Inverse solutions for a Risley prism scanner with iterative refinement by a forward solution

Risley prism scanners are increasingly used for laser beam steering due to their wide angular scanning range and high resolution. However, the inverse problem, which focuses on obtaining the required prisms' orientations for a given target position, has not been perfectly solved so far. The existing inverse solutions are not accurate or efficient enough for high-accuracy and real-time tracking. An iterative method that combines an approximate inverse solution with an iterative refinement by the forward solution is set forth in this paper. Two case studies indicate that the rotation motions of Risley prism pairs controlled by iterative solutions can slew the beam to create the desired tracking pattern quickly and accurately. Based on this method, a Risley prism scanner developed as a standard trajectory generator is implemented for the error measurement of a robotic manipulator in our experiments. The simulation and experimental results show that the inverse solution for one target point can be obtained within nine iterations for a prescribed tracking error threshold.