Influence of Lens Systematic Errors on Autocollimator Angle Measurement: Theoretical and Experimental Explanations

Highlights: What are the main findings? Among the various aberrations of a collimator objective, only coma at various orders affects the accuracy of an autocollimator. The angle errors introduced by assembly deviation are a systematic shift. This shift is independent of the field of view and is determined solely by the aberrations and the decentration of the collimator objective. It can be expressed in terms of the Sensitivity of Assembly Deviation (SAD) coefficient. What are the implications of the main findings? The coma-dominant influence can be used to correct the aberrations of a collimator objective during the design step. The Sensitivity of Assembly Deviation coefficient can be utilized to guide the positional and attitudinal adjustments of the collimator objective during the adjustment step. Autocollimators are widely used for sensor calibration. It is crucial to suppress systematic errors and enhance the measurement accuracy of autocollimators. However, the influence mechanism of systematic errors originating from the collimator objective—such as aberrations, and particularly the coupled effect of aberrations and assembly deviation—on measurement accuracy is not well understood. By switching between the perspectives of ray tracing and aberration, we analyzed the influence mechanism of aberrations. The results indicate that only coma aberrations of various orders affect the accuracy. Then we applied nodal wave aberration theory and found that the influence of assembly deviation is a factor only related to the aberration under a certain offset (composed of translational and rotational components). In this work, we defined the sensitivity of assembly deviation as the ratio of this factor and the offset. In the experimental part based on a homemade autocollimator, the maximal errors of yaw angle are decreased from 2.09 arcsecs to 1.41 arcsecs, while the one of pitch angle is decreased from 2.32 arcsecs to 1.63 arcsecs, within a measuring interval of ±500 arcsecs. The sensitivity of assembly deviation of the collimator objective used is 0.004 arcsec per micron, which agrees with the theoretical analysis.