Abstract

Both the analysis of phase errors which occur at the abrupt discontinuities in phase measuring profilometry (PMP) and the identification method are presented in this paper. The sampling effect of CCD will cause a dilution of accuracy in PMP, especially at abrupt discontinuities on the object surface. The existing methods cannot efficiently identify the abrupt discontinuities. We analyze the relationship between the phase, the height and the equivalent wavelength. By viewing the phase as the argument of a vector we find out that CCD sampling introduces errors into the measurement and the phase is nonlinear to the equivalent wavelength at the abrupt discontinuities. Therefore temporal phase unwrapping (TPU) is introduced into the measurement to identify the abrupt discontinuities. Computer simulations and practical experiment validate the feasibility of this method.

© 2010 OSA

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References

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  1. V. Srinivasan, H. C. Liu, and M. Halioua, “Automated phase-measuring profilometry of 3-D diffuse objects,” Appl. Opt. 23(18), 3105–3108 (1984).
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    [CrossRef] [PubMed]
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    [CrossRef]
  4. H. Su, J. Li, and X. Su, “Phase algorithm without the influence of carrier frequency,” Opt. Eng. 36(6), 1799–1805 (1997).
    [CrossRef]
  5. A. Asundi and Z. Wensen, “Fast phase-unwrapping algorithm based on a gray-scale mask and flood fill,” Appl. Opt. 37(23), 5416–5420 (1998).
    [CrossRef]
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    [CrossRef] [PubMed]
  7. Y. Hao, Y. Zhao, and D. Li, “Multifrequency grating projection profilometry based on the nonlinear excess fraction method,” Appl. Opt. 38(19), 4106–4110 (1999).
    [CrossRef]
  8. E. Hu, Y. He, and Y. Chen, “Study on a novel phase-recovering algorithm for partial intensity saturation in digital projection grating phase-shifting profilometry,” Opt. Int. J. Light Electron. Opt. (2008), doi:.
  9. E. Hu, Y. He, and Y. Chen, “Study on a novel phase-recovering algorithm for partial intensity saturation in digital projection grating phase-shifting profilometry,” Optik - International Journal for Light and Electron Optics 121(1), 23–28 (2010).
    [CrossRef]
  10. X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42(3), 245–261 (2004).
    [CrossRef]
  11. J. M. Huntley and H. O. Saldner, “Temporal phase-unwrapping algorithm for automated interferogram analysis,” Appl. Opt. 32(17), 3047–3052 (1993).
    [CrossRef] [PubMed]
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    [CrossRef]

2010 (1)

E. Hu, Y. He, and Y. Chen, “Study on a novel phase-recovering algorithm for partial intensity saturation in digital projection grating phase-shifting profilometry,” Optik - International Journal for Light and Electron Optics 121(1), 23–28 (2010).
[CrossRef]

2008 (1)

E. Hu, Y. He, and Y. Chen, “Study on a novel phase-recovering algorithm for partial intensity saturation in digital projection grating phase-shifting profilometry,” Opt. Int. J. Light Electron. Opt. (2008), doi:.

2004 (1)

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42(3), 245–261 (2004).
[CrossRef]

1999 (1)

1998 (1)

1997 (3)

1994 (1)

T. R. Judge and P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21(4), 199–239 (1994).
[CrossRef]

1993 (1)

1989 (1)

1984 (1)

Asundi, A.

Bryanston-Cross, P. J.

T. R. Judge and P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21(4), 199–239 (1994).
[CrossRef]

Chen, W.

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42(3), 245–261 (2004).
[CrossRef]

Chen, Y.

E. Hu, Y. He, and Y. Chen, “Study on a novel phase-recovering algorithm for partial intensity saturation in digital projection grating phase-shifting profilometry,” Optik - International Journal for Light and Electron Optics 121(1), 23–28 (2010).
[CrossRef]

E. Hu, Y. He, and Y. Chen, “Study on a novel phase-recovering algorithm for partial intensity saturation in digital projection grating phase-shifting profilometry,” Opt. Int. J. Light Electron. Opt. (2008), doi:.

