Nonlinear inverse solution by the look-up table method for Risley-prism-based scanner

A pair of rotation Risley prisms can perform superior optical pointing and tracking functions with large visual field and high accuracy. Crucial to the function implementation are the nonlinear inverse solutions to the double-prism orientation angles for tracking a given target trajectory. In the paper, a novel look-up table method is proposed to solve this problem. Because there are two groups of solutions to the rotation angles achieved from an arbitrary target point, a "jump" phenomenon occurs and generates the discontinuous curves of multi-group rotation angle solutions. According to the mapping relation between the coordinate values of the target point and the corresponding rotation angles of two prisms, we can establish the continuous solution curves by adding constraints and employing an optimization algorithm. Experimental results validate the obtained inverse solutions applicable to scan a trajectory close to the given one within an error threshold. The proposed look-up table method can provide foundation for the continuous control of the Risley-prism-based scanner in its inverse applications.Keywords: Risley prism, look-up table method, inverse solution, scanner.