A differential angle sensor is newly developed to calibrate the pitch deviations of a linear scale grating with a nominal pitch of 1.6 µm on an ultra-precision lathe. The angle sensor is composed of two angle detection units based on the laser autocollimation method. A collimated laser beam with a diameter of 1 mm, which is output from a laser diode with a wavelength of 685 nm, is projected onto the linear scale grating. The positive and the negative first-order diffracted beams from the scale are received by the two angle detection units, respectively. The X-slide of the ultra-precision lathe is employed to generate the necessary scanning motion for the calibration. Based on the fact that the pitch deviations will cause changes in the positive and the negative first-order diffraction angles, which are equal in magnitude and opposite in sign, the pitch deviations can be obtained from the differential output of the angle sensor. The tilt error motion of the X-slide, which is a major error factor in on-machine calibration, can also be removed in the differential output. The robustness of the developed angle sensor for on-machine calibration has been confirmed by testing the basic performances of the sensor on the machine tool. The feasibility of the on-machine calibration result of pitch deviations has been verified through comparing with the off-machine calibration result.

1. [1] W. Gao, S. W. Kim, H. Bosse, H. Haitjema, Y. L. Chen, X. D. Lu, W. Knapp, A. Weckenmann, W. T. Estler, and H. Kunzmann, “Measurement Technologies for Precision Positioning,” CIRP Annals, Vol.64, No.2, pp. 773-796, 2015. https://doi.org/10.1016/j.cirp.2015.05.009
2. [2] A. J. Fleming, “A Review of Nanometer Resolution Position Sensors: Operation and Performance,” Sensors and Actuators A: Physical, Vol.190, pp. 106-126, 2013. https://doi.org/10.1016/j.sna.2012.10.016
3. [3] P. C. Hu, D. Chang, J. B. Tan, R. T. Yang, H. X. Yang, and H. J. Fu, “Displacement Measuring Grating Interferometer: a Review,” Frontiers of Information Technology & Electronic Engineering, Vol.20, No.5, pp. 631-654, 2019. https://doi.org/10.1631/FITEE.1800708
4. [4] G. Ye, H. Liu, B. Lei, D. Niu, H. Xing, P. Wei, B. Lu, and H. Liu, “Optimal Design of a Reflective Diffraction Grating Scale with Sine-trapezoidal Groove for Interferential Optical Encoders,” Optics and Lasers in Engineering, Vol.134, 106196, 2020. https://doi.org/10.1016/j.optlaseng.2020.106196
5. [5] A. Kimura, W. Gao, W. J. Kim, K. Hosono, Y. Shimizu, L. Shi, and L. Zeng, “A Sub-nanometric Three-axis Surface Encoder with Short-period Planar Gratings for Stage Motion Measurement,” Precision Engineering, Vol.36, No.4, pp. 576-585, 2012. https://doi.org/10.1016/j.precisioneng.2012.04.005
6. [6] A. Teimel, “Technology and Applications of Grating Interferometers in High-precision Measurement,” Precision Engineering, Vol.14, Issue 3, pp. 147-154, 1992. https://doi.org/10.1016/0141-6359(92)90003-F
7. [7] W. Gao, H. Haitjema, F. Z. Fang, R. K. Leach, C. F. Cheung, E. Savio, and J. M. Linares, “On-machine and In-process Surface Metrology for Precision Manufacturing,” CIRP Annals, Vol.68, No.2, pp. 843-866, 2019. https://doi.org/10.1016/j.cirp.2019.05.005
