Abstract

In this article, we propose a massively parallel, real-time algorithm for the estimation of the dynamic phase map of a vibrating object. The algorithm implements a Fourier-based quadrature transform and temporal phase unwrapping technique. CUDA, a graphic processing unit programming architecture was used to implement the algorithm. It was tested on a fringe pattern sequence using three devices with different capabilities, achieving a processing rate greater than 1600 frames per second (fps).

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References

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  1. R. Legarda-Saenz, R. Rodriguez-Vera, and A. Espinosa-Romero, “Dynamic 3-D shape measurement method based on quadrature transform,” Opt. Express 18(3), 2639–2645 (2010).
    [Crossref] [PubMed]
  2. NVIDIA, NVIDIA CUDA C Programming Guide (version 3.2), http://developer.download.nvidia.com/compute/cuda/3_2_prod/toolkit/docs/ (2010).
  3. K. J. Gåsvik, Optical Metrology, 3rd ed. (John Wiley & Sons Ltd., 2002).
    [Crossref]
  4. K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18, 1862–1870 (2001).
    [Crossref]
  5. M. Servin, J. A. Quiroga, and J. L. Marroquin, “General n-dimensional quadrature transform and its application to interferogram demodulation,” J. Opt. Soc. Am. A 20, 924–934 (2003).
    [Crossref]
  6. D. Ghigila and M. D. Pritt, Two-Dimensional Phase Unwrapping. Theory, Algorithms, and Software (John Wiley & Sons Ltd., 1998).
  7. T. Kreis, Holographic Interferometry: Principles and Methods (Akademie Verlag, 1996).
  8. J. M. Huntley and H. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32, 3047–3052 (1993).
    [Crossref] [PubMed]
  9. S. De Nicola and P. Ferraro, “Fourier transform method of fringe analysis for moire interferometry,” J. Opt. A: Pure Appl. Opt. 2, 228–233 (2000).
    [Crossref]
  10. J. D. Owens, M. Houston, D. Luebke, S. Green, J. E. Stone, and J. C. Phillips “GPU computing,” Proc. IEEE 96(5), 879–899 (2008).
    [Crossref]
  11. M. Frigo and S. G. Johnson, “The design and implementation of FFTW3,” Proc. IEEE 93, 216–231 (2005).
    [Crossref]
  12. NVIDIA, NVIDIA CUDA CUFFT LIBRARY (PG-05327-032_V02), http://developer.download.nvidia.com/compute/cuda/3_2_prod/toolkit/docs/ (2010).
  13. C. Meneses-Fabian, R. Rodriguez-Vera, J. A. Rayas, F. Mendoza-Santoyo, and G. Rodriguez-Zurita, “Surface contour from a low-frequency vibrating object using phase differences and the Fourier-transform method,” Opt. Commun. 272(2), 310–313 (2007).
    [Crossref]

2010 (1)

2008 (1)

J. D. Owens, M. Houston, D. Luebke, S. Green, J. E. Stone, and J. C. Phillips “GPU computing,” Proc. IEEE 96(5), 879–899 (2008).
[Crossref]

2007 (1)

C. Meneses-Fabian, R. Rodriguez-Vera, J. A. Rayas, F. Mendoza-Santoyo, and G. Rodriguez-Zurita, “Surface contour from a low-frequency vibrating object using phase differences and the Fourier-transform method,” Opt. Commun. 272(2), 310–313 (2007).
[Crossref]

2005 (1)

M. Frigo and S. G. Johnson, “The design and implementation of FFTW3,” Proc. IEEE 93, 216–231 (2005).
[Crossref]

2003 (1)

M. Servin, J. A. Quiroga, and J. L. Marroquin, “General n-dimensional quadrature transform and its application to interferogram demodulation,” J. Opt. Soc. Am. A 20, 924–934 (2003).
[Crossref]

2001 (1)

2000 (1)

S. De Nicola and P. Ferraro, “Fourier transform method of fringe analysis for moire interferometry,” J. Opt. A: Pure Appl. Opt. 2, 228–233 (2000).
[Crossref]

1993 (1)

Bone, D. J.

De Nicola, S.

S. De Nicola and P. Ferraro, “Fourier transform method of fringe analysis for moire interferometry,” J. Opt. A: Pure Appl. Opt. 2, 228–233 (2000).
[Crossref]

Espinosa-Romero, A.

Ferraro, P.

S. De Nicola and P. Ferraro, “Fourier transform method of fringe analysis for moire interferometry,” J. Opt. A: Pure Appl. Opt. 2, 228–233 (2000).
[Crossref]

Frigo, M.

M. Frigo and S. G. Johnson, “The design and implementation of FFTW3,” Proc. IEEE 93, 216–231 (2005).
[Crossref]

Gåsvik, K. J.

K. J. Gåsvik, Optical Metrology, 3rd ed. (John Wiley & Sons Ltd., 2002).
[Crossref]

Ghigila, D.

