Abstract

This paper presents a two-frequency binary phase-shifting technique to measure three-dimensional (3D) absolute shape of beating rabbit hearts. Due to the low contrast of the cardiac surface, the projector and the camera must remain focused, which poses challenges for any existing binary method where the measurement accuracy is low. To conquer this challenge, this paper proposes to utilize the optimal pulse width modulation (OPWM) technique to generate high-frequency fringe patterns, and the error-diffusion dithering technique to produce low-frequency fringe patterns. Furthermore, this paper will show that fringe patterns produced with blue light provide the best quality measurements compared to fringe patterns generated with red or green light; and the minimum data acquisition speed for high quality measurements is around 800 Hz for a rabbit heart beating at 180 beats per minute.

© 2013 OSA

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References

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  1. Q. Lou, C. M. Ripplinger, P. V. Bayly, and I. R. Efimov, “Quantitative panoramic imaging of epicardial electrical activity,” Annals Biomed. Eng.36, 1649–1658 (2008).
    [CrossRef]
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    [CrossRef]
  3. G. Zhang, J. Sun, D. Chen, and Y. Wang, “Flapping motion measurement of honeybee bilateral wings using four virtual structured-light sensors,” Sensors and Actuators A: Physical148, 19–27 (2008).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  11. D. Malacara, ed., Optical Shop Testing, 3rd ed. (John Wiley and Sons, New York, 2007).
    [CrossRef]
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  14. B. Bayer, “An optimum method for two-level rendition of continuous-tone pictures,” IEEE International Conference on Communications1, 11–15 (1973).
  15. T. D. Kite, B. L. Evans, and A. C. Bovik, “Modeling and quality assessment of Halftoning by error diffusion,” IEEE International Conference on Image Processing9(5), 909–922 (2000).
    [CrossRef]
  16. P. Stucki, “MECCAa multiple-error correcting computation algorithm for bilevel hardcopy reproduction,” Tech. Rep., IBM Res. Lab., Zurich, Switzerland (1981).
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    [PubMed]

2012 (1)

2011 (1)

2010 (4)

2008 (2)

G. Zhang, J. Sun, D. Chen, and Y. Wang, “Flapping motion measurement of honeybee bilateral wings using four virtual structured-light sensors,” Sensors and Actuators A: Physical148, 19–27 (2008).
[CrossRef]

Q. Lou, C. M. Ripplinger, P. V. Bayly, and I. R. Efimov, “Quantitative panoramic imaging of epicardial electrical activity,” Annals Biomed. Eng.36, 1649–1658 (2008).
[CrossRef]

2002 (2)

Y. Wang and S. Zhang, “Three-dimensional shape measurement with binary dithered patterns,” Appl. Opt.51(27), 6631–6636 (2002).
[CrossRef]

J. Laughner, S. Zhang, H. Li, and I. R. Efimov, “Mapping cardiac surface mechanics with structured light imaging,” Am. J. Physiol.303(6), H712–H720 (2002).

2000 (1)

T. D. Kite, B. L. Evans, and A. C. Bovik, “Modeling and quality assessment of Halftoning by error diffusion,” IEEE International Conference on Image Processing9(5), 909–922 (2000).
[CrossRef]

1994 (1)

W. Purgathofer, R. Tobler, and M. Geiler, “Forced random dithering: improved threshold matrices for ordered dithering,” IEEE International Conference on Image Processing2, 1032–1035 (1994).

1973 (1)

B. Bayer, “An optimum method for two-level rendition of continuous-tone pictures,” IEEE International Conference on Communications1, 11–15 (1973).

1964 (1)

T. L. Schuchman, “Dither Signals and Their Effect on Quantization Noise,” IEEE Trans. Commun. Technol.12(4), 162–165 (1964).
[CrossRef]

1949 (1)

W. J. Bowen, “The absorption spectra and extinction coefficients of myoglobin,” J. Biol. Chem.179, 235–245 (1949).
[PubMed]

Ajubi, G. A.

Ayubi, J. A.

Bayer, B.

B. Bayer, “An optimum method for two-level rendition of continuous-tone pictures,” IEEE International Conference on Communications1, 11–15 (1973).

Bayly, P. V.

Q. Lou, C. M. Ripplinger, P. V. Bayly, and I. R. Efimov, “Quantitative panoramic imaging of epicardial electrical activity,” Annals Biomed. Eng.36, 1649–1658 (2008).
[CrossRef]

Bovik, A. C.

T. D. Kite, B. L. Evans, and A. C. Bovik, “Modeling and quality assessment of Halftoning by error diffusion,” IEEE International Conference on Image Processing9(5), 909–922 (2000).
[CrossRef]

Bowen, W. J.

