Abstract

In optical interferometers, fringe projection systems, and synthetic aperture radars, fringe patterns are common outcomes and usually degraded by unavoidable noises. The presence of noises makes the phase extraction and phase unwrapping challenging. Windowed Fourier transform (WFT) based algorithms have been proven to be effective for fringe pattern analysis to various applications. However, the WFT-based algorithms are computationally expensive, prohibiting them from real-time applications. In this paper, we propose a fast parallel WFT-based library using graphics processing units and computer unified device architecture. Real-time WFT-based algorithms are achieved with 4 frames per second in processing 256×256 fringe patterns. Up to 132× speedup is obtained for WFT-based algorithms using NVIDIA GTX295 graphics card than sequential C in quad-core 2.5GHz Intel(R)Xeon(R) CPU E5420.

© 2009 OSA

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References

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    [CrossRef]
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2009 (4)

H. Wang and Q. Kemao, “Frequency guided methods for demodulation of a single fringe pattern,” Opt. Express 17(17), 15118–15127 (2009), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-17-17-15118 .
[CrossRef] [PubMed]

W. Zhao, Y. Chen, L. Shen, and A. Y. Yi, “Refractive index and dispersion variation in precision optical glass molding by computed tomography,” Appl. Opt. 48(19), 3588–3595 (2009).
[CrossRef] [PubMed]

S. Gorthi and P. Rastogi, “Numerical analysis of fringe patterns recorded in holographic interferometry using high-order ambiguity function,” J. Mod. Opt. 56(8), 949–954 (2009).
[CrossRef]

W. Gao, Q. Kemao, H. Wang, F. Lin, and H. S. Seah, “Parallel computing for fringe pattern processing: A multicore CPU approach in MATLAB® environment,” Opt. Lasers Eng. 47(11), 1286–1292 (2009).
[CrossRef]

2008 (6)

2007 (4)

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations,” Opt. Lasers Eng. 45(2), 304–317 (2007).
[CrossRef]

P. Hlubina, D. Ciprian, J. Lunacek, and R. Chlebus, “Phase retrieval from the spectral interference signal used to measure thickness of SiO2 thin film on silicon wafer,” Appl. Phys. B 88(3), 397–403 (2007).
[CrossRef]

M. P. Arroyo, J. A. Bea, N. Andres, R. Osta, and M. Doblare, “Force plate for measuring small animal forces by digital speckle pattern interferometry,” Proc. SPIE 6616, 66164D (2007).
[CrossRef]

Y. Fu, R. M. Groves, G. Pedrini, and W. Osten, “Kinematic and deformation parameter measurement by spatiotemporal analysis of an interferogram sequence,” Appl. Opt. 46(36), 8645–8655 (2007).
[CrossRef] [PubMed]

2006 (1)

2005 (3)

2001 (2)

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35(5), 263–284 (2001).
[CrossRef]

R. Scott “Stream Processor Architecture,” Springer international series in Engineering and Computer Science, 664 (2001).

Andres, N.

M. P. Arroyo, J. A. Bea, N. Andres, R. Osta, and M. Doblare, “Force plate for measuring small animal forces by digital speckle pattern interferometry,” Proc. SPIE 6616, 66164D (2007).
[CrossRef]

Ang, K. T.

Argentini, G.

Arroyo, M. P.

M. P. Arroyo, J. A. Bea, N. Andres, R. Osta, and M. Doblare, “Force plate for measuring small animal forces by digital speckle pattern interferometry,” Proc. SPIE 6616, 66164D (2007).
[CrossRef]

Bea, J. A.

M. P. Arroyo, J. A. Bea, N. Andres, R. Osta, and M. Doblare, “Force plate for measuring small animal forces by digital speckle pattern interferometry,” Proc. SPIE 6616, 66164D (2007).
[CrossRef]

Cao, Y. P.

