Abstract

The nonlinear intensity response of a digital fringe-projection-profilometry (FPP) system causes the captured fringe patterns to be nonsinusoidal waveforms, which results in phase error and therefore measurement error. The theoretical analysis of the phase error due to the nonsinusoidal waveforms in Hilbert transform FPP is performed. Based on the derived phase-error expression, a cubic spline-smoothing method is proposed to eliminate the nonsinusoidal phase error. Experiments show that the proposed algorithm can be used for effective phase-error elimination in practical Hilbert transform FPP.

© 2009 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. F. Chen, G. M. Brown, and M. Song, Opt. Eng. 39, 10 (2000).
    [CrossRef]
  2. A. Asundi and C. S. Chan, Opt. Lasers Eng. 21, 31 (1994).
    [CrossRef]
  3. B. Pan, K. Qian, L. Huang, and A. Asundi, Opt. Lett. 34, 416 (2009).
    [CrossRef] [PubMed]
  4. M. Takeda and K. Mutoh, Appl. Opt. 22, 3977 (1983).
    [CrossRef] [PubMed]
  5. J. Zhong and J. Weng, Opt. Lett. 30, 2560 (2005).
    [CrossRef] [PubMed]
  6. M. A. Sutton, W. Zhao, S. R. McNeill, H. W. Schreier, and Y. J. Chao, Exp. Mech. 41, 205 (2001).
    [CrossRef]
  7. H. Miao and Y. Fu, Proc. SPIE 7155, 715518 (2008).
    [CrossRef]
  8. L. Chen and C. Quan, Opt. Lett. 30, 2101 (2005).
    [CrossRef] [PubMed]

2009

2008

H. Miao and Y. Fu, Proc. SPIE 7155, 715518 (2008).
[CrossRef]

2005

2001

M. A. Sutton, W. Zhao, S. R. McNeill, H. W. Schreier, and Y. J. Chao, Exp. Mech. 41, 205 (2001).
[CrossRef]

2000

F. Chen, G. M. Brown, and M. Song, Opt. Eng. 39, 10 (2000).
[CrossRef]

1994

A. Asundi and C. S. Chan, Opt. Lasers Eng. 21, 31 (1994).
[CrossRef]

1983

Asundi, A.

Brown, G. M.

F. Chen, G. M. Brown, and M. Song, Opt. Eng. 39, 10 (2000).
[CrossRef]

Chan, C. S.

A. Asundi and C. S. Chan, Opt. Lasers Eng. 21, 31 (1994).
[CrossRef]

Chao, Y. J.

M. A. Sutton, W. Zhao, S. R. McNeill, H. W. Schreier, and Y. J. Chao, Exp. Mech. 41, 205 (2001).
[CrossRef]

Chen, F.

F. Chen, G. M. Brown, and M. Song, Opt. Eng. 39, 10 (2000).
[CrossRef]

Chen, L.

Fu, Y.

H. Miao and Y. Fu, Proc. SPIE 7155, 715518 (2008).
[CrossRef]

Huang, L.

McNeill, S. R.

M. A. Sutton, W. Zhao, S. R. McNeill, H. W. Schreier, and Y. J. Chao, Exp. Mech. 41, 205 (2001).
[CrossRef]

Miao, H.

H. Miao and Y. Fu, Proc. SPIE 7155, 715518 (2008).
[CrossRef]

Mutoh, K.

Pan, B.

Qian, K.

Quan, C.

Schreier, H. W.

M. A. Sutton, W. Zhao, S. R. McNeill, H. W. Schreier, and Y. J. Chao, Exp. Mech. 41, 205 (2001).
[CrossRef]

Song, M.

F. Chen, G. M. Brown, and M. Song, Opt. Eng. 39, 10 (2000).
[CrossRef]

Sutton, M. A.

M. A. Sutton, W. Zhao, S. R. McNeill, H. W. Schreier, and Y. J. Chao, Exp. Mech. 41, 205 (2001).
[CrossRef]

Takeda, M.

