In order to get the actual spatial position and orientation and evaluate surface accuracy of rotating paraboloid reflector under working condition, a spatial transforming model is established by analyzing relationship between local coordinate system and global measuring coordinate system. Two optimization fitting methods, eigenvalue parameter method and rigid body displacement method, were promoted based on the principle of least squares. Two fitting methods were analyzed and compared by comparing their fitting results. Optimum fitting parameters and the best fitting paraboloid surface are obtained, which shows that parabolic surface of reflector can be effectively fitted by two methods. During calculation, rigid body displacement method performs better for its stability. This could be a useful reference for surface accuracy fitting and detecting of different reflectors.
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