W. J. Bowen, “The absorption spectra and extinction coefficients of myoglobin,” J. Biol. Chem.179, 235–245 (1949).
[PubMed]

Chen, D.

G. Zhang, J. Sun, D. Chen, and Y. Wang, “Flapping motion measurement of honeybee bilateral wings using four virtual structured-light sensors,” Sensors and Actuators A: Physical148, 19–27 (2008).
[CrossRef]

Dai, J.

Efimov, I. R.

Q. Lou, C. M. Ripplinger, P. V. Bayly, and I. R. Efimov, “Quantitative panoramic imaging of epicardial electrical activity,” Annals Biomed. Eng.36, 1649–1658 (2008).
[CrossRef]

J. Laughner, S. Zhang, H. Li, and I. R. Efimov, “Mapping cardiac surface mechanics with structured light imaging,” Am. J. Physiol.303(6), H712–H720 (2002).

Ekstrand, L.

Evans, B. L.

T. D. Kite, B. L. Evans, and A. C. Bovik, “Modeling and quality assessment of Halftoning by error diffusion,” IEEE International Conference on Image Processing9(5), 909–922 (2000).
[CrossRef]

Ferrari, J. A.

Geiler, M.

W. Purgathofer, R. Tobler, and M. Geiler, “Forced random dithering: improved threshold matrices for ordered dithering,” IEEE International Conference on Image Processing2, 1032–1035 (1994).

Kite, T. D.

T. D. Kite, B. L. Evans, and A. C. Bovik, “Modeling and quality assessment of Halftoning by error diffusion,” IEEE International Conference on Image Processing9(5), 909–922 (2000).
[CrossRef]

Laughner, J.

J. Laughner, S. Zhang, H. Li, and I. R. Efimov, “Mapping cardiac surface mechanics with structured light imaging,” Am. J. Physiol.303(6), H712–H720 (2002).

Li, H.

J. Laughner, S. Zhang, H. Li, and I. R. Efimov, “Mapping cardiac surface mechanics with structured light imaging,” Am. J. Physiol.303(6), H712–H720 (2002).

Lou, Q.

Q. Lou, C. M. Ripplinger, P. V. Bayly, and I. R. Efimov, “Quantitative panoramic imaging of epicardial electrical activity,” Annals Biomed. Eng.36, 1649–1658 (2008).
[CrossRef]

Martino, J. M. D.

Olvier, J.

Purgathofer, W.

W. Purgathofer, R. Tobler, and M. Geiler, “Forced random dithering: improved threshold matrices for ordered dithering,” IEEE International Conference on Image Processing2, 1032–1035 (1994).

Ripplinger, C. M.

Q. Lou, C. M. Ripplinger, P. V. Bayly, and I. R. Efimov, “Quantitative panoramic imaging of epicardial electrical activity,” Annals Biomed. Eng.36, 1649–1658 (2008).
[CrossRef]

Schuchman, T. L.

T. L. Schuchman, “Dither Signals and Their Effect on Quantization Noise,” IEEE Trans. Commun. Technol.12(4), 162–165 (1964).
[CrossRef]

Stucki, P.

P. Stucki, “MECCAa multiple-error correcting computation algorithm for bilevel hardcopy reproduction,” Tech. Rep., IBM Res. Lab., Zurich, Switzerland (1981).

Sun, J.

G. Zhang, J. Sun, D. Chen, and Y. Wang, “Flapping motion measurement of honeybee bilateral wings using four virtual structured-light sensors,” Sensors and Actuators A: Physical148, 19–27 (2008).
[CrossRef]

Tobler, R.

W. Purgathofer, R. Tobler, and M. Geiler, “Forced random dithering: improved threshold matrices for ordered dithering,” IEEE International Conference on Image Processing2, 1032–1035 (1994).

van der Weide, D.

Wang, Y.

Xu, Y.

Zhang, G.

G. Zhang, J. Sun, D. Chen, and Y. Wang, “Flapping motion measurement of honeybee bilateral wings using four virtual structured-light sensors,” Sensors and Actuators A: Physical148, 19–27 (2008).
[CrossRef]

Zhang, S.

Am. J. Physiol. (1)

J. Laughner, S. Zhang, H. Li, and I. R. Efimov, “Mapping cardiac surface mechanics with structured light imaging,” Am. J. Physiol.303(6), H712–H720 (2002).

Annals Biomed. Eng. (1)

Q. Lou, C. M. Ripplinger, P. V. Bayly, and I. R. Efimov, “Quantitative panoramic imaging of epicardial electrical activity,” Annals Biomed. Eng.36, 1649–1658 (2008).
[CrossRef]

Appl. Opt. (3)

IEEE International Conference on Communications (1)

B. Bayer, “An optimum method for two-level rendition of continuous-tone pictures,” IEEE International Conference on Communications1, 11–15 (1973).