W. Chen, X. Su, Y. P. Cao, Q. C. Zhang, and L. Q. Xiang, “Method for eliminating zero spectrum in Fourier transform profilometry,” Opt. Lasers Eng. 43(11), 1267–1276 (2005).
[CrossRef]

Chen, W.

W. Chen, X. Su, Y. P. Cao, Q. C. Zhang, and L. Q. Xiang, “Method for eliminating zero spectrum in Fourier transform profilometry,” Opt. Lasers Eng. 43(11), 1267–1276 (2005).
[CrossRef]

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35(5), 263–284 (2001).
[CrossRef]

Chen, Y.

Cheng, P.

P. Cheng, J. Hu, G. Zhang, L. Hou, B. Xu, and X. Wu, “Deformation measurements of dragonfly’s wings in free flight by using windowed Fourier transform,” Opt. Lasers Eng. 46(2), 157–161 (2008).
[CrossRef]

Chlebus, R.

P. Hlubina, D. Ciprian, J. Lunacek, and R. Chlebus, “Phase retrieval from the spectral interference signal used to measure thickness of SiO2 thin film on silicon wafer,” Appl. Phys. B 88(3), 397–403 (2007).
[CrossRef]

Ciprian, D.

P. Hlubina, D. Ciprian, J. Lunacek, and R. Chlebus, “Phase retrieval from the spectral interference signal used to measure thickness of SiO2 thin film on silicon wafer,” Appl. Phys. B 88(3), 397–403 (2007).
[CrossRef]

Doblare, M.

M. P. Arroyo, J. A. Bea, N. Andres, R. Osta, and M. Doblare, “Force plate for measuring small animal forces by digital speckle pattern interferometry,” Proc. SPIE 6616, 66164D (2007).
[CrossRef]

Fu, Y.

Gao, W.

Gómez-Pedrero, J. A.

Gorthi, S.

S. Gorthi and P. Rastogi, “Numerical analysis of fringe patterns recorded in holographic interferometry using high-order ambiguity function,” J. Mod. Opt. 56(8), 949–954 (2009).
[CrossRef]

Groves, R. M.

Hlubina, P.

P. Hlubina, D. Ciprian, J. Lunacek, and R. Chlebus, “Phase retrieval from the spectral interference signal used to measure thickness of SiO2 thin film on silicon wafer,” Appl. Phys. B 88(3), 397–403 (2007).
[CrossRef]

Hou, L.

P. Cheng, J. Hu, G. Zhang, L. Hou, B. Xu, and X. Wu, “Deformation measurements of dragonfly’s wings in free flight by using windowed Fourier transform,” Opt. Lasers Eng. 46(2), 157–161 (2008).
[CrossRef]

Hu, J.

P. Cheng, J. Hu, G. Zhang, L. Hou, B. Xu, and X. Wu, “Deformation measurements of dragonfly’s wings in free flight by using windowed Fourier transform,” Opt. Lasers Eng. 46(2), 157–161 (2008).
[CrossRef]

Ito, T.

Kemao, Q.

Li, P.

Lin, F.

W. Gao, Q. Kemao, H. Wang, F. Lin, and H. S. Seah, “Parallel computing for fringe pattern processing: A multicore CPU approach in MATLAB® environment,” Opt. Lasers Eng. 47(11), 1286–1292 (2009).
[CrossRef]

Liu, S.

Lunacek, J.

P. Hlubina, D. Ciprian, J. Lunacek, and R. Chlebus, “Phase retrieval from the spectral interference signal used to measure thickness of SiO2 thin film on silicon wafer,” Appl. Phys. B 88(3), 397–403 (2007).
[CrossRef]

Luo, Q.

Masuda, N.

Miura, J.

Ng, T. W.

Osta, R.

M. P. Arroyo, J. A. Bea, N. Andres, R. Osta, and M. Doblare, “Force plate for measuring small animal forces by digital speckle pattern interferometry,” Proc. SPIE 6616, 66164D (2007).
[CrossRef]

Osten, W.

Pedrini, G.

