Method for large antenna deformation measurement based on fusion of visual imaging and laser ranging

To address the need for measuring high-precision full-field deformation of large planar array synthetic aperture radar antennas in orbit, this paper proposes a measurement method that integrates visual imaging and laser ranging. First, a coordinate system involving the camera, a two-axis turntable, and a laser rangefinder is established for the measurement system, and a three-dimensional (3D) coordinate calculation model is developed based on the triangulation principle. Subsequently, using the world coordinate system as a unified reference, a calibration model is constructed to characterize the non-orthogonal and non-intersecting spatial relationship between the two rotational axes of the turntable and the laser beam. On this basis, the external parameters of the camera relative to the world coordinate system are determined via the collinearity equation. The world coordinate system then serves as an intermediary to achieve high-precision extrinsic calibration between the camera and the laser rangefinder through coordinate transformation. Furthermore, a nonlinear mapping model between the image coordinates of a target point and the rotation angles of the turntable is established. It is demonstrated that this mapping exhibits a local one-to-one correspondence under aiming conditions. Through a strict convexity analysis, an effective operational domain is identified to ensure the stability of the inverse solution. Building on this, an autonomous laser beam aiming model is developed, incorporating coarse, secondary, and fine aiming strategies to guarantee precise convergence of the laser beam and the camera's line of sight at the target point. Experimental results show that the root mean square errors of the coordinate measurements in the X, Y, and Z directions are 0.28 mm, 0.34 mm, and 0.59 mm, respectively. This performance meets the accuracy requirements for in-orbit high-precision deformation monitoring of space-borne antennas, thereby providing a feasible technical solution for their on-orbit measurement.