Abstract
This paper describes an optical measurement technique for the two-dimensional fringe pattern (by introducing the carrier frequencies in two spatial directions x and y) by the continuous wavelet transform (CWT) phase gradient method. Such transforms based on the Morlet and Paul wavelets have been applied to image rows and columns one by one and then added to find the final phase distribution, without using any unwrapping algorithms. This technique is compared with the S-transform phase gradient method. Numerical simulations and actual experiments are carried out to show the validity of this technique for finding the phase distributions.
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References
M. Takeda and K. Mutoh, “Fourier Transform Profilometry for the Automatic Measurement of 3D Object Shapes,” Appl. Opt. 22(24), 3977–3982 (1983).
S. De Nicola and P. Ferraro, “A Two-Dimensional Fast Fourier Transform Method for Measuring the Inclination Angle of Parallel Fringe Patterns,” Opt. and Laser Technol. 30(3–4), 167–173 (1998).
A. Dursun, S. Özder, and F. N. Ecevit, “Continuous Wavelet Transform Analysis of Projected Fringe Patterns,” Meas. Sci. Technol. 15(9), 1768–1772 (2004).
L. R. Watkins, S. M. Tan, and T. H. Barnes, “Determination of Interferometer Phase Distributions by Use of Wavelets,” Opt. Lett. 24(13), 905–907 (1999).
M. Afifi, A. Fassi-Fihri, M. Marjane, et al., “Paul Wavelet-Based Algorithm for Optical Phase Distribution Evaluation,” Opt. Commun. 211(1–6), 47–51 (2002).
W. Chen, X. Su, Y. Cao, et al., “Fourier Transform Profilometry Based on a Fringe Pattern with Two Frequency Components,” Optik 119(2), 57–62 (2008).
C. Quan, C. J. Tay, and L. J. Chen, “A Study on Carrier-Removal Techniques in Fringe Projection Profilometry,” Opt. Laser Technol. 39(6), 1155–1161 (2007).
W. J. Ryu, Y. J. Kang, S. H. Baik, and S. J. Kang, “A Study on the 3-D Measurement by Using Digital Projection Moiré Method,” Optik 119(10), 453–458 (2008).
H. J. Chen, J. Zhang, D. J. Lv, and J. Fang, “3-D Shape Measurement by Composite Pattern Projection and Hybrid Processing,” Opt. Express. 15(19), 12318–12330 (2007).
Z. Zhang, C. E. Towers, and D. P. Towers, “Time Efficient Color Fringe Projection System for 3D Shape and Color Using Optimum 3-Frequency Selection,” Opt. Express. 14(14), 6444–6455 (2006).
W. H. Su, “Color-Encoded Fringe Projection for 3D Shape Measurements,” Opt. Express. 15(20), 13167–13181 (2007).
Q. Kemao, “Two-Dimensional Windowed Fourier Transform for Fringe Pattern Analysis: Principles, Applications and Implementations.” Opt. Laser. Eng. 45(2), 304–317 (2007).
Z. Wang and H. Ma, “Advanced Continuous Wavelet Transform Algorithm for Digital Interferogram Analysis and Processing,” Opt. Eng. 45(4), 045601 (2006).
S. D. Meyers, B. G. Kelly, and J. J. O’Brien, “An Introduction to Wavelet Analysis in Oceanography and Meteorology: With Application to the Dispersion of Yanai Waves,” Mon. Weather Rev. 121(10), 2858–2866 (1993).
C. Torrence and G. P. Compo, “A Practical Guide to Wavelet Analysis,” Bull. Amer. Meteorol. Soc. 79(1), 61–78 (1998).
O. Köysal, S. E. San, S. Özder, and F. N. Ecevit, “A Novel Approach for the Determination of Birefringence Dispersion in Nematic Liquid Crystals by Using the Continuous Wavelet Transform,” Meas. Sci. Technol. 14(6), 790–795 (2003).
S. Özder, Ö. Kocahan, E. Coskun, and H. Göktas, “Optical Phase Distribution Evaluation by Using an S-Transform,” Opt. Lett. 32(6), 591–593 (2007).
R. G. Stockwell, L. Mansinha, and R. P. Lowe, “Localization of the Complex Spectrum: The S-Transform,” IEEE Trans. Signal Process. 44(4), 998–1001 (1996).
C. R. Pinnegar and L. Mansinha, “Time-Local Fourier Analysis with a Scalable, Phase-Modulated Analyzing Function: The S-Transform with a Complex Window,” Signal Process. 84(7), 1167–1176 (2004).
R. G. Stockwell, “S-Transform Analysis of Gravity Wave Activity from a Small Scale Network of Airglow Imagers,” Ph. D. Thesis, Faculty of Graduate Studies, University of Western Ontario (1999).
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Original Russian Text © Ö.Kocahan Yilmaz, S. Özder, and P.Demir, 2011, published in Avtometriya, 2011, Vol. 47, No. 2, pp. 33–45.
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Kocahan Yilmaz, Ö., Özder, S. & Demir, P. Two-dimensional fringe projection for three-dimensional shape measurements by using the CWT phase gradient method. Optoelectron.Instrument.Proc. 47, 130–140 (2011). https://doi.org/10.3103/S875669901102004X
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DOI: https://doi.org/10.3103/S875669901102004X