IJAT Vol.16 No.5 pp. 572-581
doi: 10.20965/ijat.2022.p0572


Design and Testing of a Compact Optical Angle Sensor for Pitch Deviation Measurement of a Scale Grating with a Small Angle of Diffraction

Lue Quan*, Yuki Shimizu**,†, Ryo Sato*, Dong Wook Shin*, Hiraku Matsukuma*, Andreas Archenti***, and Wei Gao*

*Department of Finemechanics, Tohoku University
6-6-01 Aramaki Aza Aoba, Aoba-ku, Sendai, Miyagi 980-8579, Japan

**Division of Mechanical and Space Engineering, Hokkaido University, Sapporo, Japan

Corresponding author

***Department of Production Engineering, KTH Royal Institute of Technology, Stockholm, Sweden

March 11, 2022
May 9, 2022
September 5, 2022
diffraction grating, optical head, laser autocollimation, pitch deviation

The design and testing of different optical heads were performed to evaluate the pitch deviation of a diffraction scale grating with a small diffraction angle. Based on the proposed pitch deviation evaluation method employing optical angle sensors based on laser autocollimation, a modified optical head with position-sensitive detectors (PSDs) is first designed and constructed by following the conventional optical configuration. Owing to the small angle of diffraction of the first-order diffracted beams, the modified optical head has a large working distance, resulting in poor sensor stability. Therefore, a novel and compact optical head employing a pair of small prisms is designed and developed to shorten the working distance of the optical head. An additional modification was also made to the developed compact optical head in such a way that collimator objectives (COs) in the laser autocollimation units are removed to improve the sensor sensitivity. Experimental comparisons were conducted using the three types of optical heads to verify the feasibility of the developed optical angle sensor with PSDs.