D. Ghigila and M. D. Pritt, Two-Dimensional Phase Unwrapping. Theory, Algorithms, and Software (John Wiley & Sons Ltd., 1998).

Green, S.

J. D. Owens, M. Houston, D. Luebke, S. Green, J. E. Stone, and J. C. Phillips “GPU computing,” Proc. IEEE 96(5), 879–899 (2008).
[Crossref]

Houston, M.

J. D. Owens, M. Houston, D. Luebke, S. Green, J. E. Stone, and J. C. Phillips “GPU computing,” Proc. IEEE 96(5), 879–899 (2008).
[Crossref]

Huntley, J. M.

Johnson, S. G.

M. Frigo and S. G. Johnson, “The design and implementation of FFTW3,” Proc. IEEE 93, 216–231 (2005).
[Crossref]

Kreis, T.

T. Kreis, Holographic Interferometry: Principles and Methods (Akademie Verlag, 1996).

Larkin, K. G.

Legarda-Saenz, R.

Luebke, D.

J. D. Owens, M. Houston, D. Luebke, S. Green, J. E. Stone, and J. C. Phillips “GPU computing,” Proc. IEEE 96(5), 879–899 (2008).
[Crossref]

Marroquin, J. L.

M. Servin, J. A. Quiroga, and J. L. Marroquin, “General n-dimensional quadrature transform and its application to interferogram demodulation,” J. Opt. Soc. Am. A 20, 924–934 (2003).
[Crossref]

Mendoza-Santoyo, F.

C. Meneses-Fabian, R. Rodriguez-Vera, J. A. Rayas, F. Mendoza-Santoyo, and G. Rodriguez-Zurita, “Surface contour from a low-frequency vibrating object using phase differences and the Fourier-transform method,” Opt. Commun. 272(2), 310–313 (2007).
[Crossref]

Meneses-Fabian, C.

C. Meneses-Fabian, R. Rodriguez-Vera, J. A. Rayas, F. Mendoza-Santoyo, and G. Rodriguez-Zurita, “Surface contour from a low-frequency vibrating object using phase differences and the Fourier-transform method,” Opt. Commun. 272(2), 310–313 (2007).
[Crossref]

Oldfield, M. A.

Owens, J. D.

J. D. Owens, M. Houston, D. Luebke, S. Green, J. E. Stone, and J. C. Phillips “GPU computing,” Proc. IEEE 96(5), 879–899 (2008).
[Crossref]

Phillips, J. C.

J. D. Owens, M. Houston, D. Luebke, S. Green, J. E. Stone, and J. C. Phillips “GPU computing,” Proc. IEEE 96(5), 879–899 (2008).
[Crossref]

Pritt, M. D.

D. Ghigila and M. D. Pritt, Two-Dimensional Phase Unwrapping. Theory, Algorithms, and Software (John Wiley & Sons Ltd., 1998).

Quiroga, J. A.

M. Servin, J. A. Quiroga, and J. L. Marroquin, “General n-dimensional quadrature transform and its application to interferogram demodulation,” J. Opt. Soc. Am. A 20, 924–934 (2003).
[Crossref]

Rayas, J. A.

C. Meneses-Fabian, R. Rodriguez-Vera, J. A. Rayas, F. Mendoza-Santoyo, and G. Rodriguez-Zurita, “Surface contour from a low-frequency vibrating object using phase differences and the Fourier-transform method,” Opt. Commun. 272(2), 310–313 (2007).
[Crossref]

Rodriguez-Vera, R.

R. Legarda-Saenz, R. Rodriguez-Vera, and A. Espinosa-Romero, “Dynamic 3-D shape measurement method based on quadrature transform,” Opt. Express 18(3), 2639–2645 (2010).
[Crossref] [PubMed]

C. Meneses-Fabian, R. Rodriguez-Vera, J. A. Rayas, F. Mendoza-Santoyo, and G. Rodriguez-Zurita, “Surface contour from a low-frequency vibrating object using phase differences and the Fourier-transform method,” Opt. Commun. 272(2), 310–313 (2007).
[Crossref]

Rodriguez-Zurita, G.

C. Meneses-Fabian, R. Rodriguez-Vera, J. A. Rayas, F. Mendoza-Santoyo, and G. Rodriguez-Zurita, “Surface contour from a low-frequency vibrating object using phase differences and the Fourier-transform method,” Opt. Commun. 272(2), 310–313 (2007).
[Crossref]

Saldner, H.

Servin, M.

M. Servin, J. A. Quiroga, and J. L. Marroquin, “General n-dimensional quadrature transform and its application to interferogram demodulation,” J. Opt. Soc. Am. A 20, 924–934 (2003).
[Crossref]

Stone, J. E.

