Four-beam laser interferometry for three-dimensional microscopic coordinate measurement

We propose a new method for calibrating the three-dimensional (3-D) behavior of a scanning stage. Four laser interferometers are used to determine the position of the corner point of a corner mirror attached to the stage. We calculated the 3-D coordinate of the corner point by using only the length information given by the four laser interferometers; thus a method is realized that is traceable from the practical definition of length and that facilitates the optical alignment that is necessary for the interferometers. We calibrated a commercial 3-D stage by the proposed method with a coordinate accuracy of 20-30 nm.