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IJAT Vol.18 No.1 pp. 66-76
doi: 10.20965/ijat.2024.p0066
(2024)

Research Paper:

Measurement of a Freeform Surface by Dragging Three Point Method Along with a Circular Path

Kento Tokuchi*,†, Mikio Kurita*,**, and Keisuke Takahashi**

*Department of Astronomy, Faculty of Science, Kyoto University
Kitashirakawa-Oiwake-cho, Sakyo-ku, Kyoto, Kyoto 606-8502, Japan

Corresponding author

**LogistLab Inc.
Tokyo, Japan

Received:
July 14, 2023
Accepted:
December 14, 2023
Published:
January 5, 2024
Keywords:
freeform, measurement, dragging three-point method, circular path, telescope
Abstract

Freeform surfaces can realize optical systems with a wide field of view, high throughput, and high contrast. For constructing optical systems with freeform surfaces, measuring technology is essential. However, it is difficult to measure freeform surfaces by existing measurement methods. We have developed a new measurement method of the dragging three-point method (DTPM). To realize further improvement in the accuracy of the DTPM, we propose the DTPM with a circular path. Since the circular path is closed, the measurement error can be reduced by the boundary condition that the height and slope agree with at the start and end points of the measurement. To evaluate this method, we conducted the circular path measurement of an off-axis asphere. The measurement repeatability was RMS = 1.5 nm, and the result agreed well with that of an interferometric test; the difference was RMS = 17.2 nm.

