C. Quan, W. Chen, and C. J. Tay, “Phase-retrieval techniques in fringe-projection profilometry,” Opt. Lasers Eng. 48, 235–243 (2010).

[CrossRef]

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]

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]

R. Oven, “Measurement of two-dimensional refractive index profiles of channel waveguides using an interferometric technique,” Appl. Opt. 48, 5704–5712 (2009).

[CrossRef]
[PubMed]

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]

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]

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]

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304–317 (2007).

[CrossRef]

Q. Kemao, “On window size selection in the windowed Fourier ridges algorithm,” Opt. Lasers Eng. 45, 1186–1192 (2007).

[CrossRef]

L. R. Watkins, “Phase recovery from fringe patterns using the continuous wavelet transform,” Opt. Lasers Eng. 45, 298–303(2007).

[CrossRef]

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]

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]

C. Quan, C. J. Tat, and L. Chen, “Fringe-density estimation by continuous wavelet transform,” Appl. Opt. 44, 2359–2365(2005).

[CrossRef]
[PubMed]

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]

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]

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]

A. Dursun, S. Ozder, and F. N. Ecevit, “Continuous wavelet transform analysis of projected fringe patterns,” Meas. Sci. Technol. 15, 1768–1772 (2004).

[CrossRef]

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]

A. Federico and G. H. Kaufmann, “Comparative study of wavelet thresholding methods for denoising electronic speckle interferometry fringes,” Opt. Eng. 402598–2604 (2001).

[CrossRef]

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]

L. R. Watkins, S. M. Tan, and T. H. Barnes, “Interferometer profile extraction using continuous wavelet transform,” Electron. Lett. 33, 2116–2117 (1997).

[CrossRef]

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]

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]

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]

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]

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]

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]

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]

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]

C. Quan, W. Chen, and C. J. Tay, “Phase-retrieval techniques in fringe-projection profilometry,” Opt. Lasers Eng. 48, 235–243 (2010).

[CrossRef]

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]

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).

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]

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]

W. S. Dorn and D. D. McCracken, Numerical Methods with Fortran IV Case Studies (Wiley, 1972).

A. Dursun, S. Ozder, and F. N. Ecevit, “Continuous wavelet transform analysis of projected fringe patterns,” Meas. Sci. Technol. 15, 1768–1772 (2004).

[CrossRef]

A. Dursun, S. Ozder, and F. N. Ecevit, “Continuous wavelet transform analysis of projected fringe patterns,” Meas. Sci. Technol. 15, 1768–1772 (2004).

[CrossRef]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

Q. Kemao, “On window size selection in the windowed Fourier ridges algorithm,” Opt. Lasers Eng. 45, 1186–1192 (2007).

[CrossRef]

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304–317 (2007).

[CrossRef]

C. A. Sciammarella and T. Kim, “Determination of strains from fringe patterns using space-frequency representations,” Opt. Eng. 42, 3182–3193 (2003).

[CrossRef]

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]

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]

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]

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]

W. S. Dorn and D. D. McCracken, Numerical Methods with Fortran IV Case Studies (Wiley, 1972).

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]

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]

A. Dursun, S. Ozder, and F. N. Ecevit, “Continuous wavelet transform analysis of projected fringe patterns,” Meas. Sci. Technol. 15, 1768–1772 (2004).

[CrossRef]

L. A. Pars, An Introduction to the Calculus of Variations(Heinemann, 1962).

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]

C. Quan, W. Chen, and C. J. Tay, “Phase-retrieval techniques in fringe-projection profilometry,” Opt. Lasers Eng. 48, 235–243 (2010).

[CrossRef]

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]

C. Quan, C. J. Tat, and L. Chen, “Fringe-density estimation by continuous wavelet transform,” Appl. Opt. 44, 2359–2365(2005).

[CrossRef]
[PubMed]

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]

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]

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]

C. A. Sciammarella and T. Kim, “Determination of strains from fringe patterns using space-frequency representations,” Opt. Eng. 42, 3182–3193 (2003).

[CrossRef]

G. D. Smith, Numerical Solution of Partial Differential Equations (Oxford, 1969).

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]

C. Quan, W. Chen, and C. J. Tay, “Phase-retrieval techniques in fringe-projection profilometry,” Opt. Lasers Eng. 48, 235–243 (2010).

[CrossRef]

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]

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]

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]

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]

L. R. Watkins, “Phase recovery from fringe patterns using the continuous wavelet transform,” Opt. Lasers Eng. 45, 298–303(2007).

[CrossRef]

L. R. Watkins, S. M. Tan, and T. H. Barnes, “Interferometer profile extraction using continuous wavelet transform,” Electron. Lett. 33, 2116–2117 (1997).

[CrossRef]

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]

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]

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]

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]

C. Quan, C. J. Tat, and L. Chen, “Fringe-density estimation by continuous wavelet transform,” Appl. Opt. 44, 2359–2365(2005).

[CrossRef]
[PubMed]

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]

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]

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]

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]

R. Oven, “Measurement of two-dimensional refractive index profiles of channel waveguides using an interferometric technique,” Appl. Opt. 48, 5704–5712 (2009).

[CrossRef]
[PubMed]

L. R. Watkins, S. M. Tan, and T. H. Barnes, “Interferometer profile extraction using continuous wavelet transform,” Electron. Lett. 33, 2116–2117 (1997).

[CrossRef]

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]

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]

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]

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]

A. Dursun, S. Ozder, and F. N. Ecevit, “Continuous wavelet transform analysis of projected fringe patterns,” Meas. Sci. Technol. 15, 1768–1772 (2004).

[CrossRef]

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]

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]

C. A. Sciammarella and T. Kim, “Determination of strains from fringe patterns using space-frequency representations,” Opt. Eng. 42, 3182–3193 (2003).

[CrossRef]

A. Federico and G. H. Kaufmann, “Comparative study of wavelet thresholding methods for denoising electronic speckle interferometry fringes,” Opt. Eng. 402598–2604 (2001).

[CrossRef]

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]

C. Quan, W. Chen, and C. J. Tay, “Phase-retrieval techniques in fringe-projection profilometry,” Opt. Lasers Eng. 48, 235–243 (2010).

[CrossRef]

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]

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]

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations,” Opt. Lasers Eng. 45, 304–317 (2007).

[CrossRef]

Q. Kemao, “On window size selection in the windowed Fourier ridges algorithm,” Opt. Lasers Eng. 45, 1186–1192 (2007).

[CrossRef]

L. R. Watkins, “Phase recovery from fringe patterns using the continuous wavelet transform,” Opt. Lasers Eng. 45, 298–303(2007).

[CrossRef]

L. A. Pars, An Introduction to the Calculus of Variations(Heinemann, 1962).

S.I.Najafi, ed., Introduction to Glass Integrated Optics(Artech, 1992).

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).

W. S. Dorn and D. D. McCracken, Numerical Methods with Fortran IV Case Studies (Wiley, 1972).

G. D. Smith, Numerical Solution of Partial Differential Equations (Oxford, 1969).