Analytical inverse solution of a rotational achromatic Risley prism based on Fourier series fitting

Abstract

High-precision analytical inverse solution is a significant issue faced by the rotational achromatic Risley prism system. The current inverse solution method is based on numerical iteration, which is time-consuming. To solve this problem, we propose an analytical inverse solution method for a rotational achromatic Risley prism system based on Fourier series fitting. In the proposed method, the expression of the difference between the rotation angle and elevation angle of beam deflection is inversely fitted using the forward solution model. The analytical inverse solution is achieved using a two-step method based on this fitted expression. Simulation results of the analytical inverse solution show that the maximum azimuthal error was less than 2.23e−8 arcsec and the maximum elevation error was less than 1.33e−4 arcsec. Experimental results prove that with 1 arcsec pointing accuracy, the time consumption of the proposed method is only 0.108 ms, whereas that of the previous numerical-iteration-based method is 1.480 ms.