IEEE International Conference on Image Processing (2)

T. D. Kite, B. L. Evans, and A. C. Bovik, “Modeling and quality assessment of Halftoning by error diffusion,” IEEE International Conference on Image Processing9(5), 909–922 (2000).
[CrossRef]

W. Purgathofer, R. Tobler, and M. Geiler, “Forced random dithering: improved threshold matrices for ordered dithering,” IEEE International Conference on Image Processing2, 1032–1035 (1994).

IEEE Trans. Commun. Technol. (1)

T. L. Schuchman, “Dither Signals and Their Effect on Quantization Noise,” IEEE Trans. Commun. Technol.12(4), 162–165 (1964).
[CrossRef]

J. Biol. Chem. (1)

W. J. Bowen, “The absorption spectra and extinction coefficients of myoglobin,” J. Biol. Chem.179, 235–245 (1949).
[PubMed]

Opt. Express (1)

Opt. Laser Eng. (1)

S. Zhang, “Recent progresses on real-time 3-D shape measurement using digital fringe projection techniques,” Opt. Laser Eng.48(2), 149–158 (2010).
[CrossRef]

Opt. Lett. (2)

Sensors and Actuators A: Physical (1)

G. Zhang, J. Sun, D. Chen, and Y. Wang, “Flapping motion measurement of honeybee bilateral wings using four virtual structured-light sensors,” Sensors and Actuators A: Physical148, 19–27 (2008).
[CrossRef]

Other (2)

D. Malacara, ed., Optical Shop Testing, 3rd ed. (John Wiley and Sons, New York, 2007).
[CrossRef]

P. Stucki, “MECCAa multiple-error correcting computation algorithm for bilevel hardcopy reproduction,” Tech. Rep., IBM Res. Lab., Zurich, Switzerland (1981).

Supplementary Material (3)

» Media 1: MOV (2697 KB)     
» Media 2: MOV (2914 KB)     
» Media 3: MOV (4073 KB)     

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Figures (8)

Fig. 1
Fig. 1

Quarter-wave symmetric OPWM waveform.

Fig. 2
Fig. 2

Comparison of Bayer dithering and error-diffusion dithering. (a) Bayer-dithering pattern; (b) Cross section of (a) after Gaussian smoothing; (c) Phase error (rms error of 0.012 rad); (d) Error-diffusion dithered pattern; (e) Cross section of (c) after Gaussian smoothing; (f) Phase error (rms 0.008 rad).

Fig. 3
Fig. 3

Photograph of live heart measurement system.

Fig. 4
Fig. 4

Wrapped phase maps for dead heart measurement. (a)–(c) High-frequency fringe patterns; (d) Wrapped phase map of high frequency patterns; (e)–(g) Low-frequency fringe patterns; (h) Wrapped phase map of low frequency pattern

Fig. 5
Fig. 5

Unwrapped phase map for dead heart measurement. (a) Unwrapped phase map; (b) 3D reconstructed shape of the heart surface

Fig. 6
Fig. 6

Comparison of different spectrum for fixed heart measurements. (a) One fringe pattern using blue light; (b) One fringe pattern using green light; (c) One fringe pattern using red light; (d) 3D result using blue light; (e) 3D result using green light; (f) 3D result using red light.

Fig. 7
Fig. 7

Comparison of different spectrum for beating heart measurements ( Media 1 and Media 2). (a) One fringe pattern using blue light; (b) One fringe pattern using green light; (c) One fringe pattern using red light; (d) 3D result using blue light; (e) 3D result using green light; (f) 3D result using red light.

Fig. 8
Fig. 8

Comparison of different speed for beating heart measurements ( Media 3). (a)–(f) respectively shows the 3D results with 200, 300, 400, 500, 800 and 1000 Hz.

Equations (7)

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

I 1 ( x , y ) = I ( x , y ) + I ( x , y ) cos ( ϕ 2 π / 3 ) ,
I 2 ( x , y ) = I ( x , y ) + I ( x , y ) cos ( ϕ ) ,
I 3 ( x , y ) = I ( x , y ) + I ( x , y ) cos ( ϕ + 2 π / 3 ) .
ϕ ( x , y ) = tan 1 [ 3 ( I 1 I 3 ) / ( 2 I 2 I 1 I 3 ) ] .
b k = 4 π θ = 0 π / 2 f ( θ ) sin ( k θ ) d θ .
f ˜ ( i , j ) = f ( i , j ) + k , l S h ( k , l ) e ( i k , j l ) .
h = [ * 8 / 42 4 / 42 2 / 42 4 / 42 8 / 42 4 / 42 2 / 42 1 / 42 2 / 42 4 / 42 2 / 42 1 / 42 ] .

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