Cite this article as:
K. Tokuchi, M. Kurita, and K. Takahashi, “Measurement of a Freeform Surface by Dragging Three Point Method Along with a Circular Path,” Int. J. Automation Technol., Vol.18 No.1, pp. 66-76, 2024.
Data files:
References
  1. [1] E. Muslimov, E. Hugot, W. Jahn, S. Vives, M. Ferrari, B. Chambion, D. Henry, and C. Gaschet, “Combining freeform optics and curved detectors for wide field imaging: A polynomial approach over squared aperture,” Opt. Express, Vol.25, No.13, pp. 14598-14610, 2017. https://doi.org/10.1364/OE.25.014598
  2. [2] Q. Meng, H. Wang, W. Liang, Z. Yan, and B. Wang, “Design of off-axis three-mirror systems with ultrawide field of view based on an expansion process of surface freeform and field of view,” Appl. Opt., Vol.58, No.3, pp. 609-615, 2019. https://doi.org/10.1364/AO.58.000609
  3. [3] A. Maréchal, “Étude des effets combinés de la diffraction et des aberrations géometriques sur l’image d’un point lumineux,” Rev. Opt. Theor. Instrum., Vol.26, pp. 257-277, 1947.
  4. [4] L. Ye, W. Wang, X. Zhang, M. Xu, J. Zhang, and L. Zheng, “Testing of large-aperture aspheric mirrors using a single coated lens,” Appl. Opt., Vol.59, No.15, pp. 4577-4582, 2020. https://doi.org/10.1364/AO.388276
  5. [5] B. Saif, D. Chaney, W. S. Smith, P. Greenfield, W. Hack, J. Bluth, A. V. Otten, M. Bluth, J. Sanders, R. Keski-Kuha, L. Feinberg, M. North-Morris, and J. Millerd, “Nanometer level characterization of the James Webb Space Telescope optomechanical systems using high-speed interferometry,” Appl. Opt., Vol.54, No.13, pp. 4285-4298, 2015. https://doi.org/10.1364/AO.54.004285
  6. [6] S. Chen, S. Xue, D. Zhai, and G. Tie, “Measurement of Freeform Optical Surfaces: Trade-Off between Accuracy and Dynamic Range,” Laser & Photonics Reviews, Vol.14, No.5, Article No.1900365, 2020. https://doi.org/10.1002/lpor.201900365
  7. [7] P. Dierickx, D. Enard, R. Geyl, J. Paseri, M. Cayrel, and P. Beraud, “VLT primary mirrors: mirror production and measured performance,” Proc. of SPIE, Vol.2871, Optical Telescopes of Today and Tomorrow, pp. 385-392, 1997. https://doi.org/10.1117/12.269061
  8. [8] J. H. Burge, L. B. Kot, H. M. Martin, R. Zehnder, and C. Zhao, “Design and analysis for interferometric measurements of the GMT primary mirror segments,” E. Atad-Ettedgui, J. Antebi, and D. Lemke (Eds.), “Optomechanical Technologies for Astronomy,” Proc. of SPIE, Vol.6273, Article No.62730M, 2006. https://doi.org/10.1117/12.672484
  9. [9] P. Gloesener, F. Wolfs, and M. Cola, “Polishing and figuring of the GAIA M2, M4 and M5 mirrors,” E. Armandillo, B. Cugny, and N. Karafolas (Eds.), “Int. Conf. on Space Optics – ICSO 2010,” Proc. of SPIE, Vol.10565, Article No.105655Z, 2019. https://doi.org/10.1117/12.2552612
  10. [10] F. Yan, B. Fan, X. Hou, and F. Wu, “Measurement of large convex hyperbolic mirrors using hindle and stitching methods,” Optics and Lasers in Engineering, Vol.51, No.7, pp. 856-860, 2013. https://doi.org/10.1016/j.optlaseng.2013.01.020
  11. [11] H. Duan, S. Morita, T. Hosobata, M. Takeda, and Y. Yamagata, “Profile Measurement Using Confocal Chromatic Probe on Ultrahigh Precision Machine Tool,” Int. J. Automation Technol., Vol.15, No.2, pp. 225-233, 2021. https://doi.org/10.20965/ijat.2021.p0225
  12. [12] I. Ogura and Y. Okazaki, “Development of Micro Probe System for Micro Measurement Center,” Int. J. Automation Technol., Vol.3, No.4, pp. 471-477, 2009. https://doi.org/10.20965/ijat.2009.p0471
  13. [13] E. Kirkland, T. R. Kurfess, and S. Y. Liang, “An Optical Coordinate Measuring Machine for Nanoscale Dimensional Metrology,” J. Adv. Comput. Intell. Intell. Inform., Vol.8, No.1, pp. 39-44, 2004. https://doi.org/10.20965/jaciii.2004.p0039
  14. [14] “Specifications-Ultrahigh Accurate 3-D Profilometer UA3P.” https://www.panasonic.com/global/business/ua3p/specification.html [Accessed June 27, 2023]
  15. [15] M. Kurita, Y. Morimoto, N. Emi, and T. Shimoda, “Dragging three-point method for measurement of telescope optics,” Opt. Continuum, Vol.1, No.7, pp. 1552-1564, 2022. https://doi.org/10.1364/OPTCON.462036
  16. [16] S. Kiyono, “Multi-point Methods for Precision Measurement,” J. of the Japan Society of Precision Engineering, Vol.76, No.2, pp. 165-168, 2010. https://doi.org/10.2493/jjspe.76.165
  17. [17] M. Kurita and A. Ishii, “Data-stitching algorithm based on elasticity,” Appl. Opt., Vol.61, No.28, pp. 8333-8340, 2022. https://doi.org/10.1364/AO.466327
  18. [18] M. Kurita, H. Tokoro, K. Takahashi, and M. Kino, “A new manufacturing system for free form and large optics,” R. Navarro and R. Geyl (Eds.), “Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation IV,” Proc. of SPIE, Vol.11451, Article No.114510N, 2020. https://doi.org/10.1117/12.2562049
  19. [19] M. Obi and Y. Kobayashi, “A Measuring Method of the Displacement along a Circle Based on the Sequential-Three-Point Method (A Study of the Measuring Principle and Error,” Trans. of the Japan Society of Mechanical Engineers, Series C, Vol.58, No.548, pp. 1278-1283, 1992. https://doi.org/10.1299/kikaic.58.1278
  20. [20] M. Kurita, M. Kino, F. Iwamuro, K. Ohta, D. Nogami, H. Izumiura, M. Yoshida, K. Matsubayashi, D. Kuroda, Y. Nakatani, K. Yamamoto, H. Tsutsui, M. Iribe, I. Jikuya, H. Ohtani, K. Shibata, K. Takahashi, H. Tokoro, T. Maihara, and T. Nagata, “The Seimei telescope project and technical developments,” Publications of the Astronomical Society of Japan, Vol.72, No.3, 2020. https://doi.org/10.1093/pasj/psaa036
  21. [21] E. S. Mumpuni, L. Puspitarini, R. Priyatikanto, C. Y. Yatini, and M. Putra, “Future astronomy facilities in Indonesia,” Nature Astronomy, Vol.2, pp. 930-932, 2018. https://doi.org/10.1038/s41550-018-0642-6
  22. [22] M. Kino and M. Kurita, “Interferometric testing for off-axis aspherical mirrors with computer-generated holograms,” Appl. Opt., Vol.51, No.19, pp. 4291-4297, 2012. https://doi.org/10.1364/AO.51.004291

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Last updated on Jul. 12, 2024