Abstract

Phase demodulation from carrier-frequency fringe patterns is the core of many optic measurements. We propose spatial quasi-phase-shifting technique by expressing the fringe signal in the frequency-modulated form, which requires only one frame fringe pattern for instantaneous and dynamic measurements. In an area smaller than a fringe period, there substantially exists an approximately constant phase shift between spatially adjacent sample points. The technique is capable of demodulating the phase with such intra-frame phase shifts, which makes the instantaneous and dynamic measurement possible. The technique implements demodulation within three spatially adjacent neighbors, achieving spatial localization as good as a several-point level. Both numerical simulation and experiment are presented to verify its performance.

© 2014 Optical Society of America

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  1. M. Takeda, “Spatial-carrier fringe-pattern analysis and its applications to precision interferometry and profilometry: An overview,” Industrial Metrology 1(2), 79–99 (1990).
    [CrossRef]
  2. Q. Kemao, “Windowed Fourier Transform for Fringe Pattern Analysis,” Appl. Opt. 43(13), 2695–2702 (2004).
    [CrossRef] [PubMed]
  3. J. Zhong, J. Weng, “Phase retrieval of optical fringe patterns from the ridge of a wavelet transform,” Opt. Lett. 30(19), 2560–2562 (2005).
    [CrossRef] [PubMed]
  4. I. Yamaguchi, T. Zhang, “Phase-shifting digital holography,” Opt. Lett. 22(16), 1268–1270 (1997).
    [CrossRef] [PubMed]
  5. Z. Zhang, J. Zhong, “Applicability analysis of wavelet-transform profilometry,” Opt. Express 21(16), 18777–18796 (2013).
    [CrossRef] [PubMed]
  6. B. Li, Y. Wang, J. Dai, W. Lohry, S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54, 236–246 (2014).
    [CrossRef]
  7. M. Kujawinska, J. Wojciak, “Spatial-carrier phase-shifting technique of fringe pattern analysis,” Proc. SPIE 1508, 61–67 (1991).
    [CrossRef]
  8. P. Chan, P. Bryanston-Cross, S. Parker, “Spatial phase stepping method of fringe-pattern analysis,” Opt. Lasers Eng. 23(5), 343–354 (1995).
    [CrossRef]
  9. Y. Du, G. Feng, H. Li, J. Vargas, S. Zhou, “Spatial carrier phase-shifting algorithm based on principal component analysis method,” Opt. Express 20(15), 16471–16479 (2012).
    [CrossRef]
  10. Y. Awatsuji, M. Sasada, T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069 (2004).
    [CrossRef]
  11. J. Ville, “Theory and applications of the notion of complex signal,” RAND Corp., Santa Monica, CA, Tech. Rep. T-92 (1958).
  12. H. Kwok, D. Jones, “Improved instantaneous frequency estimation using an adaptive short-time Fourier transform,” IEEE Trans. Signal Process. 48(10), 2964–2972 (2000).
    [CrossRef]
  13. I. Daubechies, “The wavelet transform, time-frequency localization and signal analysis,” IEEE Trans. Inf. Theory 36(5), 961–1005 (1990).
    [CrossRef]
  14. Z. Peng, G. Meng, F. Chu, Z. Lang, W. Zhang, Y. Yang, “Polynomial chirplet transform with application to instantaneous frequency estimation,” IEEE Trans. Instrum. Meas. 60(9), 3222–3229 (2011).
    [CrossRef]
  15. P. O'Shea, B. Boashash, “Instantaneous frequency estimation using the cross Wigner-Ville distribution with application to nonstationary transient detection,” Acoustics, Speech, and Signal Processing 5, 2887–2890 (1990).
    [CrossRef]
  16. L. R. Watkins, S. M. Tan, T. H. Barnes, “Determination of interferometer phase distributions by use of wavelets,” Opt. Lett. 24(13), 905–907 (1999).
    [CrossRef] [PubMed]
  17. S. Gorthi, P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
    [CrossRef]
  18. A. Asundi, Z. Wensen, “Fast phase-unwrapping algorithm based on a gray-scale mask and flood fill,” Appl. Opt. 37(23), 5416–5420 (1998).
    [CrossRef] [PubMed]

2014

B. Li, Y. Wang, J. Dai, W. Lohry, S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54, 236–246 (2014).
[CrossRef]

2013

2012

2011

Z. Peng, G. Meng, F. Chu, Z. Lang, W. Zhang, Y. Yang, “Polynomial chirplet transform with application to instantaneous frequency estimation,” IEEE Trans. Instrum. Meas. 60(9), 3222–3229 (2011).
[CrossRef]

