Journal of the Optical Society of Korea

Optical Society of Korea (한국광학회)
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Unambiguous 3D Surface Measurement Method for a Micro-Fresnel Lens-Shaped Lenticular Lens Based on a Transmissive Interferometer

  • Yoon, Do-Young (School of Mechanical and Aerospace Engineering, Seoul National University) ;
  • Kim, Tai-Wook (SNU Precision Co., Ltd.) ;
  • Kim, Minsu (School of Mechanical and Aerospace Engineering, Seoul National University) ;
  • Pahk, Heui-Jae (School of Mechanical and Aerospace Engineering, Seoul National University)
  • Received : 2013.11.05
  • Accepted : 2013.12.10
  • Published : 2014.02.25
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Abstract

The use of a laser interferometer as a metrological tool in micro-optics measurement is demonstrated. A transmissive interferometer is effective in measuring an optical specimen having a high angle slope. A configuration that consists of an optical resolution of 0.62 micron is adapted to measure a specimen, which is a micro-Fresnel lens-shaped lenticular lens. The measurement result shows a good repeatability at each fraction of facets, however, a reconstruction of the lens shape profile is disturbed by a known problem of $2{\pi}$-ambiguity. To solve this $2{\pi}$-ambiguity problem, we propose a two-step phase unwrapping method. In the first step, an unwrapped phase map is obtained by using a conventional unwrapping method. Then, a proposed unwrapping method based on the shape modeling is applied to correct the wrongly unwrapped phase. A measured height of each facet is compared with a profile result measured by AFM.

