# Optical Pupil Shift Correction Method for Large Ground-Based Optical Telescopes
## 3 Calculation of Optical Pupil Shift and Active Compensation  
### Causes of Optical Pupil Shift  
We consider the classic primary and secondary mirror system with a Cassegrain structure as an example. The misalignment error of the optical system is mainly due to the gravitational bending and sinking of the primary and secondary mirrors, as well as temperature-induced changes in their relative positions, resulting in a shift in the system's optical axis. An unstable optical axis of the system can cause a change in the position of the focal point of the primary and secondary mirrors, causing a shift in the pupil surface of the primary mirror [21, 22, 23, 24].  
For the adaptive optical imaging system, the Hartmann measurement and deformation mirror systems were placed at the optical pupil position of the primary mirror. The pupil shift caused the mapping surface of the primary mirror to circumscribe the deformation mirror. As the aperture of the primary mirror increased, the influence of drawing the circle becomes more evident, which severely impedes the correction of the adaptive optical high-resolution imaging system and, consequently, the quality of image. From the perspective of the telescope's structure, the main causes of the shift may include [24]:  
* The position deviation of the primary mirror is caused by the deformation of its support assembly: The use of flexible rods in the primary mirror-support structure to reduce the deviation of the optical material and the temperature change of the structural material, which could lead to a decrease in the stiffness of the structure, cause the primary mirror under the action of gravity to deviate its position and angle relative to the primary mirror cell. This deviation varies with the telescope elevation angle. In this study, the active optical technology ensured an absolute position deviation of 0.02 mm for the primary mirror, which had a negligible effect on the optical axis offset [25, 26, 27, 28] (Figure 4).
* The deviation of the secondary mirror is due to the gravitational deformation of the truss: As illustrated in Figure 1, the span of the truss is very large in height (approximately 5.5 m). Despite the use of large-diameter bars in the truss structure, the position and angular deviation of the secondary mirror occurs with the change of elevation angle, owing to the high structural load from, for example, the ring beam and four wing beams [29, 30] (Figure 5).
* Thermal deformation causes the misalignment error: The change in the ambient temperature will result in the thermal deformation of the structure. Therefore, the primary and secondary mirrors will deviate from the theoretical position, which is the major cause of the interval deviation of the primary and secondary mirrors. With the increase in the telescope aperture, the influence of deviation of the primary mirror optical axis relative to the perpendicular four-way plane is aggravated. Deviations in the primary and secondary mirror intervals will also trigger a deviation in the relative position of the primary and secondary mirrors [31] (Figure 5).