2010

S. Gorthi, P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
[CrossRef]

2005

2004

Q. Kemao, “Windowed Fourier Transform for Fringe Pattern Analysis,” Appl. Opt. 43(13), 2695–2702 (2004).
[CrossRef] [PubMed]

Y. Awatsuji, M. Sasada, T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069 (2004).
[CrossRef]

2000

H. Kwok, D. Jones, “Improved instantaneous frequency estimation using an adaptive short-time Fourier transform,” IEEE Trans. Signal Process. 48(10), 2964–2972 (2000).
[CrossRef]

1999

1998

1997

1995

P. Chan, P. Bryanston-Cross, S. Parker, “Spatial phase stepping method of fringe-pattern analysis,” Opt. Lasers Eng. 23(5), 343–354 (1995).
[CrossRef]

1991

M. Kujawinska, J. Wojciak, “Spatial-carrier phase-shifting technique of fringe pattern analysis,” Proc. SPIE 1508, 61–67 (1991).
[CrossRef]

1990

M. Takeda, “Spatial-carrier fringe-pattern analysis and its applications to precision interferometry and profilometry: An overview,” Industrial Metrology 1(2), 79–99 (1990).
[CrossRef]

I. Daubechies, “The wavelet transform, time-frequency localization and signal analysis,” IEEE Trans. Inf. Theory 36(5), 961–1005 (1990).
[CrossRef]

P. O'Shea, B. Boashash, “Instantaneous frequency estimation using the cross Wigner-Ville distribution with application to nonstationary transient detection,” Acoustics, Speech, and Signal Processing 5, 2887–2890 (1990).
[CrossRef]

Asundi, A.

Awatsuji, Y.

Y. Awatsuji, M. Sasada, T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069 (2004).
[CrossRef]

Barnes, T. H.

Boashash, B.

P. O'Shea, B. Boashash, “Instantaneous frequency estimation using the cross Wigner-Ville distribution with application to nonstationary transient detection,” Acoustics, Speech, and Signal Processing 5, 2887–2890 (1990).
[CrossRef]

Bryanston-Cross, P.

P. Chan, P. Bryanston-Cross, S. Parker, “Spatial phase stepping method of fringe-pattern analysis,” Opt. Lasers Eng. 23(5), 343–354 (1995).
[CrossRef]

Chan, P.

P. Chan, P. Bryanston-Cross, S. Parker, “Spatial phase stepping method of fringe-pattern analysis,” Opt. Lasers Eng. 23(5), 343–354 (1995).
[CrossRef]

Chu, F.

Z. Peng, G. Meng, F. Chu, Z. Lang, W. Zhang, Y. Yang, “Polynomial chirplet transform with application to instantaneous frequency estimation,” IEEE Trans. Instrum. Meas. 60(9), 3222–3229 (2011).
[CrossRef]

Dai, J.

B. Li, Y. Wang, J. Dai, W. Lohry, S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54, 236–246 (2014).
[CrossRef]

Daubechies, I.

I. Daubechies, “The wavelet transform, time-frequency localization and signal analysis,” IEEE Trans. Inf. Theory 36(5), 961–1005 (1990).
[CrossRef]

Du, Y.

Feng, G.

Gorthi, S.

S. Gorthi, P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
[CrossRef]

Jones, D.

H. Kwok, D. Jones, “Improved instantaneous frequency estimation using an adaptive short-time Fourier transform,” IEEE Trans. Signal Process. 48(10), 2964–2972 (2000).
[CrossRef]

Kemao, Q.

Kubota, T.

Y. Awatsuji, M. Sasada, T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069 (2004).
[CrossRef]

Kujawinska, M.

M. Kujawinska, J. Wojciak, “Spatial-carrier phase-shifting technique of fringe pattern analysis,” Proc. SPIE 1508, 61–67 (1991).
[CrossRef]

Kwok, H.

H. Kwok, D. Jones, “Improved instantaneous frequency estimation using an adaptive short-time Fourier transform,” IEEE Trans. Signal Process. 48(10), 2964–2972 (2000).
[CrossRef]

Lang, Z.

Z. Peng, G. Meng, F. Chu, Z. Lang, W. Zhang, Y. Yang, “Polynomial chirplet transform with application to instantaneous frequency estimation,” IEEE Trans. Instrum. Meas. 60(9), 3222–3229 (2011).
[CrossRef]

Li, B.

B. Li, Y. Wang, J. Dai, W. Lohry, S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54, 236–246 (2014).
[CrossRef]

Li, H.

Lohry, W.

