Synchrotron radiation sources have become brighter in recent years. In order to profit all this brilliance, optical surfaces of the beamlines must have slope errors below 1-2 microradians RMS. Thus, it is necessary to have accurate and repeatable measurements of these surfaces (plane, elliptical, toroid, etc.). In this work, a Fizeau interferometer is used for their characterization. The accuracy of the measurement is limited by quality of the reference surfaces of the interferometer. Lateral shearing technique is applied in order to remove the influence of the reference surfaces. This technique requires to use two or more images of the surface displaced each other. Then, systematic errors of the linear stage (guidance and positioning errors) become the limit for an accurate characterization. Different algorithms for the estimation and compensation of these systematic errors have been developed. They are based on the two dimensional redundancy of the data obtained from multiple measurements. In addition, algorithms to control the alignment of the setup have been developed and implemented in a stand-alone application. As a result, once errors introduced by the stage are controlled, an accurate characterization of the optical surfaces for beamlines is obtained. With this extended data analysis, the accuracy of the mirror characterization can be improved with independence of the quality of the reference optics of the interferometer.