Cite this article as:
L. Quan, Y. Shimizu, R. Sato, D. 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.
Data files:
  1. [1] T. Oiwa, M. Katsuki, M. Karita, W. Gao, S. Makinouchi, K. Sato, and Y. Oohashi, “Questionnaire Survey on Ultra-Precision Positioning,” Int. J. Automation. Technol., Vol.5, No.6, pp. 766-772, 2011.
  2. [2] H. V. Brussel, “Evaluation and testing of robots,” CIRP Ann. – Manuf. Technol., Vol.39, No.2, pp. 657-664, 1990.
  3. [3] A. Mekis, S. Gloeckner, G. Masini, A. Narasimha, T. Pinguet, S. Sahni, and P. D. Dobbelaere, “A grating coupler-enabled CMOS photonics platform,” IEEE J. Sel. Top. Quant. Electron., Vol.17, No.3, pp. 597-608, 2011.
  4. [4] 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 Ann. – Manuf. Technol., Vol.68, No.2, pp. 843-866, 2019.
  5. [5] W. T. Estler, K. L. Edmundson, G. N. Peggs, and D. H. Parker, “Large-scale metrology – an update,” CIRP Ann. – Manuf. Technol., Vol.51, pp. 587-609, 2002.
  6. [6] C. J. Evans, R. J. Hocken, and W. T. Estler, “Self-calibration: reversal, redundancy, error separation, and absolute testing,” CIRP Ann. – Manuf. Technol., Vol.45, No.2, pp. 617-634, 1996.
  7. [7] H. Kunzmann, T. Pfeifer, and J. Flügge, “Scales vs. Laser interferometers performance and comparison of two measuring systems,” CIRP Ann. – Manuf. Technol., Vol.42, No.2, pp. 753-767, 1993.
  8. [8] J. Mayr, J. Jedrzejewski, E. Uhlmann, M. A. Donmez, W. Knapp, F. Härtig, K. Wendt, T. Moriwaki, P. Shore, R. Schmitt, C. Brecher, T. Würz, and K. Wegener, “Thermal issues in machine tools,” CIRP Ann. – Manuf. Technol., Vol.61, pp. 771-791, 2012.
  9. [9] L. Uriarte, M. Zatarain, D. Axinte, J. Yagüe-Fabra, S. Ihlenfeldt, J. Eguia, and A. Olarra, “Machine tools for large parts,” CIRP Ann. – Manuf. Technol., Vol.62, No.2, pp. 731-750, 2013.
  10. [10] H. Schwenke, W. Knapp, H. Haitjema, A Weckenmann, R. Schmitt, and F. Delbressine, “Geometric error measurement and compensation of machines-An update,” CIRP Ann. – Manuf. Technol., Vol.57, No.2, pp. 660-75, 2008.
  11. [11] D. Acosta, J. A. Albajez, J. A. Yagüe-Fabra, and J. Velázquez, “Verification of machine tools using multilateration and a geometrical approach,” Nanomanufacturing Metrology, Vol.1, No.1, pp. 39-44, 2018.
  12. [12] W. Gao, “Precision Nanometrology – Sensors and Measuring Systems for Nanomanufacturing,” Springer, 2010.
  13. [13] 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 Ann. – Manuf. Technol., Vol.64, No.2, pp. 773-796, 2015.
  14. [14] W. Gao, T. Araki, S. Kiyono, Y. Okazaki, and M. Yamanaka, “Precision nano-fabrication and evaluation of a large area sinusoidal grid surface for a surface encoder,” Precision Engineering, Vol.27, Issue 3, pp. 289-298, 2003.
  15. [15] W. Gao and A. Kimura, “A fast evaluation method for pitch deviation and out-of-flatness of a planar scale grating,” CIRP Ann. – Manuf. Technol., Vol.59, No.1, pp. 505-508, 2010.
  16. [16] A. Teimel, “Technology and applications of grating interferometers in high-precision measurement,” Precision Engineering, Vol.14, Issue 3, pp. 147-154, 1992.
  17. [17] M. Sawabe, F. Maeda, Y. Yamaryo, T. Shimomura, 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, Issue 3, pp. 320-328, 2004.
  18. [18] T. Coveney, “A review of state-of-the-art 1D length scale calibration instruments,” Measurement Science and Technol., Vol.31, No.4, 042002, 2020.
  19. [19] S. W. Hell and J. Wichmann, “Breaking the diffraction resolution limit by stimulated emission: stimulated-emission-depletion fluorescence microscopy,” Opt. Lett., Vol.19, No.11, pp. 780-782, 1994.
  20. [20] 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.
  21. [21] M. V. Salapaka and S. M. Salapaka, “Scanning probe microscopy,” IEEE Control Systems, Vol.28, No.2, pp. 65-83, 2008.
  22. [22] X. Chen, Y. Shimizu, X. Xiong, Y. L. Chen, and W. Gao, “Self-calibration of Fizeau interferometer and planar scale gratings in Littrow setup,” Optics Express, Vol.25, Issue 18, pp. 21567-21582, 2017.
  23. [23] X. Xiong, H. Matsukuma, Y. Shimizu, and W. Gao, “Evaluation of the pitch deviation of a linear scale based on a self-calibration method with a Fizeau interferometer,” Measurement Science and Technol., Vol.31, No.9, 094002, 2020.
  24. [24] S. Yang and G. Zhang, “A review of interferometry for geometric measurement,” Measurement Science and Technol., Vol.29, No.10, 102001, 2018.
  25. [25] X. Xiong, Y. Shimizu, H. Matsukuma, and W. Gao, “A Self-Calibration Stitching Method for Pitch Deviation Evaluation of a Long-Range Linear Scale by Using a Fizeau Interferometer,” Sensors, Vol.21, No.21, 7412, 2021.
  26. [26] 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.
  27. [27] A. E. Ennos and M. S. Virdee, “High accuracy profile measurement of quasi-conical mirror surfaces by laser autocollimation,” Precision Engineering, Vol.4, No.1, pp. 5-8, 1982.
  28. [28] E. Hecht, “Optics, 5th edition,” Pearson Education Limited, 2021.
  29. [29] Z. M, Odibat and N. T. Shawagfeh, “Generalized Taylor’s formula,” Applied Mathematics and Computation, Vol.186, pp. 286-293, 2007.
  30. [30] HEIDENHAIN, “Linear encoders.” [Accessed July 5, 2020]
  31. [31] W. Gao, Y. Saito, H. Muto, Y. Araia, and Y. Shimizu, “A three-axis autocollimator for detection of angular error motions of a precision stage,” CIRP Ann. – Manuf. Technol., Vol.60, No.1, pp. 515-518, 2011.
  32. [32] Y. Shimizu, S. L. Tan, D. Murata, T. Maruyama, S. Ito, Y. L. Chen, and W. Gao, “Ultra-sensitive angle sensor based on laser autocollimation for measurement of stage tilt motions,” Optics Express, Vol.24, No.3, pp. 2788-2805, 2016.
  33. [33] SONY, “Imaging and Sensing Technology.” [Accessed February 9, 2022]
  34. [34] HAMAMATSU, “Optical sensors.” [Accessed February 9, 2022]
  35. [35] A. G. Lopez and H. G. Craighead, “Wave-plate polarizing beam splitter based on a form-birefringent multilayer grating,” Opt. Lett., Vol.23, No.20, pp. 1627-1629, 1998.
  36. [36] Kodenshi corp., “POSITION SENSITIVITY DIODES, SD-503.” [Accessed April 8, 2022]
  37. [37] Y. Saito, Y. Arai, and W. Gao, “Detection of three-axis angles by an optical sensor,” Sensors and Actuators A: Physical, Vol.150, Issue 2, pp. 175-83, 2009.
  38. [38] K. M. Rocha, E. S. Soriano, W. Chamon, M. R. Chalita, and W. Nosé, “Spherical aberration and depth of focus in eyes implanted with aspheric and spherical intraocular lenses: a prospective randomized study,” Ophthalmology, Vol.114, No.11, pp. 2050-2054, 2007.

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Last updated on Sep. 22, 2022