B. Li, Y. Wang, J. Dai, W. Lohry, S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54, 236–246 (2014).
[CrossRef]

Meng, G.

Z. Peng, G. Meng, F. Chu, Z. Lang, W. Zhang, Y. Yang, “Polynomial chirplet transform with application to instantaneous frequency estimation,” IEEE Trans. Instrum. Meas. 60(9), 3222–3229 (2011).
[CrossRef]

O'Shea, P.

P. O'Shea, B. Boashash, “Instantaneous frequency estimation using the cross Wigner-Ville distribution with application to nonstationary transient detection,” Acoustics, Speech, and Signal Processing 5, 2887–2890 (1990).
[CrossRef]

Parker, S.

P. Chan, P. Bryanston-Cross, S. Parker, “Spatial phase stepping method of fringe-pattern analysis,” Opt. Lasers Eng. 23(5), 343–354 (1995).
[CrossRef]

Peng, Z.

Z. Peng, G. Meng, F. Chu, Z. Lang, W. Zhang, Y. Yang, “Polynomial chirplet transform with application to instantaneous frequency estimation,” IEEE Trans. Instrum. Meas. 60(9), 3222–3229 (2011).
[CrossRef]

Rastogi, P.

S. Gorthi, P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
[CrossRef]

Sasada, M.

Y. Awatsuji, M. Sasada, T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069 (2004).
[CrossRef]

Takeda, M.

M. Takeda, “Spatial-carrier fringe-pattern analysis and its applications to precision interferometry and profilometry: An overview,” Industrial Metrology 1(2), 79–99 (1990).
[CrossRef]

Tan, S. M.

Vargas, J.

Wang, Y.

B. Li, Y. Wang, J. Dai, W. Lohry, S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54, 236–246 (2014).
[CrossRef]

Watkins, L. R.

Weng, J.

Wensen, Z.

Wojciak, J.

M. Kujawinska, J. Wojciak, “Spatial-carrier phase-shifting technique of fringe pattern analysis,” Proc. SPIE 1508, 61–67 (1991).
[CrossRef]

Yamaguchi, I.

Yang, Y.

Z. Peng, G. Meng, F. Chu, Z. Lang, W. Zhang, Y. Yang, “Polynomial chirplet transform with application to instantaneous frequency estimation,” IEEE Trans. Instrum. Meas. 60(9), 3222–3229 (2011).
[CrossRef]

Zhang, S.

B. Li, Y. Wang, J. Dai, W. Lohry, S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54, 236–246 (2014).
[CrossRef]

Zhang, T.

Zhang, W.

Z. Peng, G. Meng, F. Chu, Z. Lang, W. Zhang, Y. Yang, “Polynomial chirplet transform with application to instantaneous frequency estimation,” IEEE Trans. Instrum. Meas. 60(9), 3222–3229 (2011).
[CrossRef]

Zhang, Z.

Zhong, J.

Zhou, S.

Acoustics, Speech, and Signal Processing

P. O'Shea, B. Boashash, “Instantaneous frequency estimation using the cross Wigner-Ville distribution with application to nonstationary transient detection,” Acoustics, Speech, and Signal Processing 5, 2887–2890 (1990).
[CrossRef]

Appl. Opt.

Appl. Phys. Lett.

Y. Awatsuji, M. Sasada, T. Kubota, “Parallel quasi-phase-shifting digital holography,” Appl. Phys. Lett. 85(6), 1069 (2004).
[CrossRef]

IEEE Trans. Inf. Theory

I. Daubechies, “The wavelet transform, time-frequency localization and signal analysis,” IEEE Trans. Inf. Theory 36(5), 961–1005 (1990).
[CrossRef]

IEEE Trans. Instrum. Meas.

Z. Peng, G. Meng, F. Chu, Z. Lang, W. Zhang, Y. Yang, “Polynomial chirplet transform with application to instantaneous frequency estimation,” IEEE Trans. Instrum. Meas. 60(9), 3222–3229 (2011).
[CrossRef]

IEEE Trans. Signal Process.

H. Kwok, D. Jones, “Improved instantaneous frequency estimation using an adaptive short-time Fourier transform,” IEEE Trans. Signal Process. 48(10), 2964–2972 (2000).
[CrossRef]

Industrial Metrology

M. Takeda, “Spatial-carrier fringe-pattern analysis and its applications to precision interferometry and profilometry: An overview,” Industrial Metrology 1(2), 79–99 (1990).
[CrossRef]

Opt. Express

Opt. Lasers Eng.