Halioua, M.

Hao, Y.

He, Y.

E. Hu, Y. He, and Y. Chen, “Study on a novel phase-recovering algorithm for partial intensity saturation in digital projection grating phase-shifting profilometry,” Optik - International Journal for Light and Electron Optics 121(1), 23–28 (2010).
[CrossRef]

E. Hu, Y. He, and Y. Chen, “Study on a novel phase-recovering algorithm for partial intensity saturation in digital projection grating phase-shifting profilometry,” Opt. Int. J. Light Electron. Opt. (2008), doi:.

Hu, E.

E. Hu, Y. He, and Y. Chen, “Study on a novel phase-recovering algorithm for partial intensity saturation in digital projection grating phase-shifting profilometry,” Optik - International Journal for Light and Electron Optics 121(1), 23–28 (2010).
[CrossRef]

E. Hu, Y. He, and Y. Chen, “Study on a novel phase-recovering algorithm for partial intensity saturation in digital projection grating phase-shifting profilometry,” Opt. Int. J. Light Electron. Opt. (2008), doi:.

Huntley, J. M.

Huntley, M.

Judge, T. R.

T. R. Judge and P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21(4), 199–239 (1994).
[CrossRef]

Li, D.

Li, J.

H. Su, J. Li, and X. Su, “Phase algorithm without the influence of carrier frequency,” Opt. Eng. 36(6), 1799–1805 (1997).
[CrossRef]

Liu, H. C.

Saldner, H. O.

Srinivasan, V.

Su, H.

H. Su, J. Li, and X. Su, “Phase algorithm without the influence of carrier frequency,” Opt. Eng. 36(6), 1799–1805 (1997).
[CrossRef]

Su, X.

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42(3), 245–261 (2004).
[CrossRef]

H. Su, J. Li, and X. Su, “Phase algorithm without the influence of carrier frequency,” Opt. Eng. 36(6), 1799–1805 (1997).
[CrossRef]

Wensen, Z.

Zhao, Y.

Appl. Opt. (6)

J. Opt. Soc. Am. A (1)

Opt. Eng. (1)

H. Su, J. Li, and X. Su, “Phase algorithm without the influence of carrier frequency,” Opt. Eng. 36(6), 1799–1805 (1997).
[CrossRef]

Opt. Int. J. Light Electron. Opt. (1)

E. Hu, Y. He, and Y. Chen, “Study on a novel phase-recovering algorithm for partial intensity saturation in digital projection grating phase-shifting profilometry,” Opt. Int. J. Light Electron. Opt. (2008), doi:.

Opt. Lasers Eng. (2)

T. R. Judge and P. J. Bryanston-Cross, “A review of phase unwrapping techniques in fringe analysis,” Opt. Lasers Eng. 21(4), 199–239 (1994).
[CrossRef]

X. Su and W. Chen, “Reliability-guided phase unwrapping algorithm: a review,” Opt. Lasers Eng. 42(3), 245–261 (2004).
[CrossRef]

Optik - International Journal for Light and Electron Optics (1)

E. Hu, Y. He, and Y. Chen, “Study on a novel phase-recovering algorithm for partial intensity saturation in digital projection grating phase-shifting profilometry,” Optik - International Journal for Light and Electron Optics 121(1), 23–28 (2010).
[CrossRef]

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Figures (15)

Fig. 1
Fig. 1

The optical geometry of PMP system.

Fig. 2
Fig. 2

The schematic of CCD.

Fig. 3
Fig. 3

the intensity distribution of CCD cells.

Fig. 4
Fig. 4

(a) The vector summing in cell (i 1,j 1) (b) the vector summing in cell (i 2,j 2).

Fig. 5
Fig. 5

The object with abrupt discontinuities in simulation.