Quiroga, J. A.

Rastogi, P.

S. Gorthi and P. Rastogi, “Numerical analysis of fringe patterns recorded in holographic interferometry using high-order ambiguity function,” J. Mod. Opt. 56(8), 949–954 (2009).
[CrossRef]

Sato, Y.

Scott, R.

R. Scott “Stream Processor Architecture,” Springer international series in Engineering and Computer Science, 664 (2001).

Seah, H. S.

W. Gao, Q. Kemao, H. Wang, F. Lin, and H. S. Seah, “Parallel computing for fringe pattern processing: A multicore CPU approach in MATLAB® environment,” Opt. Lasers Eng. 47(11), 1286–1292 (2009).
[CrossRef]

Servín, M.

Shen, L.

Shimobaba, T.

Shiraki, A.

Su, X.

W. Chen, X. Su, Y. P. Cao, Q. C. Zhang, and L. Q. Xiang, “Method for eliminating zero spectrum in Fourier transform profilometry,” Opt. Lasers Eng. 43(11), 1267–1276 (2005).
[CrossRef]

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35(5), 263–284 (2001).
[CrossRef]

Sugie, T.

Takenouchi, M.

Tanaka, T.

Wang, H.

Wu, X.

P. Cheng, J. Hu, G. Zhang, L. Hou, B. Xu, and X. Wu, “Deformation measurements of dragonfly’s wings in free flight by using windowed Fourier transform,” Opt. Lasers Eng. 46(2), 157–161 (2008).
[CrossRef]

Xiang, L. Q.

W. Chen, X. Su, Y. P. Cao, Q. C. Zhang, and L. Q. Xiang, “Method for eliminating zero spectrum in Fourier transform profilometry,” Opt. Lasers Eng. 43(11), 1267–1276 (2005).
[CrossRef]

Xu, B.

P. Cheng, J. Hu, G. Zhang, L. Hou, B. Xu, and X. Wu, “Deformation measurements of dragonfly’s wings in free flight by using windowed Fourier transform,” Opt. Lasers Eng. 46(2), 157–161 (2008).
[CrossRef]

Yi, A. Y.

Yoshimura, K.

Zhang, G.

P. Cheng, J. Hu, G. Zhang, L. Hou, B. Xu, and X. Wu, “Deformation measurements of dragonfly’s wings in free flight by using windowed Fourier transform,” Opt. Lasers Eng. 46(2), 157–161 (2008).
[CrossRef]

Zhang, Q. C.

W. Chen, X. Su, Y. P. Cao, Q. C. Zhang, and L. Q. Xiang, “Method for eliminating zero spectrum in Fourier transform profilometry,” Opt. Lasers Eng. 43(11), 1267–1276 (2005).
[CrossRef]

Zhao, W.

Appl. Opt. (6)

Appl. Phys. B (1)

P. Hlubina, D. Ciprian, J. Lunacek, and R. Chlebus, “Phase retrieval from the spectral interference signal used to measure thickness of SiO2 thin film on silicon wafer,” Appl. Phys. B 88(3), 397–403 (2007).
[CrossRef]

J. Mod. Opt. (1)

S. Gorthi and P. Rastogi, “Numerical analysis of fringe patterns recorded in holographic interferometry using high-order ambiguity function,” J. Mod. Opt. 56(8), 949–954 (2009).
[CrossRef]

Opt. Express (5)

Opt. Lasers Eng. (5)

P. Cheng, J. Hu, G. Zhang, L. Hou, B. Xu, and X. Wu, “Deformation measurements of dragonfly’s wings in free flight by using windowed Fourier transform,” Opt. Lasers Eng. 46(2), 157–161 (2008).
[CrossRef]

W. Chen, X. Su, Y. P. Cao, Q. C. Zhang, and L. Q. Xiang, “Method for eliminating zero spectrum in Fourier transform profilometry,” Opt. Lasers Eng. 43(11), 1267–1276 (2005).
[CrossRef]

