Calibration of the straightness and orthogonality error of a laser feedback high-precision stage using self-calibration methods

An ultra high-precision 3-DOF air-bearing stage is developed and calibrated in this study. The stage was developed for the transportation of a glass or wafer with x and y following errors in the nanometer regime. To apply the proposed stage to display or semiconductor fabrication equipment, x and y straightness errors should be at the sub-micron level and the x–y orthogonality error should be in the region of several arcseconds with strokes of several hundreds of mm. Our system was designed to move a 400 mm stroke on the x axis and a 700 mm stroke on the y axis. To do this, 1000 mm and 550 mm bar-type mirrors were adopted for real time Δx and Δy laser measurements and feedback control. In this system, with the laser wavelength variation and instability being kept to a minimum through environmental control, the straightness and orthogonality become purely dependent upon the surface shape of the bar mirrors. Compensation for the distortion of the bar mirrors is accomplished using a self-calibration method. The successful application of the method nearly eliminated the straightness and orthogonality errors of the stage, allowing their specifications to be fully satisfied. As a result, the straightness and orthogonality errors of the stage were successfully decreased from 4.4 μm to 0.8 μm and from 0.04° to 2.48 arcsec, respectively. (paper)