Modeling and calibration of pointing errors with alt-az telescope

• I/we use the Denavit-Hartenberg convention to analyze kinematics of an alt-az telescope.
• A physical model is established to illustrate the effects of geometric errors.
• An improved hybrid model denoted as SPRM model is developed to compensate for remaining nonlinear errors.
• The measured experiment confirmed that the proposed SPRM model provides higher accuracy than does the conventional KM.

This paper presents a new model for improving the pointing accuracy of a telescope. The Denavit–Hartenberg (D–H) convention was used to perform an error analysis of the telescope's kinematics. A kinematic model was used to relate pointing errors to mechanical errors and the parameters of the kinematic model were estimated with a statistical model fit using data from two large astronomical telescopes. The model illustrates the geometric errors caused by imprecision in manufacturing and assembly processes and their effects on the pointing accuracy of the telescope. A kinematic model relates pointing error to axis position when certain geometric errors are assumed to be present in a telescope. In the parameter estimation portion, the semi-parametric regression model was introduced to compensate for remaining nonlinear errors. The experimental results indicate that the proposed semi-parametric regression model eliminates both geometric and nonlinear errors, and that the telescope's pointing accuracy significantly improves after this calibration.