General model for the pointing error analysis of Risley-prism system based on ray direction deviation in light refraction

The Risley-prism-based light beam steering apparatus delivers superior pointing accuracy and it is used in imaging LIDAR and imaging microscopes. A general model for pointing error analysis of the Risley prisms is proposed in this paper, based on ray direction deviation in light refraction. This model captures incident beam deviation, assembly deflections, and prism rotational error. We derive the transmission matrixes of the model firstly. Then, the independent and cumulative effects of different errors are analyzed through this model. Accuracy study of the model shows that the prediction deviation of pointing error for different error is less than 4.1×10^-5° when the error amplitude is 0.1°. Detailed analyses of errors indicate that different error sources affect the pointing accuracy to varying degree, and the major error source is the incident beam deviation. The prism tilting has a relative big effect on the pointing accuracy when prism tilts in the principal section. The cumulative effect analyses of multiple errors represent that the pointing error can be reduced by tuning the bearing tilting in the same direction. The cumulative effect of rotational error is relative big when the difference of these two prism rotational angles equals 0 or π, while it is relative small when the difference equals π/2. The novelty of these results suggests that our analysis can help to uncover the error distribution and aid in measurement calibration of Risley-prism systems.