OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: Joseph N. Mait
  • Vol. 49, Iss. 22 — Aug. 1, 2010
  • pp: 4228–4236

Extraction of phase derivative data from interferometer images using a continuous wavelet transform to determine two-dimensional refractive index profiles

R. Oven  »View Author Affiliations

Applied Optics, Vol. 49, Issue 22, pp. 4228-4236 (2010)

View Full Text Article

Enhanced HTML    Acrobat PDF (1011 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



Two-dimensional refractive index profiles of ion exchanged channel waveguides in glass have been obtained from the analysis of interferometer data. To obtain depth data, a shallow bevel is produced in the glass by polishing. The refractive index profile information that is contained within the derivative of the phase data is extracted directly using a continuous wavelet transform algorithm. The algorithm used to characterize and smooth the wavelet ridge is discussed in detail.

© 2010 Optical Society of America

OCIS Codes
(100.5070) Image processing : Phase retrieval
(100.7410) Image processing : Wavelets
(180.3170) Microscopy : Interference microscopy
(230.7380) Optical devices : Waveguides, channeled

ToC Category:
Image Processing

Original Manuscript: April 23, 2010
Revised Manuscript: July 1, 2010
Manuscript Accepted: July 2, 2010
Published: July 27, 2010

R. Oven, "Extraction of phase derivative data from interferometer images using a continuous wavelet transform to determine two-dimensional refractive index profiles," Appl. Opt. 49, 4228-4236 (2010)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. L. R. Watkins, S. M. Tan, and T. H. Barnes, “Interferometer profile extraction using continuous wavelet transform,” Electron. Lett. 33, 2116–2117 (1997). [CrossRef]
  2. L. R. Wilkins, S. M. Tan, and T. H. Barnes, “Determination of interferometry phase distributions by use of wavelets,” Opt. Lett. 24905–907 (1999). [CrossRef]
  3. L. R. Watkins, “Phase recovery from fringe patterns using the continuous wavelet transform,” Opt. Lasers Eng. 45, 298–303(2007). [CrossRef]
  4. A. Federico and G. H. Kaufmann, “Comparative study of wavelet thresholding methods for denoising electronic speckle interferometry fringes,” Opt. Eng. 402598–2604 (2001). [CrossRef]
  5. A. Federico and G. H. Kaufmann, “Evaluation of the continuous wavelet transform method for the phase measurement of electronic speckle pattern interferometry fringes,” Opt. Eng. 41, 3209–3216 (2002). [CrossRef]
  6. A. Dursun, S. Ozder, and F. N. Ecevit, “Continuous wavelet transform analysis of projected fringe patterns,” Meas. Sci. Technol. 15, 1768–1772 (2004). [CrossRef]
  7. H. Liu, A. N. Cartwright, and C. Basaran, “Moire interferogram phase extraction: a ridge detection algorithm for continuous wavelet transforms,” Appl. Opt. 43, 850–857 (2004). [CrossRef] [PubMed]
  8. C. Quan, C. J. Tat, and L. Chen, “Fringe-density estimation by continuous wavelet transform,” Appl. Opt. 44, 2359–2365(2005). [CrossRef] [PubMed]
  9. M. A. Gdeisat, A. Abid, D. R. Burton, and M. L. Lalor, “Spatial carrier pattern demodulation by use of a two-dimensional continuous wavelet transform,” Appl. Opt. 45, 8722–8732 (2006). [CrossRef] [PubMed]
  10. A. Z. Abid, M. A. Gdeisat, D. R. Burton, M. J. Lalor, and F. Lilley, “Spatial fringe pattern analysis using two-dimensional continuous wavelet transform employing a cost function,” Appl. Opt. 46, 6120–6126 (2007). [CrossRef] [PubMed]
  11. C. Quan, W. Chen, and C. J. Tay, “Phase-retrieval techniques in fringe-projection profilometry,” Opt. Lasers Eng. 48, 235–243 (2010). [CrossRef]
  12. C. A. Sciammarella and T. Kim, “Determination of strains from fringe patterns using space-frequency representations,” Opt. Eng. 42, 3182–3193 (2003). [CrossRef]
