network (BP) algorithm. The model has been experimentally validated using a developed pointing mechanism, achieving a deflection accuracy better than 18 nrad within the range of deflection, thereby ensuring high-precision deflection of the beam and demonstrating the effectiveness of the algorithm.