Abstract

A new two-step phase-shifting fringe projection profilometry is proposed. The slowly variable background intensity of fringe patterns is removed by the use of an intensity differential algorithm. The high-resolution differential algorithm is achieved based on global interpolation of fringe gray level on a subpixel scale. Compared with the traditional three- or four-step phase-shifting method, the profile measurement is sped up with this approach. Computer simulation and experimental performance are evaluated to demonstrate the validity of the proposed measurement method. The experimental results compared with those of the four-step phase-shifting method are presented.

© 2007 Optical Society of America

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References

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    [CrossRef]
  2. C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, "Shape measurement of small objects using LCD fringe projection with phase shifting," Opt. Commun. 189, 21-29 (2001).
    [CrossRef]
  3. C. Quan, C. Tay, X. Kang, X. He, and H. Shang, "Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting," Appl. Opt. 42, 2329-2335 (2003).
    [CrossRef] [PubMed]
  4. Z. Wang and H. Du, "Out-of-plane shape determination in generalized fringe projection profilometry," Opt. Express 14, 12122-12133 (2006).
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    [CrossRef] [PubMed]
  7. K. Qian and S. H. Soon, "Two-dimensional windowed Fourier frames for noise reduction in fringe pattern analysis," Opt. Eng. 44, 075601 (2005).
    [CrossRef]
  8. H. Liu, A. N. Cartwright, and C. Basaran, "Sensitivity improvement in phase shifted moiré interferometry using 1D continuous wavelet transform image processing," Opt. Eng. 42, 2646-2652 (2003).
    [CrossRef]
  9. B. K. A. Ngoi, K. Venkatakrishnan, N. R. Sivakumar, and T. Bo, "Instantaneous phase shifting arrangement for microsurface profiling of flat surface," Opt. Commun. 190, 109-116 (2001).
    [CrossRef]
  10. X. Y. He, D. Q. Zou, S. Liu, and Y. F. Guo, "Phase-shifting analysis in moiré interferometry and its application in electronic packaging," Opt. Eng. 37, 1410-1419 (1998).
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    [CrossRef] [PubMed]
  14. T. W. Ng, "The one-step phase-shifting technique for wave-front interferometry," J. Mod. Opt. 43, 2129-2138 (1996).
    [CrossRef]

2006 (3)

2005 (1)

K. Qian and S. H. Soon, "Two-dimensional windowed Fourier frames for noise reduction in fringe pattern analysis," Opt. Eng. 44, 075601 (2005).
[CrossRef]

2003 (2)

H. Liu, A. N. Cartwright, and C. Basaran, "Sensitivity improvement in phase shifted moiré interferometry using 1D continuous wavelet transform image processing," Opt. Eng. 42, 2646-2652 (2003).
[CrossRef]

C. Quan, C. Tay, X. Kang, X. He, and H. Shang, "Shape measurement by use of liquid-crystal display fringe projection with two-step phase shifting," Appl. Opt. 42, 2329-2335 (2003).
[CrossRef] [PubMed]

2001 (2)

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, "Shape measurement of small objects using LCD fringe projection with phase shifting," Opt. Commun. 189, 21-29 (2001).
[CrossRef]

B. K. A. Ngoi, K. Venkatakrishnan, N. R. Sivakumar, and T. Bo, "Instantaneous phase shifting arrangement for microsurface profiling of flat surface," Opt. Commun. 190, 109-116 (2001).
[CrossRef]

2000 (1)

F. Chen, G. M. Brown, and M. Song, "Overview of three-dimensional shape measurement using optical methods," Opt. Eng. 39, 10-22 (2000).
[CrossRef]

1998 (1)

X. Y. He, D. Q. Zou, S. Liu, and Y. F. Guo, "Phase-shifting analysis in moiré interferometry and its application in electronic packaging," Opt. Eng. 37, 1410-1419 (1998).
[CrossRef]

1996 (1)

T. W. Ng, "The one-step phase-shifting technique for wave-front interferometry," J. Mod. Opt. 43, 2129-2138 (1996).
[CrossRef]

1985 (1)

1984 (1)

Appl. Opt. (4)

J. Mod. Opt. (1)

T. W. Ng, "The one-step phase-shifting technique for wave-front interferometry," J. Mod. Opt. 43, 2129-2138 (1996).
[CrossRef]

Opt. Commun. (2)

B. K. A. Ngoi, K. Venkatakrishnan, N. R. Sivakumar, and T. Bo, "Instantaneous phase shifting arrangement for microsurface profiling of flat surface," Opt. Commun. 190, 109-116 (2001).
[CrossRef]

C. Quan, X. Y. He, C. F. Wang, C. J. Tay, and H. M. Shang, "Shape measurement of small objects using LCD fringe projection with phase shifting," Opt. Commun. 189, 21-29 (2001).
[CrossRef]

Opt. Eng. (4)

F. Chen, G. M. Brown, and M. Song, "Overview of three-dimensional shape measurement using optical methods," Opt. Eng. 39, 10-22 (2000).
[CrossRef]

