OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 51, Iss. 28 — Oct. 1, 2012
  • pp: 6700–6707

Multiwavelength-integrated local model fitting method for interferometric surface profiling

Akihiro Yamashita, Masashi Sugiyama, Katsuichi Kitagawa, and Hisashi Kobayashi  »View Author Affiliations

Applied Optics, Vol. 51, Issue 28, pp. 6700-6707 (2012)

View Full Text Article

Enhanced HTML    Acrobat PDF (1055 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The local model fitting (LMF) method is a useful single-shot surface profiling algorithm that features fast measurement speed and robustness against vibration. However, the measurement range of the LMF method (i.e., measurable height difference between two neighboring pixels) is limited up to a quarter of the light source wavelength. To cope with this problem, the multiwavelength-matched LMF (MM-LMF) method was proposed, where the plain LMF method is first applied individually to interference images obtained from multiple light sources with different wavelengths, and then the LMF solutions are matched to obtain a range-extended solution. Although the MM-LMF method was shown to provide high measurement accuracy under moderate noise, phase unwrapping errors can occur if individual LMF solutions are erroneous. In this paper, we propose the multiwavelength-integrated LMF (MI-LMF) method, which directly computes a range-extended solution from multiple interference images in an integrated way. The effectiveness of the proposed MI-LMF method is demonstrated through simulations and actual experiments.

© 2012 Optical Society of America

OCIS Codes
(240.0240) Optics at surfaces : Optics at surfaces
(240.6700) Optics at surfaces : Surfaces

ToC Category:
Optics at Surfaces

Original Manuscript: March 6, 2012
Revised Manuscript: June 12, 2012
Manuscript Accepted: August 28, 2012
Published: September 24, 2012

Akihiro Yamashita, Masashi Sugiyama, Katsuichi Kitagawa, and Hisashi Kobayashi, "Multiwavelength-integrated local model fitting method for interferometric surface profiling," Appl. Opt. 51, 6700-6707 (2012)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. S. W. Kim, High-speed 3d inspection for densely packed semiconductor chips, http://spie.org/x24235.xml?ArticleID=x24235 .
  2. J. H. Brunning, D. R. Herriott, J. E. Gallagher, D. P. Rosenfeld, A. D. White, and D. J. Brangaccio, “Digital wave front measuring interferometer for testing optical surface and lenses,” Appl. Opt. 13, 2693–2703 (1974). [CrossRef]
  3. M. Takeda, H. Ina, and S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982). [CrossRef]
  4. S. Toyooka and Y. Iwaasa, “Automatic profilometry of 3-d diffuse objects by spatial phase detection,” Appl. Opt. 25, 1630–1633 (1986). [CrossRef]
  5. J. Kato, I. Yamaguchi, T. Nakamura, and S. Kuwashima, “Video-rate fringe analyzer based on phase-shifting electronic moiré patterns,” Appl. Opt. 36, 8403–8412 (1997). [CrossRef]
  6. Q. Kemao, “Windowed Fourier transform for fringe pattern analysis,” Appl. Opt. 43, 2695–2702 (2004). [CrossRef]
  7. D. C. Williams, N. S. Nassar, J. E. Banyard, and M. S. Virdee, “Digital phase-step interferometry: a simplified approach,” Opt. Laser Technol. 23, 147–150 (1991). [CrossRef]
  8. N. Brock, J. Hayes, B. Kimbrough, J. Millerd, M. North-Morris, M. Novak, and J. C. Wyant, “Dynamic interferometry,” Proc. SPIE 5875, 58750F (2005). [CrossRef]
  9. M. Sugiyama, H. Ogawa, K. Kitagawa, and K. Suzuki, “Single-shot surface profiling by local model fitting,” Appl. Opt. 45, 7999–8005 (2006). [CrossRef]
  10. K. Kitagawa, “Fast surface profiling by multi-wavelength single-shot interferometry,” Int. J. Optomechatronics 4, 136–156 (2010). [CrossRef]
  11. M. Takeda and T. Abe, “Phase unwrapping by a maximum cross-amplitude spanning tree algorithm: A comparative study,” Opt. Eng. 35, 2345–2351 (1996). [CrossRef]
  12. In this paper, we use the following method: we first apply the plain LMF method to each interference image and obtain estimates of the bias aj(x,y) and amplitude bj(x,y). Then we apply a 7×7 pixel median filter to the entire images of aj(x,y) and bj(x,y) and use the obtained values as a^j(x,y) and b^j(x,y).
  13. See http://www.scn.tv/user/torayins/ for details.
  14. In this experiment, we were interested in the sharpness of the steps along the x axis. A practical heuristic for accurate measurement is to introduce a spatial carrier orthogonal to the direction of interest, i.e., along the y axis. Following this heuristic, we decided to use a rectangular-shaped local area along the y axis.

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


Fig. 1. Fig. 2. Fig. 3.
Fig. 4.

Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited