# A Geometric Error Measurement System for Linear Guideway Assembly and Calibration  
[PERSON]  
1 Smart Machine and Intelligent Manufacturing Research Center, National Formosa University, Yunlin 632, Taiwan; [EMAIL_ADDRESS] (T.-H.H. ); [EMAIL_ADDRESS] (W.-Y.J. ); [EMAIL_ADDRESS] (G.-W.C.)  
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[PERSON]  
four interferometers and one corner cube for measuring three dimensional (3-D) coordinates of a microscopic scanning stage. [PERSON] et al. [3] proposed a method with two laser interferometers to measure wafer planar positioning errors and a laser interferometer to measure angular errors. [PERSON] et al. [4] designed an interferometer system for the measurement of \(x\)-\(y\) motion errors of wafer stages. In this system, incident beams are tilted with certain angle using a wedge prism, and an additional corner cube and a plane mirror are placed off the stage to help return the measuring beam. [PERSON] et al. [5] developed a laser interferometric system for real-time measurements of six-axis motions of a magnetic levitation stage by utilizing two corner cubes, six plane mirrors, and six polarization beam splitters (PBS). [PERSON] et al. [6] utilized two laser interferometers and two plane mirrors to measure three degrees of freedom (3-DOF) of the dual-axis nano-positioning stage, and successfully obtained the nano-scale positioning accuracy of linear and rotation motions. For the geometric error measurement systems based on multi-beam with PSD and/or QD, [PERSON] et al. [7; 8] proposed a laser optical multi-degree-of-freedom measurement (MDFM) system, which utilized two sets of PSDs to calibrate five degrees of freedom (5-DOF) of coordinate measuring machines. [PERSON] et al. [9] proposed an optical measurement system using one laser interferometer and three QDs for the measurement of 6-DOF linear motion errors of a machine tool table. [PERSON] et al. [10] also developed an MDFM system based on two dimensional (2-D) charge-coupled device (CCD) cameras instead of QD in order to correct the geometric errors of coordinate measuring machines. For the research on multi-beam measurement devices integrated with PSD or QD, [PERSON] et al. [11] proposed a multi-function error measuring system using three sets of quadrant detectors for inspecting the 5-DOF of CNC machine tools. [PERSON] et al. [12] developed a six degrees of freedom (6-DOF) measuring system by using four laser Doppler scales, two L-shaped plane mirrors, one long right-angle mirror, and two QDs for the measurement of six motion errors of a wafer stage. [PERSON] et al. [13] proposed a simple and low-cost technique using a laser diode, a one dimensional (1-D) grating, two PSDs, and a reference rotary table with good repeatability to measure the four degrees of freedom (4-DOF) errors of a rotary table for a 360\({}^{\circ}\) full circle. [PERSON] et al. [14] proposed a straightness error measurement device based on common-path compensation for the elimination of laser beam drift by utilizing an optical module consisting of a PSD and a QD. [PERSON] et al. [15] developed a novel optical calibration system using two sets of QDs and one ball lens module to obtain the total error associated with simultaneous multi-axis movements of CNC machine tools. [PERSON] et al. [16] utilized a method for measuring 5-DOF errors of a moving stage with a monolithic prism and three PSDs. [PERSON] et al. [17] proposed a laser straightness interferometer system that is able to compensate the rotational error and simultaneously detect the 6-DOF error of a linear stage by using one PSD, two QDs, one Wollaston prism, one corner cube, and other optical components. In view of the literature, the repeatability of geometric error measurements using a pentaprism could be further improved by introducing a calibration mechanism to detect the altitude angle between the incident beam and the pentaprism.