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References

  1. T. G. Edwards, "Approaches to non-eglassese-based 3D displays," in Proc. SMPTE Conferences (Hollywood, CA, USA, Oct. 2009), pp. 1-16.
  2. G. Brakenhoff, P. Blom, and P. Barends, "Confocal scanning light microscopy with high aperture immersion lenses," Journal of Microscopy 117, 219-232 (1979). https://doi.org/10.1111/j.1365-2818.1979.tb01178.x
  3. K. Carlsson and N. Aslund, "Confocal imaging for 3-D digital microscopy," Appl. Opt. 26, 3232-3238 (1987). https://doi.org/10.1364/AO.26.003232
  4. M. Francon, Optical Interferometry (Academic Press, New York, USA, 1966).
  5. W. D. Joo and M. S. Jung, "A study of optical properties of intraocular lenses and of measurement of the index of reflection for an unknown liquid," J. Opt. Soc. Korea 16, 236-242 (2012). https://doi.org/10.3807/JOSK.2012.16.3.236
  6. V. Kebbel, J. Mueller, and W. P. Jueptner, "Characterization of aspherical microeoptics using digital holography: improvement of accuracy," in Proc. International Symposium on Optical Science and Technology (Washington State Convention Center, Seattle, WA, USA, Jul. 2002), pp. 188-197.
  7. F. Charriere, J. Kuhn, T. Colomb, F. Montfort, E. Cuche, Y. Emery, K. Weible, P. Marquet, and C. Depeursinge, "Characterization of microlenses by digital holographic microscopy," Appl. Opt. 45, 829-835 (2006). https://doi.org/10.1364/AO.45.000829
  8. J. Garcia-Sucerquia, W. Xu, S. K. Jericho, P. Klages, M. H. Jericho, and H. J. Kreuzer, "Digital in-line holographic microscopy," Appl. Opt. 45, 836-850 (2006). https://doi.org/10.1364/AO.45.000836
  9. Q. Weijuan, Y. Yingjie, C. O. Choo, and A. Asundi, "Digital holographic microscopy with physical phase compensation," Opt. Lett. 34, 1276-1278 (2009). https://doi.org/10.1364/OL.34.001276
  10. M.-S. Kim, T. Scharf, and H. P. Herzig, "Small-size microlens characterization by multiwavelength higheresolution interference microscopy," Opt. Express 18, 14319-14329 (2010). https://doi.org/10.1364/OE.18.014319
  11. A. Harasaki, J. Schmit, and J. C. Wyant, "Improved vertical-scanning interferometry," Appl. Opt. 39, 2107-2115 (2000). https://doi.org/10.1364/AO.39.002107
  12. J.-H. Kim, S.-W. Yoon, J.-H. Lee, W.-J. Ahn, and H.-J. Pahk, "New algorithm of white-light phase shifting interferometry pursing higher repeatability by using numerical phase error correction schemes of pre-processor, main processor, and post-processor," Optics and Lasers in Engineering 46, 140- 148 (2008). https://doi.org/10.1016/j.optlaseng.2007.08.008
  13. G. S. Kino and S. S. Chim, "Mirau correlation microscope," Appl. Opt. 29, 3775-3783 (1990). https://doi.org/10.1364/AO.29.003775
  14. L. Deck and P. De Groot, "High-speed noncontact profiler based on scanning white-light interferometry," Appl. Opt. 33, 7334-7338 (1994). https://doi.org/10.1364/AO.33.007334
  15. Y.-Y. Cheng and J. C. Wyant, "Two-wavelength phase shifting interferometry," Appl. Opt. 23, 4539-4543 (1984). https://doi.org/10.1364/AO.23.004539
  16. K. Creath, "Step height measurement using two-wavelength phase-shifting interferometry," Appl. Opt. 26, 2810-2816 (1987). https://doi.org/10.1364/AO.26.002810
  17. J. C. Wyant and K. Creath, "Two-wavelength phase-shifting interferometer and method," U.S. Patent 4832489 (1989).
  18. P. J. de Groot, "Extending the unambiguous range of two-color interferometers," Appl. Opt. 33, 5948-5953 (1994). https://doi.org/10.1364/AO.33.005948
  19. E. Hecht, Optics, 4th ed. (Addison Wesley, Boston, USA, 2002).
  20. W. Pliskin and R. Esch, "Effect of numerical aperture of microscope objectives on film‐thickness determinations," J. Appl. Phys. 39, 3274-3276 (1968). https://doi.org/10.1063/1.1656767
  21. T.-W. Kim, J.-Y. Lee, D.-H. Kim, and H.-J. Pahk, "Ultrashort laser patterning of thin-film CIGS solar cells through glass substrate," Int. J. Precis. Eng. Manuf., J. of KSPE 14, 1287-1292 (2013). https://doi.org/10.1007/s12541-013-0175-y
  22. J. C. Wyant, C. L. Koliopoulos, B. Bhushan, and O. E. George, "An optical profilometer for surface characterization of magnetic media," ASLE Transactions 27, 101-113 (1984). https://doi.org/10.1080/05698198408981550
  23. J. C. Wyant, "Use of an ac heterodyne lateral shear interferometer with real-time wavefront correction systems," Appl. Opt. 14, 2622-2626 (1975). https://doi.org/10.1364/AO.14.002622
  24. J. Schwider, R. Burow, K.-E. Elssner, J. Grzanna, R. Spolaczyk, and K. Merkel, "Digital wav-efront measuring interferometry: some systematic error sources," Appl. Opt. 22, 3421-3432 (1983). https://doi.org/10.1364/AO.22.003421
  25. Y. Surrel, "Phase stepping: a new selfecalibrating algorithm," Appl. Opt. 32, 3598-3600 (1993). https://doi.org/10.1364/AO.32.003598
  26. P. Hariharan, B. Oreb, and T. Eiju, "Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm," Appl. Opt. 26, 2504-2506 (1987). https://doi.org/10.1364/AO.26.002504
  27. K. Itoh, "Analysis of the phase unwrapping algorithm," Appl. Opt. 21, 2470-2470 (1982). https://doi.org/10.1364/AO.21.002470
  28. D. C. Ghiglia and M. D. Pritt, Twoedimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, New York, USA, 1998).
  29. S.-R. Kim, J.-H. Kim, and H.-J. Pahk, "Fringe-order determination method in white-light phase-shifting interferometry for the compensation of the phase delay and the suppression of excessive phase unwrapping," J. Opt. Soc. Korea 17, 415-422 (2013). https://doi.org/10.3807/JOSK.2013.17.5.415
  30. V. V. Volkov and Y. Zhu, "Deterministic phase unwrapping in the presence of noise," Opt. Lett. 28, 2156-2158 (2003). https://doi.org/10.1364/OL.28.002156
  31. M. A. Schofield and Y. Zhu, "Fast phase unwrapping algorithm for interferometric applications," Opt. Lett. 28, 1194-1196 (2003). https://doi.org/10.1364/OL.28.001194
  32. B. G. Broome and J. A. Richard, "Single objective lens for use with cd or dvd optical disks," U.S. Patent 6088322 (1999).

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