S. Gorthi, P. Rastogi, “Fringe projection techniques: Whither we are?” Opt. Lasers Eng. 48(2), 133–140 (2010).
[CrossRef]

B. Li, Y. Wang, J. Dai, W. Lohry, S. Zhang, “Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques,” Opt. Lasers Eng. 54, 236–246 (2014).
[CrossRef]

P. Chan, P. Bryanston-Cross, S. Parker, “Spatial phase stepping method of fringe-pattern analysis,” Opt. Lasers Eng. 23(5), 343–354 (1995).
[CrossRef]

Opt. Lett.

Proc. SPIE

M. Kujawinska, J. Wojciak, “Spatial-carrier phase-shifting technique of fringe pattern analysis,” Proc. SPIE 1508, 61–67 (1991).
[CrossRef]

Other

J. Ville, “Theory and applications of the notion of complex signal,” RAND Corp., Santa Monica, CA, Tech. Rep. T-92 (1958).

Supplementary Material (1)

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Figures (11)

Fig. 1
Fig. 1

Illustration of local frequency. Sine waves (solid lines) of different local frequencies fit fringe signal (dotted line) locally.

Fig. 2
Fig. 2

Illustration of SQPS: (a) k = 3 and (b) k = 1.

Fig. 3
Fig. 3

Simulation without noise: (a) generated 1-D fringe for demodulation, (b) detected local frequency by WT, (c) demodulated phase by SQPS with k = 1, k = 5, and k = 7 and (d) demodulation errors.

Fig. 4
Fig. 4

Simulation with noise: (a.1) generated 1-D fringe for demodulation, (a.2) additional white noise, (b) detected local frequency by WT, (c) demodulated phase by SQPS with k = 1, k = 3, and k = 5 and (d) demodulation errors.

Fig. 5
Fig. 5

Optical geometry of fringe projection profilometry.

Fig. 6
Fig. 6

Captured deformed fringe pattern used in experiment (a) where red line indicates 516th column. (b) is intensity distribution of fringe at 516th column and (c) is its Fourier amplitude spectrum where dotted box represents the rectangle filter window used in FT and dash dot line indicates the cutoff frequency of low-pass filter.

Fig. 7
Fig. 7

Local frequency of 516th column detected by WT.

Fig. 8
Fig. 8

Comparison of demodulation results at 516th column.

Fig. 9
Fig. 9

Comparisons of demodulated results in (a) slow-varying-frequency area and (b) rapid-varying-frequency area.

Fig. 10
Fig. 10

3-D distributions of demodulated phases (a) by PS technique, (b) by SQPS (k = 1) technique, (c) by WT method, and (d) by FT method.

Fig. 11
Fig. 11

Result of the dynamic profilometry: (a) 138th frame of captured video of deform fringe pattern, (b) 2-D distribution of demodulated phase, (c) 3-D presentation of demodulated phase, and (d) 2-D distribution of unwrapped phase.

Equations (9)

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I( x )=a( x )+b( x )cos[ 2π f 0 x+Δϕ( x ) ],
I( x )=a( x )+b( x )cos[ 2π f L ( x )x+ ϕ 0,L ( x ) ],
2π f 0 x+Δϕ( x )=2π f L ( x )x+ ϕ 0 ,L ( x ).
I( x )=a+bcos[ 2π f L ( x )x+ ϕ 0 ,L ( x ) ].
{ I 1 = x 3kΔx /2 x kΔx /2 I( x )dx , =A+Bcos( 2π f ¯ L x+ ϕ 0,L 2π f ¯ L kΔx ), I 2 = x kΔx /2 x+ kΔx /2 I( x )dx =A+Bcos( 2π f ¯ L x+ ϕ 0,L ), I 3 = x+ kΔx /2 x+ 3kΔx /2 I( x )dx =A+Bcos( 2π f ¯ L x+ ϕ 0,L +2π f ¯ L kΔx ),
{ f ¯ L = 1 3kΔx x 3kΔx /2 x+ 3kΔx /2 f L ( x )dx , A=akΔx, B=2bsin( π f ¯ L kΔx ),
Δϕ( x )=arctan[ I 1 I 3 2 I 2 I 3 I 1 tan( kπ f ¯ L ) ]2π f 0 x.
I( x )=127+127cos[ 2π f 0 x+Δϕ( x ) ],
Δϕ( x )=3 ( 1x/ 512 ) 2 exp[ ( x/ 512 ) 2 1 ] 10[ 5x / 512 ( x/ 512 ) 3 ]exp[ ( x/ 512 ) 2 ] 1/3 exp[ ( x/ 512 +1 ) 2 ].

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