K. Qian and S. H. Soon, "Two-dimensional windowed Fourier frames for noise reduction in fringe pattern analysis," Opt. Eng. 44, 075601 (2005).
[CrossRef]

H. Liu, A. N. Cartwright, and C. Basaran, "Sensitivity improvement in phase shifted moiré interferometry using 1D continuous wavelet transform image processing," Opt. Eng. 42, 2646-2652 (2003).
[CrossRef]

X. Y. He, D. Q. Zou, S. Liu, and Y. F. Guo, "Phase-shifting analysis in moiré interferometry and its application in electronic packaging," Opt. Eng. 37, 1410-1419 (1998).
[CrossRef]

Opt. Express (1)

Opt. Lett. (1)

Other (1)

D. Malacara and B. J. Thompson, Handbook of Optical Engineering (Marcel Dekker, 2001).

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Figures (12)

Fig. 1
Fig. 1

Simulation of 1D sinusoidal fringe intensity distribution.

Fig. 2
Fig. 2

Sinusoidal fringe intensity distributions corresponding to the counterpart in Fig. 1 obtained by computer simulation, Eqs. (7) and (9).

Fig. 3
Fig. 3

Simulation results, part I.

Fig. 4
Fig. 4

Simulation results, part II:(a) Two sets of simulated sinusoidal fringe patterns with a phase shift of π / 2 based on Eq. (11). (b) Unwrapped phases extracted from the fringe patterns shown in (a) by the proposed method.

Fig. 5
Fig. 5

Absolute errors in radians between computer-simulated phase and that demodulated by the proposed method.

Fig. 6
Fig. 6

Tested shape made by thick white paper.

Fig. 7
Fig. 7

Two phase-shifted sinusoidal fringe images projected onto the tested object with a phase shift of π / 2 .

Fig. 8
Fig. 8

Two images resulting from the proposed derivative operation on those shown in Fig. 7.

Fig. 9
Fig. 9

(a) Gray level plot of a cross section marked by AA in Fig. 7. (b) Derivative plot of the same cross section AA.

Fig. 10
Fig. 10

Reconstructed 3D maps of unwrapped phase extracted by (a) the proposed method and (b) the four-step phase-shifting method.

Fig. 11
Fig. 11

Comparison of phase distributions corresponding to the same cross sections in Fig. 10(a) and Fig. 10(b).

Fig. 12
Fig. 12

Intensity response of the LCD projector is nonlinear to the generated sinusoidal fringe pattern.

Tables (2)

Tables Icon

Table 1 Error Caused by Use of Derivative Derived from Eqs. (7) and (9)

Tables Icon

Table 2 Surface Reflectivity and Fringe Contrast Influence on Measured Phase by Use of Proposed Profilometer

Equations (14)

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I ( x , y ) = R ( x , y ) { A ( x , y ) + B ( x , y ) sin [ 2 π f x + ϕ ( x , y ) ] } ,
I ( x , y ) = a ( x , y ) + b ( x , y ) sin [ 2 π f x + ϕ ( x , y ) ] ,
  I 0 ( x , y ) = a ( x , y ) + b ( x , y ) sin [ 2 π f x + ϕ ( x , y ) ] ,
I 1 ( x , y ) = a ( x , y ) + b ( x , y ) sin [ 2 π f x + ϕ ( x , y ) + π 2 ] ,
I 0 ( x , y ) = d I 0 ( x , y ) d x = b ( x , y ) [ 2 π f + d ϕ ( x , y ) d x ] × cos [ 2 π f x + ϕ ( x , y ) ] ,
I 1 ( x , y ) = d I 1 ( x , y ) d x = b ( x , y ) [ 2 π f + d ϕ ( x , y ) d x ] × sin [ 2 π f x + ϕ ( x , y ) ] ,
ϕ ( x , y ) = arctan I 1 ( x , y ) I 0 ( x , y ) 2 π f x ,
Δ I ( x , y ) = I ( x + 1 , y ) I ( x , y ) ,
g ( x , y ) = i = k k + 7 I ( x i , y ) j = k j i k + 7 [ ( x x j ) / ( x i x j ) ] ,
d I ( x , y ) d x = I ( x + d x , y ) I ( x , y ) d x ,
I i ( x ) = R ( x ) { A + B sin [ 2 π f x + ϕ ( x ) + i π 2 ] }   ( i = 0 , 1 ) ,
g i ( x , y ) = 110 ( 1 0.4 cos x 50 ) × { 0.5 + sin [ 0 .1 π x + ϕ ( x , y ) + i π 2 ] } + rand ( 20 )   ( i = 0 , 1 ) ,
ϕ ( x , y ) = { φ ( x , y ) = 1.5 π [ ( x 256 ) 2 + ( y 256 ) 2 ] / 3276.8 0 if φ ( x , y ) < 0 ,
f ( x , y ) = g ( x , y ) + λ [ g ( x 1 , y ) + 2 g ( x , y ) g ( x + 1 , y ) g ( x , y 1 ) + 2 g ( x , y ) g ( x , y + 1 ) ] ,

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