8. [8] W. Gao, S. Ibaraki, M. A. Donmez, D. Kono, J. R. R. Mayer, Y. L. Chen, K. Szipka, A. Archenti, J. M. Linares, and N. Suzuki, “Machine Tool Calibration: Measurement, Modeling, and Compensation of Machine Tool Errors,” Int. J. of Machine Tool Design & Research, Vol.187, 104017, 2023. https://doi.org/10.1016/j.ijmachtools.2023.104017
9. [9] F. Meli and R. Thalmann, “Long-range AFM Profiler Used for Accurate Pitch Measurements,” Measurement Science and Technology, Vol.9, Issue 7, pp. 1087-1092, 1998. https://dx.doi.org/10.1088/0957-0233/9/7/014
10. [10] G. Dai, L. Koenders, J. Fluegge, and M. Hemmleb, “Fast and Accurate: High-speed Metrological Large-range AFM for Surface and Nanometrology,” Measurement Science and Technol., Vol.29, No.5, 054012, 2018. https://dx.doi.org/10.1088/1361-6501/aaaf8a
11. [11] M. V. Salapaka and S. M. Salapaka, “Scanning Probe Microscopy,” IEEE Control Systems, Vol 28, Issue 2, pp. 65-83, 2008. https://dx.doi.org/10.1109/MCS.2007.914688
12. [12] M. Sawabe, F. Maeda, Y. Yamaryo, T. Simomura, Y. Saruki, T. Kubo, H. Sakai, and S. Aoyagi, “A New Vacuum Interferometric Comparator for Calibrating the Fine Linear Encoders and Scales,” Precision Engineering, Vol.28, No.3, pp. 320-328, 2004. https://doi.org/10.1016/j.precisioneng.2003.11.007
13. [13] T. Coveney, “A Review of State-of-the-art 1D Length Scale Calibration Instruments,” Measurement Science and Technol., Vol.31, No.4, 042002, 2020. https://dx.doi.org/10.1088/1361-6501/ab5f71
14. [14] J. R. Pekelsky, B. J. Eves, P. R. Nistico, and J. E. Decker, “Imaging Laser Diffractometer for Traceable Grating Pitch Calibration,” Measurement Science and Technology, Vol.18, No.2, pp. 375-383, 2007. https://dx.doi.org/10.1088/0957-0233/18/2/S08
15. [15] D. A. Brasil, J. A. P. Alves, and J. R. Pekelsky, “An Imaging Grating Diffractometer for Traceable Calibration of Grating Pitch in the Range 20 µm to 350 nm,” J. of Physics: Conf. Series, Vol.648, No.1, 012013, 2015. https://dx.doi.org/10.1088/1742-6596/648/1/012013
16. [16] Y. F. Xie, W. Jia, D. Zhao, Z. H. Ye, P. Sun, C. C. Xiang, J. Wang, and C. Zhou, “Traceable and Long-range Grating Pitch Measurement with Picometer Resolution,” Optics Communications, Vol.476, 126316, 2020. https://doi.org/10.1016/j.optcom.2020.126316
17. [17] L. Quan, Y. Shimizu, X. Xiong, H. Matsukuma, and W. Gao, “A New Method for Evaluation of the Pitch Deviation of a Linear Scale Grating by an Optical Angle Sensor,” Precision Engineering, Vol.67, pp. 1-13, 2021. https://doi.org/10.1016/j.precisioneng.2020.09.008
18. [18] L. Quan, Y. Shimizu, R. Sato, D. W. Shin, H. Matsukuma, A. Archenti, and W. Gao, “Design and Testing of a Compact Optical Angle Sensor for Pitch Deviation Measurement of a Scale Grating with a Small Angle of Diffraction,” Int. J. Automation Technol., Vol.16, No.5, pp. 572-581, 2022. https://doi.org/10.20965/ijat.2022.p0572
19. [19] Y. Shimizu, “Laser Interference Lithography for Fabrication of Planar Scale Gratings for Optical Metrology,” Nanomanufacturing and Metrology, Vol.4 Issue 1, pp. 3-27, 2021. https://doi.org/10.1007/s41871-020-00083-2
20. [20] Z. M. Odibat and N. T. Shawagfeh, “Generalized Taylor’s formula,” Applied Mathematics and Computation, Vol.186, Issue 1, pp. 286-293, 2007. https://doi.org/10.1016/j.amc.2006.07.102
21. [21] K. Li, Z. Zhang, J. Lin, R. Sato, H. Matsukuma, and W. Gao, “Angle Measurement Based on Second Harmonic Generation Using Artificial Neural Network,” Nanomanuf. Metrol., Vol.6, No.1, 28, 2023. https://doi.org/10.1007/s41871-023-00206-5