# Precision Analysis and Error Compensation of a Telescope Truss Structure Based on Robotics
## 4 Secondary Mirror Adjustment Experiment
### Experiment Analysis  
It should be noted that this experiment is an a priori experiment. This experiment verifies the correctness of the high-order sensitivity matrix method in the system aberration compensation problem. At the same time, the feasibility of the secondary mirror truss of the robotic arm can be proved to a certain extent with the theoretical calculation and simulation in Section 2. In the experiment, the Stewart platform was used to adjust the SM. After multiple adjustments, the wavefront aberration can be adjusted to \(\lambda/15\), verifying the adjustment ability of the SM. Because the robotics-based SM truss achieves the same adjustment ability as the Stewart platform, it also demonstrates a similar adjustment accuracy. Therefore, the experiment verifies the feasibility of the new structure of the SM scheme and verifies its compensation ability regarding the SM misalignment.  
According to the results before and after the adjustment, although the high-order sensitivity matrix method can compensate for the wavefront aberration effectively, it does not correlate exactly with the simulated adjustment results presented in Section 3. In practice, the adjustment process requires multiple iterations to achieve an image quality comparable to the initial design of the optical system. There are several significant sources of error, as follows.  
First, in principle, the sensitivity matrix method does not involve optical knowledge and aberration theory but applies a mathematical method and uses a data model to fit localized optimal solutions. Therefore, it is not possible to compensate entirely for the aberration of the full field of view point. The sensitivity matrix method only calculates the misalignment amount based on the data of the on-axis field of view modeling, and then adjusts the position of the SM several times to make the axis the upper point aberration and the off-axis aberration of each field of view as consistent as possible with reference to the wavefront aberration of the edge field of view. This is demonstrated by the adjustment experiment (Section 4.2). After the initial adjustment of the position of the SM, the aberration of the on-axis field of view is improved significantly, but the aberration of the edge field of view is still far from the target value.  
Second, in terms of processing errors, the error associated with the radius of curvature of the vertex of the PM processing is \(\pm 1\) mm, and the wavefront aberration generated by the system is \(\lambda/50\) (RMS), with a surface error of \(\lambda/40\) (RMS), and the wavefront aberration generated by the system is \(\lambda/20\) (RMS). Moreover, owing to the horizontal construction of the optical system, it can be seen from the finite element simulation conclusions in Section 3.3 that the surface error of the main mirror in the vertical state is the largest error source, and the sensitivity matrix method is limited in the extent that it can compensate for the wave aberration caused by the main mirror surface. In addition, the SM also has processing errors and other factors that cause residual aberration of the system and affect the adjustment effect and imaging quality.  
Finally, in the actual adjustment process, there are several environmental factors, such as airflow disturbance, vibration, and field of view detection error, that affect the wavefront detection accuracy. These error sources lead to inaccuracies in the Zernike coefficients obtained by the interferometer, thereby increasing the error in the solution of the offset. The adjustment mechanism is limited by the adjustment accuracy, which will also impact the influence of computer-aided adjustments. Therefore, it needs to make many adjustments to obtain the optimal wavefront state during the actual adjustment.