Weng, J.

Zhao, W.

M. A. Sutton, W. Zhao, S. R. McNeill, H. W. Schreier, and Y. J. Chao, Exp. Mech. 41, 205 (2001).
[CrossRef]

Zhong, J.

Appl. Opt.

Exp. Mech.

M. A. Sutton, W. Zhao, S. R. McNeill, H. W. Schreier, and Y. J. Chao, Exp. Mech. 41, 205 (2001).
[CrossRef]

Opt. Eng.

F. Chen, G. M. Brown, and M. Song, Opt. Eng. 39, 10 (2000).
[CrossRef]

Opt. Lasers Eng.

A. Asundi and C. S. Chan, Opt. Lasers Eng. 21, 31 (1994).
[CrossRef]

Opt. Lett.

Proc. SPIE

H. Miao and Y. Fu, Proc. SPIE 7155, 715518 (2008).
[CrossRef]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1
Fig. 1

Fringe pattern projected onto (a) a reference plane and (b) a test arch model.

Fig. 2
Fig. 2

Phase distribution of an arch (a) before and (b) after phase-error elimination (in radians).

Fig. 3
Fig. 3

Comparison of the phase errors of the hundredth column obtained by the traditional HTP method and the proposed method.

Equations (14)

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

I c ( x , y ) = f [ I ( x , y ) ] = a 0 + k = 1 + a k cos [ k ϕ ( x , y ) ] ,
I ( x , y ) = a ( x , y ) + b ( x , y ) cos [ ϕ ( x , y ) ] ,
ϕ c ( x , y ) = arctan { k = 1 + a k sin [ k ϕ ( x , y ) ] k = 1 + a k cos [ k ϕ ( x , y ) ] } .
ϕ ( x , y ) = arctan { b ( x , y ) sin [ ϕ ( x , y ) ] b ( x , y ) cos [ ϕ ( x , y ) ] } = arctan { sin [ ϕ ( x , y ) ] cos [ ϕ ( x , y ) ] } .
Δ ϕ ( x , y ) = ϕ c ( x , y ) ϕ ( x , y ) = arctan { cos [ ϕ ( x , y ) ] k = 1 + a k sin [ k ϕ ( x , y ) ] sin [ ϕ ( x , y ) ] k = 1 + a k cos [ k ϕ ( x , y ) ] sin [ ϕ ( x , y ) ] k = 1 + a k sin [ k ϕ ( x , y ) ] + cos [ ϕ ( x , y ) ] k = 1 + a k cos [ k ϕ ( x , y ) ] } = arctan { k = 1 + a k sin [ ( k 1 ) ϕ ( x , y ) ] k = 1 + a k cos [ ( k 1 ) ϕ ( x , y ) ] } k = 1 + a k + 1 a 1 sin [ k ϕ ( x , y ) ] = k = 1 + d k sin [ k ϕ ( x , y ) ] ,
ϕ c ( x , y ) = ϕ ( x , y ) + k = 1 + d k sin [ k ϕ ( x , y ) ] .
ϕ c ( x , y ) = ϕ ( x , y ) + k = 1 M d k sin [ k ϕ ( x , y ) ] ,
S i ( x ) = A i ( x x i ) 3 + B i ( x x i ) 2 + C i ( x x i ) + D i ,
i = 1 , 2 , , n 1 ,
S i 1 ( x i ) = S i ( x i ) ,
S i 1 ( x i ) = S i ( x i ) ,
S i 1 ( x i ) = S i ( x i ) .
E = p i = 0 n [ ϕ c ( x i , y 0 ) S ( x i ) ] 2 + ( 1 p ) x 0 x n [ S ( x ) ] 2 d x ,
p = x 0 x n [ ϕ r ( x , y 0 ) ] 2 d x i = 0 n [ ϕ r c ( x i , y 0 ) ϕ r ( x i , y 0 ) ] 2 + x 0 x n [ ϕ r ( x , y 0 ) ] 2 d x ,

Metrics