This paper presents a new method to reveal the relation between the surface deformation and near-field amplitude of a reflector antenna based on complex geometrical optics, which could be used as an efficient way to estimate the antenna surface verified by simulation results. The measurement process based on this method is envisaged to be realized by a single scanning of the near-field amplitude which would overcome many limitations of radio holography and phase retrieval methods such as the frequency and elevation. The largest source of error in the original deformation-amplitude equation (DAE) has been corrected by considering the Gaussian feed as a complex point source. To track the ray trajectory so that the improved DAE could be solved, an iteration method including a golden section search algorithm is designed to make the solution converge. By solving the modified DAE, simulation result shows that a more accurate solution could be obtained, and the antenna surface could be recovered to a root mean square error of under 30 microns.