J. D. Owens, M. Houston, D. Luebke, S. Green, J. E. Stone, and J. C. Phillips “GPU computing,” Proc. IEEE 96(5), 879–899 (2008).
[Crossref]

Appl. Opt. (1)

J. Opt. A: Pure Appl. Opt. (1)

S. De Nicola and P. Ferraro, “Fourier transform method of fringe analysis for moire interferometry,” J. Opt. A: Pure Appl. Opt. 2, 228–233 (2000).
[Crossref]

J. Opt. Soc. Am. A (2)

K. G. Larkin, D. J. Bone, and M. A. Oldfield, “Natural demodulation of two-dimensional fringe patterns. I. General background of the spiral phase quadrature transform,” J. Opt. Soc. Am. A 18, 1862–1870 (2001).
[Crossref]

M. Servin, J. A. Quiroga, and J. L. Marroquin, “General n-dimensional quadrature transform and its application to interferogram demodulation,” J. Opt. Soc. Am. A 20, 924–934 (2003).
[Crossref]

Opt. Commun. (1)

C. Meneses-Fabian, R. Rodriguez-Vera, J. A. Rayas, F. Mendoza-Santoyo, and G. Rodriguez-Zurita, “Surface contour from a low-frequency vibrating object using phase differences and the Fourier-transform method,” Opt. Commun. 272(2), 310–313 (2007).
[Crossref]

Opt. Express (1)

Proc. IEEE (2)

J. D. Owens, M. Houston, D. Luebke, S. Green, J. E. Stone, and J. C. Phillips “GPU computing,” Proc. IEEE 96(5), 879–899 (2008).
[Crossref]

M. Frigo and S. G. Johnson, “The design and implementation of FFTW3,” Proc. IEEE 93, 216–231 (2005).
[Crossref]

Other (5)

NVIDIA, NVIDIA CUDA CUFFT LIBRARY (PG-05327-032_V02), http://developer.download.nvidia.com/compute/cuda/3_2_prod/toolkit/docs/ (2010).

D. Ghigila and M. D. Pritt, Two-Dimensional Phase Unwrapping. Theory, Algorithms, and Software (John Wiley & Sons Ltd., 1998).

T. Kreis, Holographic Interferometry: Principles and Methods (Akademie Verlag, 1996).

NVIDIA, NVIDIA CUDA C Programming Guide (version 3.2), http://developer.download.nvidia.com/compute/cuda/3_2_prod/toolkit/docs/ (2010).

K. J. Gåsvik, Optical Metrology, 3rd ed. (John Wiley & Sons Ltd., 2002).
[Crossref]

Supplementary Material (1)

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Figures (2)

Algorithm 1
Algorithm 1

Retrieval of the dynamic phase ϕ k

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Fig. 1
Fig. 1

3D representations of the phase map with the projected fringe pattern on it.

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Tables (1)

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Table 1 The Execution Time of Algorithm 1 on Different Computing Platforms

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Equations (15)

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I   ( r ,   t )   =   a   ( r )   +   b ( r ,   t )   cos   ψ   ( r ,   t )
ψ   ( r ,   t )   =   ϕ   ( r )   +   φ   ( r ,   t )
z   ( r )   =   𝒯   ( φ   ( r ,   t ) )
ϕ   ( r )   =   ω →   ⋅   f ( r )
{ I   ( r ,   t 0 ) ,   I ( r ,   t 0   +   Δ t ,   I ( r ,   t 0   +   2 Δ t ) ,   ⋯   ,   I ( r ,   t 0   +   ( N   −   1 ) Δ t }
I k   ( r )   =   a ( r )   +   b k ( r )   cos   ψ k ( r )
g k   ( r )   =   b k   cos   ψ k   ( r )
g ^ ( r )   =   − b k   ( r )   sin   ψ k   ( r )
g k   −   i g ^ ( r )   =   b k   ( r )   exp   [ i ψ k   ( r ) ]
Q n   { g k   ( r ) } = − b k   ( r ) sin ( ψ k   ( r ) ) = ℱ − 1   { − i ω →   ⋅ q | ω →   ⋅   q |   ℱ   { g k   ( r ) } }
b k   ( r )   exp   [ i ψ k   ( r ) ]   =   g k   ( r )   − i ℱ − 1   { − i ω →   ⋅   q | ω →   ⋅ q |   ℱ   { g k   ( r ) } }
b k   ( r )   exp   [ i ψ k   ( r ) ]   =   ℱ − 1   { ( 1   −   ω →   ⋅   q | ω →   ⋅   q | )   ℱ   { g k   ( r ) } }
ψ ^ k   ( r )   =   W   { ψ k }   =   arctan   ( − Q { g k   ( r ) } g k )
φ M   ( r )   =   ∑ k = 1 M arctan   cos   ψ ^ k   sin   ψ ^ k − 1   −   sin   ψ ^ k   cos   ψ ^ k − 1 cos   ψ ^ k   cos   ψ ^ k − 1   −   sin   ψ ^ k   sin ψ ^ k − 1
Q n   ( g k   ( r ) )   =   ℱ − 1   { η Flt   ( q )   ℱ   { I k   ( q ) } } ,   η   =   { 0 ω →   ⋅   q   <   0 2 otherwise

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