Abstract

A recently proposed flexible 3D shape measurement technique using a defocused projector [Opt. Lett. 34, 3080 (2009) ] shows great potential because of its elimination of projector’s gamma calibration. However, it cannot handle step-height surfaces. I present here a technique to extend its measurement range to an arbitrary shape by integrating a binary coding method. A computational framework is also proposed to tackle the problems related to the defocusing.

© 2010 Optical Society of America

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References

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  1. S. Lei and S. Zhang, Opt. Lett. 34, 3080 (2009).
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  7. D. Malacara, ed., Optical Shop Testing, 3rd ed. (Wiley, 2007).
    [CrossRef]
  8. D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).
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    [CrossRef]

2009 (2)

2007 (1)

D. Malacara, ed., Optical Shop Testing, 3rd ed. (Wiley, 2007).
[CrossRef]

2005 (1)

2003 (1)

1999 (1)

1998 (1)

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

1985 (1)

1973 (1)

Carocci, M.

Cheng, Y.-Y.

Fu, Y.

Ghiglia, D. C.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Jones, J. D. C.

Lei, S.

Malacara, D.

D. Malacara, ed., Optical Shop Testing, 3rd ed. (Wiley, 2007).
[CrossRef]

Polhemus, C.

Pritt, M. D.

D. C. Ghiglia and M. D. Pritt, Two-Dimensional Phase Unwrapping: Theory, Algorithms, and Software (Wiley, 1998).

Quan, C.

Rodella, R.

Sansoni, G.

Tan, J. M.

Tay, C. J.

Towers, C. E.

Towers, D. P.

Wyant, J. C.

Zhang, S.

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Figures (6)

Fig. 1
Fig. 1

Schematic diagram of proposed algorithm.

Fig. 2
Fig. 2

Experimental results of a flat white surface: (a),(b) widest and narrowest binary patterns; (c) sinusoidal pattern; (d) unwrapped phase map.

Fig. 3
Fig. 3

480th cross section of the wrapped and unwrapped phase. (a) Original unwrapped phase map; (b) map with removed global slope of the unwrapped phase.

Fig. 4
Fig. 4

Phase map after applying the computational framework step by step: (a) step 1; (b) step 2; (c) step 3; (d) 480 th cross section.

Fig. 5
Fig. 5

Experimental results of a complex object: (a) one fringe image; (b) 3-D raw data; (c) 3-D data after applying computational framework.

Fig. 6
Fig. 6

Step-height objects can be correctly measured: (a) unwrapped phase map; (b) cross section.

Equations (9)

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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 ) ] .
Φ ( x , y ) = ϕ ( x , y ) + k ( x , y ) × 2 π .
I min ( x , y ) = I ( x , y ) I ( x , y ) ,
I max ( x , y ) = I ( x , y ) + I ( x , y ) .
I k n b ( x , y ) = ( I k b I min ) ( I max I min ) .
n = N n = N { Φ ( i 0 , j 0 + n ) [ ϕ ( i 0 , j 0 ) + k × 2 π ] } ,

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