Measurement by Multidirectional Interferometers of the Position and Orientation of a Positioning Stage

A multidirectional interferometer system is developed to determine the position and orientation of a stage moved in a two-dimensional (2-D) space. In this system four corner-cube prisms are mounted on the moving stage, and four laser beams are incident on the corner cubes in different directions. Moving distances in the observed directions are measured by laser interferometers. The position and orientation of the stage are calculated from the moving distances of the corner cubes. Some experiments are done on the 2-D moving stage with four interferometers, and measurement errors are estimated from redundant data. The estimated accuracy is higher than 0.2 (mu)m for translation and 0.3 * 10^-3 deg for rotation for a measurement range of 0.5 mm and 0.5 deg.