  13. C. J. Tay, C. Quan, W. Sun, and X. Y. He, “Demodulation of a single interferogram based on continuous wavelet transform and phase derivative,” Opt. Commun. 280, 327–336 (2007). [CrossRef]
  14. M. A. Gdeisat, A. Abid, D. R. Burton, M. L. Lalor, F. Lilley, C. Moore, and M. Qudeisat, “Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous wavelet transform: recent progress, challenges, and suggested developments,” Opt. Lasers Eng. 47, 1348–1361 (2009). [CrossRef]
  15. A. Darudi and S. M. R. S. Hosseini, “An interferometric method for refractive index profiling of planar gradient index waveguides,” Opt. Lasers Eng. 47, 133–138 (2009). [CrossRef]
  16. R. Oven, “Measurement of two-dimensional refractive index profiles of channel waveguides using an interferometric technique,” Appl. Opt. 48, 5704–5712 (2009). [CrossRef] [PubMed]
  17. Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304–317 (2007). [CrossRef]
  18. Q. Kemao, “On window size selection in the windowed Fourier ridges algorithm,” Opt. Lasers Eng. 45, 1186–1192 (2007). [CrossRef]
  19. A. Federico and G. H. Kaufmann, “Phase retrieval in digital speckle pattern interferometry by use of a smoothed space-frequency distribution,” Appl. Opt. 42, 7066–7071 (2003). [CrossRef] [PubMed]
  20. H. Guo, Q. Yang, and M. Chen, “Local frequency estimation for the fringe pattern with a spatial carrier: principles and applications,” Appl. Opt. 46, 1057–1065 (2007). [CrossRef] [PubMed]
  21. C. J. Tay and Y. Fu, “Determination of curvature and twist by digital shearography and wavelet transform,” Opt. Lett. 30, 2873–2875 (2005). [CrossRef] [PubMed]
  22. Y. Fu, C. J. Tay, C. Quan, and H. Miao, “Wavelet analysis of speckle patterns with a temporal carrier,” Appl. Opt. 44, 959–965 (2005). [CrossRef] [PubMed]
  23. Y. Fu, R. Groves, G. Pedrini, and W. Osten, “Kinematic and deformation parameter measurement by spatiotemporal analysis of an interferogram sequence,” Appl. Opt. 46, 8645–8655 (2007). [CrossRef] [PubMed]
  24. G. H. Kaufman, “Phase measurement in temporal speckle pattern interferometry using the Fourier transform method with and without a temporal carrier,” Opt. Commun. 217, 141–149 (2003). [CrossRef]
  25. X. Colonna de Lega, “Processing of non-stationary interference patterns: adapted phase shifting algorithms and wavelet analysis. Application to dynamic deformation measurement by holographic and speckle interferometry,” Ph.D. dissertation 1666 (Swiss Federal Institute of Technology, 1997).
  26. R. A. Carmona, W. L. Hwang, and B. Torresani, “Characterization of signals by the ridges of their continuous wavelet transforms,” IEEE Trans. Signal Process. 45, 2586–2590(1997). [CrossRef]
  27. L. A. Pars, An Introduction to the Calculus of Variations(Heinemann, 1962).
  28. S.I.Najafi, ed., Introduction to Glass Integrated Optics(Artech, 1992).
  29. R. Oven, M. Yin, and P. A. Davies, “Characterization of planar optical waveguides formed by copper-sodium electric field assisted ion exchange in glass,” J. Phys. D 37, 2207–2215 (2004). [CrossRef]
  30. T. Poszner, G. Schreiter, and R. Muller, “Stripe waveguides with matched refractive index profiles fabricated by ion exchange in glass,” J. Appl. Phys. 70, 1966–1974 (1991). [CrossRef]
  31. K. S. Chiang, “Construction of refractive index profiles of planar dielectric waveguides from the distribution of effective indexes,” J. Lightwave Technol. 3385–391 (1985). [CrossRef]
  32. W. S. Dorn and D. D. McCracken, Numerical Methods with Fortran IV Case Studies (Wiley, 1972).
  33. G. D. Smith, Numerical Solution of Partial Differential Equations (Oxford, 1969).

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.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited