To improve the performance of a Risley-prism system for optical detection and measuring applications, it is necessary to be able to determine the direction of the outgoing beam with high accuracy. In previous works, error sources and their impact on the performance of the Risley-prism system have been analyzed, but their numerical approximation accuracy was not high. Besides, pointing error analysis of the Risley-prism system has provided results for the case when the component errors, prism orientation errors, and assembly errors are certain. In this work, the prototype of a Risley-prism system was designed. The first-order approximations of the error analysis were derived and compared with the exact results. The directing errors of a Risley-prism system associated with wedge-angle errors, prism mounting errors, and bearing assembly errors were analyzed based on the exact formula and the first-order approximation. The comparisons indicated that our first-order approximation is accurate. In addition, the combined errors produced by the wedge-angle errors and mounting errors of the two prisms together were derived and in both cases were proved to be the sum of errors caused by the first and the second prism separately. Based on these results, the system error of our prototype was estimated. The derived formulas can be implemented to evaluate beam directing errors of any Risley-prism beam directing system with a similar configuration.
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