X. Su and W. Chen, “Fourier transform profilometry: a review,” Opt. Lasers Eng. 35(5), 263–284 (2001).
[CrossRef]

Q. Kemao, “Two-dimensional windowed Fourier transform for fringe pattern analysis: Principles, applications and implementations,” Opt. Lasers Eng. 45(2), 304–317 (2007).
[CrossRef]

W. Gao, Q. Kemao, H. Wang, F. Lin, and H. S. Seah, “Parallel computing for fringe pattern processing: A multicore CPU approach in MATLAB® environment,” Opt. Lasers Eng. 47(11), 1286–1292 (2009).
[CrossRef]

Proc. SPIE (1)

M. P. Arroyo, J. A. Bea, N. Andres, R. Osta, and M. Doblare, “Force plate for measuring small animal forces by digital speckle pattern interferometry,” Proc. SPIE 6616, 66164D (2007).
[CrossRef]

Other (9)

X. Wang, X. Peng, and T. Jindong, “Tree-dimensional digital imaging based on temporal phase unwrapping with parallel DSP,” Proc. SPIE 6723 (2007)

D. W. Robinson, and G. T. Reid, in Interferogram analysis: digital fringe pattern measurement techniques, (Bristol, England: Institute of Physics 1993)

D. C. Ghiglia, and M. D. Pritt, in Two-dimensional phase unwrapping: theory, algorithms and software, (John Wiley& Sons, Inc 1998).

C. V. Loan, Computational frameworks for the fast Fourier transform data, (SIAM 1992)

NVIDIA, “Tesla GPU computing solutions,” 2009 GPU workshop, http://www.idre.ucla.edu/events/2009/gpu-workshop/

R. Scott “Stream Processor Architecture,” Springer international series in Engineering and Computer Science, 664 (2001).

NVIDIA, “ CUDA Programming Guide Version 2.3” (2009) http://developer.download.nvidia.com/compute/cuda/2_3/toolkit/docs/

NVIDIA, “The CUDA compiler Driver NVCC” (2009) http://moss.csc.ncsu.edu/~mueller/cluster/nvidia/2.0/nvcc_2.0.pdf

NVIDIA, “CUDA CUFFT library 2.3” (2009), http://www.nvidia.com/object/cuda_develop.html

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Figures (2)

Fig. 1
Fig. 1

Pseudo code for WFF using one GPU.

Fig. 2
Fig. 2

Sequential and parallel WFF result for processing a digital holographic fringe pattern. (a) a digital holographic fringe pattern, (b) the WFF filtering result using CPU, (c)the WFF filtering result using the proposed system based on GPU (single precision), (d) the difference map of the two results.

Tables (1)

Tables Icon

Table 1 Execution time for different size of fringe pattern by WFF and WFR algorithm

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

S f ( u , v ; ξ , η ) = + + f ( x , y ) g ( x u , y v ) exp ( j ξ x j η y ) d x d y
f ( x , y ) = 1 4 π 2 + + + + S f ( u , v , ξ , η ) g ( x u , y v ) exp ( j ξ x + j η y ) d ξ d η d u d v
g ( x , y ) = 1 / π σ x σ y exp ( x 2 / 2 σ x 2 y 2 / 2 σ y 2 )
f ¯ ( x , y ) = ξ i η i 4 π 2 η s = η l η h ξ s = ξ l ξ h [ f ( x , y ) h ξ s , η s ( x , y ) ¯ h ξ s , η s ( x , y ) ]
f ¯ ( x , y ) = ξ i η i 4 π 2 η s = η l η h ξ s = ξ l ξ h 1 ( { 1 [ ( f ) × ( h ξ s , η s ) ] ¯ } × ( h ξ s , η s ) )
( h ξ s , η s ) = 4 π σ x σ y exp { [ σ x 2 ( ξ ξ s ) 2 + σ y 2 ( η η s ) 2 ] / 2 }

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