Telescope mirrors determine the imaging quality and observation ability of telescopes. Unfortunately, manufacturing highly accurate mirrors remains a bottleneck problem in space optics. One main factor is the lack of a technique for measuring the 3D shapes of mirrors accurately for inverse engineering. Researchers have studied and developed techniques for testing the quality of telescope mirrors and methods for measuring the 3D shapes of mirrors for centuries. Among these, interferometers have become popular in evaluating the surface errors of manufactured mirrors. However, interferometers are unable to measure some important mirror parameters directly and accurately, e.g. the paraxial radius, geometry dimension and eccentric errors, and these parameters are essential for mirror manufacturing. In this paper, we aim to remove the noise and lens distortion inherent in the system to improve the accuracy of a previously proposed one-shot projection mirror measurement method. To this end, we propose a ray modeling and a pattern modeling method. The experimental results show that the proposed ray modeling and pattern modeling method can improve the accuracy of the one-shot projection method significantly, making it feasible as a commercial device to measure the shapes of mirrors quantitatively and accurately.