Abstract

Phase unwrapping is an important and challenging issue in fringe pattern profilometry. In this Letter we propose an approach to recover absolute phase maps of two fringe patterns with selected frequencies. Compared to existing temporal multiple frequency algorithms, the two frequencies in our proposed algorithm can be high enough and thus enable efficient and accurate recovery of absolute phase maps. Experiment results are presented to confirm the effectiveness of the proposed technique.

© 2011 Optical Society of America

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References

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2010 (1)

2009 (3)

K. Houairi and F. Cassaing, J. Opt. Soc. Am. A 26, 2503 (2009).
[CrossRef]

S. Zhang, Proc. SPIE 7432, 74320N (2009).
[CrossRef]

S. Zhang, Opt. Eng. 48, 105601 (2009).
[CrossRef]

2008 (1)

2007 (1)

2003 (1)

1997 (2)

1994 (2)

1971 (1)

Cassaing, F.

Chen, W.

de Groot, P. J.

Guan, C.

Hao, Q.

Hassebrook, L. G.

Houairi, K.

Huntley, J. M.

Lau, D. L.

Li, J.

Li, S.

Li, X.

Liu, K.

Saldner, H. O.

Su, X.

Tan, Y.

Wang, Y.

Wyant, J. C.

Yau, S. T.

Zhang, S.

S. Zhang, Proc. SPIE 7432, 74320N (2009).
[CrossRef]

S. Zhang, Opt. Eng. 48, 105601 (2009).
[CrossRef]

S. Zhang, X. Li, and S. T. Yau, Appl. Opt. 46, 50 (2007).
[CrossRef]

Zhao, H.

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Figures (1)

Fig. 1
Fig. 1

(a) Fringe patterns on the object at f 2 = 8 . (b) Fringe pattern on the object at f 1 = 5 . (c) Wrapped phase map on the object at f 2 = 8 . (d) Wrapped phase map at f 1 = 5 . (e) Recovered absolute phase at f 2 = 8 . (f) Recovered absolute phase at f 1 = 5 .

Tables (3)

Tables Icon

Table 1 Mapping from Φ 0 ( x ) to m 2 ( x ) f 1 m 1 ( x ) f 2

Tables Icon

Table 2 Mapping from m 2 ( x ) f 1 m 1 ( x ) f 2 to m 1 ( x ) , m 2 ( x )

Tables Icon

Table 3 Mapping from m 2 ( x ) f 1 m 1 ( x ) f 2 to m 1 ( x ) , m 2 ( x )

Equations (10)

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{ d 1 ( x , y ) = A ( x , y ) + B ( x , y ) cos [ Φ 1 ( x ) ] d 2 ( x , y ) = A ( x , y ) + B ( x , y ) cos [ Φ 2 ( x ) ] ,
f 1 π < Φ 1 ( x ) < f 1 π , f 2 π < Φ 2 ( x ) < f 2 π .
{ Φ 1 ( x ) = 2 π m 1 ( x ) + ϕ 1 ( x ) Φ 2 ( x ) = 2 π m 2 ( x ) + ϕ 2 ( x ) .
f 2 Φ 1 ( x ) = f 1 Φ 2 ( x ) .
f 2 ϕ 1 ( x ) f 1 ϕ 2 ( x ) 2 π = m 2 ( x ) f 1 m 1 ( x ) f 2 .
m 1 ( x ) = { f 1 / 2 [ f 1 ( f 1 mod 2 + 1 ) ] π Φ 1 ( x ) < f 1 π 1 π Φ 1 ( x ) < 3 π 0 π < Φ 1 ( x ) < π 1 3 π < Φ 1 ( x ) π f 1 / 2 f 1 π < Φ 1 ( x ) [ f 1 ( f 1 mod 2 + 1 ) ] π ,
m 2 ( x ) = { f 2 / 2 [ f 2 ( f 2 mod 2 + 1 ) ] π Φ 2 ( x ) < f 2 π 1 π Φ 2 ( x ) < 3 π 0 π < Φ 2 ( x ) < π 1 3 π < Φ 2 ( x ) π f 2 / 2 f 2 π < Φ 2 ( x ) [ f 2 ( f 2 mod 2 + 1 ) ] π ,
Φ 1 ( x ) = f 1 Φ 0 ( x ) , Φ 2 ( x ) = f 2 Φ 0 ( x ) .
m 1 ( x ) = { f 1 / 2 [ f 1 ( f 1 mod 2 + 1 ) ] π f 1 Φ 0 ( x ) < f 1 π 1 π f 1 Φ 0 ( x ) < 3 π 0 π < f 1 Φ 0 ( x ) < π 1 3 π < f 1 Φ 0 ( x ) π f 1 / 2 f 1 π < f 1 Φ 0 ( x ) [ f 1 ( f 1 mod 2 + 1 ) ] π ,
m 2 ( x ) = { f 2 / 2 [ f 2 ( f 2 mod 2 + 1 ) ] π f 2 Φ 0 ( x ) < f 2 π 1 π f 2 Φ 0 ( x ) < 3 π 0 π < f 2 Φ 0 ( x ) < π 1 3 π < f 2 Φ 0 ( x ) π f 2 / 2 f 2 π < f 2 Φ 0 ( x ) [ f 2 ( f 2 mod 2 + 1 ) ] π .

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