Abstract

This Letter presents a novel absolute phase recovery technique with phase coding. Unlike the conventional gray-coding method, the codeword is embedded into the phase and then used to determine the fringe order for absolute phase retrieval. This technique is robust because it uses phase instead of intensity to determine codewords, and it could achieve a faster measurement speed, since three additional images can represent more than 8(23) unique codewords for phase unwrapping. Experimental results will be presented to verify the performance of the proposed technique.

© 2012 Optical Society of America

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References

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2010

2003

1999

1994

1993

1987

1985

Carocci, M.

Chen, W.

Cheng, Y.

Creath, K.

Ghiglia, D. C.

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

Gorthi, S.

S. Gorthi and P. Rastogi, Opt. Lasers Eng. 48, 133 (2010).
[CrossRef]

Huntley, J. M.

Jones, J. DC.

Malacara, D.

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

Pritt, M. D.

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

Rastogi, P.

S. Gorthi and P. Rastogi, Opt. Lasers Eng. 48, 133 (2010).
[CrossRef]

Rodella, R.

Saldner, H.

Sansoni, G.

Tan, Y.

Towers, C. E.

Towers, D. P.

Wyant, J.

Zhao, H.

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Figures (5)

Fig. 1.
Fig. 1.

Principle of the proposed technique. (a) Wrapped phase obtained from sinusoidal fringe patterns, (b) codewords extracted from encoded fringe patterns.

Fig. 2.
Fig. 2.

(a)–(c) Three sinusoidal phase-shifted fringe images, (d) wrapped phase map, (e)–(g) three phase encoded fringe patterns, (h) wrapped stair phase map.

Fig. 3.
Fig. 3.

Framework for absolute phase retrieval. (a) One cross section of the original extracted coded phase, (b) codeword after normalization and quantization, (c) the same cross sections of the wrapped phase and the codeword, (d) recovered absolute phase.

Fig. 4.
Fig. 4.

Stair phase recovery for different quality fringe patterns. (a)–(c) One of the phase coded fringe patterns with high exposure, middle exposure, and low exposure, respectively; (d) cross sections of the extracted stair coded phase.

Fig. 5.
Fig. 5.

3D shape measurement results of more complex sculptures. (a)–(c) One of the fringe patterns with different exposures, (d)–(f) the reconstructed 3D results.

Equations (8)

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I1(x,y)=I(x,y)+I(x,y)cos(ϕ2π/3),
I2(x,y)=I(x,y)+I(x,y)cos(ϕ),
I3(x,y)=I(x,y)+I(x,y)cos(ϕ+2π/3),
ϕ(x,y)=tan1[3(I1I3)/(2I2I1I3)].
ϕs(x,y)=π+[x/P]×2πN.
Ik(x,y)=I(x,y)+I(x,y)cos(ϕs+δk).
k=Round[N(ϕs+π)/(2π)].
Φ(x,y)=ϕ(x,y)+k×2π.

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