## 1 Introduction  
The shape error of a reflector has a great influence on the electrical performance of an antenna, which will cause a loss of the antenna gain. In recent years, with the continuous improvement of the aperture and working frequency of the radio telescope antenna, the required antenna surface accuracy is getting higher and higher. Precisely gauging the surface precision of an antenna significantly contributes to the enhancement of its electrical performance. Microwave antenna holography is a technology to accurately measure and evaluate the accuracy of the antenna surface. It has the characteristics of a simple principle, convenient operation, fast measurement speed, high measurement efficiency, and no special requirements for antenna attitude during the measurement process. It is widely used in large antenna surface measurements [1; 2; 3]: for example, GBT [4], SRT [5], Tianma [6], and so on. The technology mainly uses the Fourier transform relationship between the antenna aperture field and the radiation far field. The complex distribution of the far field is obtained by measuring the emission source signal, and then obtaining the aperture field distribution by the two-dimensional Fourier transform. The measured actual aperture distribution is compared with the ideal aperture distribution, and then the surface shape distribution of the antenna reflector is derived [7; 8; 9]. However, in the process of microwave holographic measurement, the existence of both feed offset error and pointing error will affect the reconstructed surface shape error distribution results and reduce the antenna measurement accuracy. Therefore, it is particularly important to study and compensate for the influence of these error sources in the process of microwave holographic measurement. A large number of studies have been carried out in the academic community on the feed offset error in order to deeply explore its impact on antenna performance. [PERSON] [10]used geometrical optics to derive expressions for the feed lateral offset error and feed axial offset error and investigated their effects on the antenna far-field pattern, respectively. [PERSON] [11] studied the determination method of the feed position, using a combination of polynomial fitting and geometrical optics to derive the actual positional coordinates of the feed. [PERSON] [12] proposed a new method to determine the amount of feed adjustment based on the far field without knowing the deformation. [PERSON] [13] proposed an innovative analytical method for assessing the directivity patterns of cluster-fed reflector antennas with random feed element positions and orientation displacements. [PERSON] [14] studied the comprehensive influence of different reflector subtended angles and feed displacements on the antenna. However, these studies have not thoroughly explored the underlying mechanisms that different feed offset errors have on the effect of the accuracy of the antenna surface shape in a microwave holography measurement. The pointing error is divided into systematic error and random error [15]. The systematic error is the pointing deviation, which is mainly caused by the structural deformation of the antenna pedestal and the reflector. The random error is the scanning error mainly caused by inertial vibrations, wind load effects, and temperature effects during antenna movement. Many studies focus on the analysis of the influence of the pointing error caused by the systematic error on the electrical performance of antennas, as well as on the study of the systematic error compensation methods. [PERSON] [16] derived an algorithm for pointing error estimation and azimuth axis tilt using tiltmeter data. [PERSON] [17] proposed a pointing error analysis model to estimate the pointing error caused by antenna structural deformation under wind loading based on the full working condition dynamic model (EWCDM). [PERSON] [18] proposed a pointing error analysis method based on coordinate transformation and a dynamic model correction method based on modal weighting.