Plane mirror type laser interferometers are popularly being used in many modern ultraprecision machines, as they can perform simultaneous measurements of multiple axis positions with nanometer resolution capabilities. One important issue in this application of laser interferometers is to provide a good level of alignment between the reflecting mirrors and the laser beams so that measurement errors due to undesirable coupling effects can be avoided in multiple axis measurements. In this investigation, a thorough metrological analysis is given to develop an suitable mathematical model for a precision x-y stage in which the orthogonality misalignment between the reflecting mirrors significantly affects overall x-y measurement results. Then a noble calibration method is suggested in which two-dimensional displacement sensors of moire gratings of concentric circles are used to realize the reversal principle of orthogonality evaluation in situ. Finally, actual experimental results are discussed to verify that the suggested method can effectively calibrate the orthogonality error with an uncertainty of 0.2667 arcsec.
