한국광학회지 (Korean Journal of Optics and Photonics)

  • 제27권2호
  • /
  • Pages.61-66
  • /
  • 2016
  • /
  • 1225-6285(pISSN)
  • /
  • 2287-321X(eISSN)
한국광학회 (Optical Society of Korea)
권호 표지
DOI QR코드

DOI QR Code

Hilbert 변환과 투과형 편향법을 이용한 3차원 측정연구

A Study of Three-Dimensional Measurement By Transmission Deflectometry and Hilbert Transform

  • Na, Silin (Department of Physics, Jeju National University) ;
  • Yu, Younghun (Department of Physics, Jeju National University)
  • 투고 : 2015.10.19
  • 심사 : 2016.04.08
  • 발행 : 2016.04.25
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

광학 부품 표면의 3차원 측정을 위하여 투과형 편향법을 이용하였다. 한 장의 영상으로부터 변화된 위상을 추출하기 위하여 Hilbert 변환을 이용하였다. 편향법은 면적이 비교적 크고 거울과 같이 산란이 거의 없는 물체의 3차원 측정을 하는데 유용하다. 편향법을 통해 얻은 왜곡 무늬와 hilbert 변환한 영상을 이용하여 위상을 구했으며, 이로부터 파면의 기울기를 측정하고, 구한 기울기로부터 3차원 프로파일을 구하기 위해 최소자승법을 이용하였다. 전산기 시늉과 실험을 통해 Hilbert 변환을 이용한 3차원 측정법이 유용함을 확인하였다.

We used transmission deflectometry to measure the three-dimensional shapes of optical components, and we used the Hilbert transform to retrieve the phases from measured deformed fringe images. Deflectometry is useful for measuring large-scale samples, and specular samples. We have retrieved the phases from deformed fringe images and Hilbert-transformed images, and have used the least-squares method to find the height information. We have verified that phase retrieval using Hilbert transform is useful by computer simulation and experiment.

키워드

참고문헌

  1. D. Malacara, Optical Shop Testing (New York: Wiley Interscience; USA, 2007), Chapter 1-4.
  2. G. G. Torales, M. Strojnik, and G. Paez, "Risley prisms to control wave-front tilt and displacement in a vectorial shearing interferometer," Appl. Opt. 41, 1380-1384 (2002). https://doi.org/10.1364/AO.41.001380
  3. G. G. Torales, G. Paez, M. Strojnik, J. Villa, J.L. Flores, and A.G. Alvarez, "Experimental intensity patterns obtained from a 2D shearing interferometer with adaptable sensitivity," Opt. Commun. 257, 16-26 (2006). https://doi.org/10.1016/j.optcom.2005.07.014
  4. J. Pfund, N. Lindlein, J. Schwider, R. Burow, T. Blumel, and K.-E. Elssner, "Absolute sphericity measurement: a comparative study of the use of interferometry and a Shack-Hartmann sensor," Opt. Lett. 23, 742-744 (1998). https://doi.org/10.1364/OL.23.000742
  5. H. Canabal and J. Alonso, "Automatic wavefront measurement technique using a computer display and a charge-coupled device camera," Opt. Eng. 41, 822-826 (2002). https://doi.org/10.1117/1.1459055
  6. C. Quan, W. Chen, and C. J. Tay, "Phase-retrieval techniques in fringe-projection profilometry," Opt. Lasers Eng. 48, 235-243 (2010). https://doi.org/10.1016/j.optlaseng.2009.06.013
  7. C. D. Perciante and J.A. Ferrari, "Visualization of twodimensional phase gradients by subtraction of a reference periodic pattern," Appl. Opt. 39, 2081-2083 (2000). https://doi.org/10.1364/AO.39.002081
  8. Z. Liu, X. Huang, and H. Xie, "A novel orthogonal transmission-virtual grating method and its applications in measuring micro 3-D shape of deformed liquid surface," Opt. Lasers Eng. 51, 167-171 (2013). https://doi.org/10.1016/j.optlaseng.2012.08.009
  9. W. Shi, X. Huang, and Z. Liu, "Transmission-lattice based geometric phase analysis for evaluating the dynamic deformation of a liquid surface," Opt. Express, 22, 10559-10569 (2014). https://doi.org/10.1364/OE.22.010559
  10. M. C. Knauer, J. Kaminski, and G. Hausler, "Phase measuring deflectometry: a new approach to measure specular free-form surfaces," Proc. SPIE 5457, 366-376 (2004).
  11. J. Horbach and T. Dang, "3D reconstruction of specular surfaces using a calibrated projector-camera setup," Mach. Vis. Appl. 21, 331-340 (2010). https://doi.org/10.1007/s00138-008-0165-8
  12. Y. Tang, X. Su, Y. Liu, and H. Jing, "3d shape measurement of the aspheric mirror by advanced phase measuring deflectometry," Opt. Express 16, 15090-15096 (2008). https://doi.org/10.1364/OE.16.015090
  13. G. Hausler, C. Richter, K.H. Leitz, and M. C. Knauer, "Micro deflectometry a novel tool to acquire 3D micro topography with nanometer height resolution," Opt. Lett. 33, 396-398 (2008). https://doi.org/10.1364/OL.33.000396
  14. S. Shin and Y. Yu, "Determining the reractive index distribution of an optical component using transmission deflectometry with liquids," Korean J. Optics and Photonics. 25, 326-333 (2014). https://doi.org/10.3807/KJOP.2014.25.6.326
  15. M. Takeda and K. Mutoh, "Fourier transform profilometry for the automatic measurement of 3-D object shapes," Appl. Opt. 22, 3977-3982 (1983). https://doi.org/10.1364/AO.22.003977
  16. J. M. Huntley and H. O. Saldner, "Temporal phase unwrapping algorithm for automated interferogram analysis," Appl. Opt. 32, 3047-3052 (1993). https://doi.org/10.1364/AO.32.003047
  17. M. A. sutto, W. Zhao, S. R. McNeill, H. W. Schreier, and Y. J. Chao, "Development and assessment of single-image fringe projection method for dynamic application," Exp. Mech. 42, 205-217 (2001).
  18. V. D. Madjarova and H. kadono, "Dynamic electronic speckle pattern interferometry phase analysises with temporal hilbert transform," Opt. Express 11, 617-623 (2003). https://doi.org/10.1364/OE.11.000617
  19. U. P. Kumar, N. K. Mohan, and M. P. Kothiyal, "Time average vibration fringe analysis using hilbert transformation," Appl. Opt. 49, 5777-5786 (2010). https://doi.org/10.1364/AO.49.005777
  20. M. M. Hasan, K. Teramoto, and S. Tanemura, "Windowed fourier assisted two-dimensional hilbert transform fro fringe phase extraction," Optik 124, 3996-4000 (2013) https://doi.org/10.1016/j.ijleo.2012.11.070
  21. W. H. Southwell, "Wave-front estimation from wave-front slope measurements," J. Opt. Soc. Am. 70, 998-1006 (1980). https://doi.org/10.1364/JOSA.70.000998
  22. L. Huang and A. Asundi, "Improvement of least-squares integration method with iterative compensations in fringe reflectometry," Appl. Opt. 51, 7459-7465 (2012). https://doi.org/10.1364/AO.51.007459
  23. B. Rappaz, P. Marquet, E. Cuche, Y. Emery, C. Depeursinge, and P. J. Magistretti, "Measurement of the integral refractive index and dynamic cell morphometry of living cells with digital holographic microscopy," Opt. Express 13, 9361-9373 (2005). https://doi.org/10.1364/OPEX.13.009361