## 4 Pointing Errors Caused by Thermal Gradient
### Inclinometer Measurement Compared with Astronomical Observation  
To verify the applicability of the inclinometer measurement system in measuring pointing errors during astronomical observation, an experiment was conducted from 12:00 on 14 February 2019, to 12:00 on 16 February 2019. The pulsar 1800 + 7828, located near the North Pole, was subjected to continuous K-band observation for a period of 48 h during which pointing error was measured using the cross-scan method. Concurrently, the inclinometer measurement system was activated to sample the alidade tilt at a rate of 1 Hz. The Pulsar 1800 + 7828 is highly suitable for this experiment due to its strong flux in K-band. Its proximity to the North Pole on the celestial sphere results in minimal changes in antenna azimuth and elevation during observation, as depicted in Figure 14. The antenna's azimuth shifts by only \(\pm 15^{\circ}\), rendering any pointing errors caused by track unevenness negligible. Figure 14: AZ and EL trajectory of Pulsar 1800 + 7828. Figure 13: The antenna alidade’s orientation and the apparent motion of the sun on 4 February 2019. As the weather remained sunny and windless throughout the 48 h experiment, it can be inferred that thermal gradients were primarily responsible for the antenna pointing errors observed. The inclinometer measurement data were filtered and compared with astronomical observations to generate the curve depicted in Figure 15.  
The inclinometer measurement system demonstrates a high level of agreement with astronomical observation measurements in terms of pointing errors, as illustrated by Figure 15. Even during the period from 12:00 to 18:00 when thermal gradients significantly impact the antenna alidade, the difference between pointing errors obtained through the measurement system and those derived from astronomical observation is only 2\({}^{\prime\prime}\) (RMS). It illustrates that the experiment exhibits thermally induced pointing errors, which peak earlier in the AZ direction than in the EL direction. This phenomenon is similar to that observed in Section 4.1 when the alidade was held stationary. Figure 16 depicts a schematic diagram illustrating the correlation between the apparent solar motion and the orientation of the alidade on 14 February. The rapid increase in antenna pointing errors after 9:00 is attributed to the sun's illumination of the N-E side of the alidade post-sunrise, causing an elevation in temperature that surpasses other areas, thereby resulting in an initial rise in azimuth direction for pointing errors. As the sun gradually shifted to illuminate the southeast side, pointing errors in elevation direction increased rapidly. As it was noon at this time, the thermal gradients on the alidade intensified, resulting in greater pointing errors in elevation than azimuth direction. Figure 16: The antenna alidade’s orientation and the apparent motion of the sun on 14 February 2019. Figure 15: A comparison of thermally induced pointing errors measured by astronomical observation and by the inclinometer measurement system: pointing errors in AZ and EL direction. The difference between pointing errors obtained from inclinometer measurement and those measured by astronomical observation during the period of 12:00 to 18:00 may be attributed to thermal gradients causing deformation in other parts of the antenna, particularly changes in the position of the secondary reflector or shape of the main reflector. The experiment clearly demonstrates that the thermal deformation of the alidade is a significant factor affecting the daytime pointing accuracy of the antenna. As this aspect of pointing deviation can be gauged by an inclinometer, it can be rectified using data from the said instrument. As the stability of the inclinometer measurement system has been demonstrated in previous experiments and its accuracy has been verified through astronomical observations, it shows great potential for correcting thermally induced pointing errors during daytime.