It is important to calibrate the straightness and the squareness of the XY-stage for precision manufacturing and measurement. Normally it is calibrated using much higher precise and accurate measuring instruments and/or artifacts. The high precision and accurate instruments and artifacts are expensive. So, in this paper, Self-calibration method is applied to XY-stage. This method does not require any much high precision and accurate instruments and artifacts. The normal XY-stage moves to the location at the unique coordinates. In this case, it is difficult to apply self-calibration method. Therefore, XY-stage is expanded to XYθ-stage with parallel mechanism. As this stage moves to the location at a lot of coordinates, self-calibration method is applied. This method is confirmed in simulation and experiment. In simulation, the extension lengths of mechanism are estimated from known kinematic parameters and the target coordinates. After that, estimated kinematic parameters are calculated by least-squares method from the extension lengths and the target coordinates. Finally, the positioning coordinates are calculated from the estimated kinematic parameters and the extension lengths. It is proved that the calibration method is effective by comparing the target coordinates and the positioning coordinates. In experiment, the experimental process is similar to the simulation without the estimation of extension lengths. The results of simulation and experiment are shown in this paper.
First Detection of the GI-type of Intrinsic Alignments of Galaxies Using the Self-calibration Method in a Photometric Galaxy Survey