Fig. 6
Fig. 6

The deformed fringe patterns (P 0 = 12.8cm, 6.4cm, 3.2cm, 1.6cm, 0.8cm, 0 θ = 27°).

Fig. 7
Fig. 7

The reconstructed object obtained by TPU.

Fig. 8
Fig. 8

Measurements and fitting curves.

Fig. 9
Fig. 9

The mask generated from standard deviations.

Fig. 10
Fig. 10

The reconstructed object after deleting and interpolation.

Fig. 11
Fig. 11

The deformed fringe patterns.

Fig. 12
Fig. 12

The phase distribution obtained from TPU.

Fig. 13
Fig. 13

The grayscale of the standard deviations.

Fig. 14
Fig. 14

The mask generated from standard deviations.

Fig. 15
Fig. 15

The final phase distribution after deleting and interpolation.

Tables (1)

Tables Icon

Table 1 the results of vector summing

Equations (11)

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ϕ ( x , y ) = 2 π h / λ e
ϕ ( x , y ) = atan [ n = 1 N I n ( x , y ) sin ( 2 n π / N ) / n = 1 N I n ( x , y ) cos ( 2 n π / N ) ]
V ( x , y ) = [ n = 1 N I n ( x , y ) cos ( 2 n π / N ) ] i + [ n = 1 N I n ( x , y ) sin ( 2 n π / N ) ] j
I n ( i , j ) = x 1 i , y 1 j x 2 i , y 2 j I n ( x , y ) d x d y
ϕ ( i , j ) = atan n = 1 N I n ( i , j ) sin ( 2 n π / N ) n = 1 N I n ( i , j ) cos ( 2 n π / N ) = atan x 1 i , y 1 j x 2 i , y 2 j n = 1 N I n ( x , y ) sin ( 2 n π / N ) d x d y x 1 i , y 1 j x 2 i , y 2 j n = 1 N I n ( x , y ) cos ( 2 n π / N ) d x d y
V ( i , j ) = [ x 1 i , y 1 j x 2 i , y 2 j n = 1 N I n ( x , y ) cos ( 2 n π / N ) d x d y ] i + [ x 1 i , y 1 j x 2 i , y 2 j n = 1 N I n ( x , y ) sin ( 2 n π / N ) d x d y ] j = x 1 i , y 1 j x 2 i , y 2 j [ n = 1 N I n ( x , y ) cos ( 2 n π / N ) i + n = 1 N I n ( x , y ) sin ( 2 n π / N ) j ] d x d y = x 1 i , y 1 j x 2 i , y 2 j V ( x , y ) d x d y
V A ( i 2 , j 2 ) = [ n = 1 N I A n ( i 2 , j 2 ) cos ( 2 n π / N ) ] i + [ n = 1 N I A n ( i 2 , j 2 ) sin ( 2 n π / N ) ]
V B ( i 2 , j 2 ) = [ n = 1 N I B n ( i 2 , j 2 ) cos ( 2 n π / N ) ] i + [ n = 1 N I B n ( i 2 , j 2 ) sin ( 2 n π / N ) ]
I n ( i 2 , j 2 ) = k A I A n + k B I B n
V ( i 2 , j 2 ) = [ n = 1 N I n ( i 2 , j 2 ) cos ( 2 n π / N ) ] i + [ n = 1 N I n ( i 2 , j 2 ) sin ( 2 n π / N ) ] j = k A [ n = 1 N I A n ( i 2 , j 2 ) cos ( 2 n π / N ) i + n = 1 N I A n ( i 2 , j 2 ) sin ( 2 n π / N ) j ] + k B [ n = 1 N I B n ( i 2 , j 2 ) cos ( 2 n π / N ) i + n = 1 N I B n ( i 2 , j 2 ) sin ( 2 n π / N ) j ] = k A V A ( i 2 , j 2 ) + k B V B ( i 2 , j 2 )
ω = v = 0 log 2 s 2 v φ u ( 2 v ) / v = 0 log 2 s 2 2 v

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