Abstract

A three-dimensional (3D) profilometry method without phase unwrapping is proposed. The key factors of the proposed profilometry are the use of composite projection of multi-frequency and four-step phase-shift sinusoidal fringes and its geometric analysis, which enable the proposed method to extract the depth information of even largely separated discontinuous objects as well as lumped continuous objects. In particular, the geometric analysis of the multi-frequency sinusoidal fringe projection identifies the shape and position of target objects in absolute coordinate system. In the paper, the depth extraction resolution of the proposed method is analyzed and experimental results are presented.

© 2009 Optical Society of America

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References

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2008 (3)

2007 (2)

E. A. Barbosa, E. A. Lima, M. R. R. Gesualdi, and M. Muramatsu, "Enhanced multiwavelength holographic profilometry by laser mode selection," Opt. Eng. 46, 075601-075607 (2007).
[CrossRef]

W.-J. Ryu, Y.-J. Kang, S.-H. Baik, and S.-J. Kang, "A study on the 3-D measurement by using digital projection Moiré method," Opt. Int. J. Light Electron. Opt. 119, 453-458 (2007).
[CrossRef]

2006 (3)

2005 (1)

2004 (1)

J. Salvi, J. Pagès, and J. Batlle, "Pattern codification strategies in structured light systems," Pattern Recogn. 37, 827-849 (2004).
[CrossRef]

2003 (3)

1997 (2)

1994 (1)

1993 (1)

M. Chang and C. S. Ho, "Phase measuring profilometry using sinusoidal grating," Exp. Mech. 33, 117-122 (1993).
[CrossRef]

1970 (2)

Allen, J. B.

Baik, S.-H.

W.-J. Ryu, Y.-J. Kang, S.-H. Baik, and S.-J. Kang, "A study on the 3-D measurement by using digital projection Moiré method," Opt. Int. J. Light Electron. Opt. 119, 453-458 (2007).
[CrossRef]

Barbosa, E. A.

E. A. Barbosa, E. A. Lima, M. R. R. Gesualdi, and M. Muramatsu, "Enhanced multiwavelength holographic profilometry by laser mode selection," Opt. Eng. 46, 075601-075607 (2007).
[CrossRef]

Batlle, J.

J. Salvi, J. Pagès, and J. Batlle, "Pattern codification strategies in structured light systems," Pattern Recogn. 37, 827-849 (2004).
[CrossRef]

Brémand, F.

Buytaert, J. A. N.

Cai, L. Z.

Chang, M.

M. Chang and C. S. Ho, "Phase measuring profilometry using sinusoidal grating," Exp. Mech. 33, 117-122 (1993).
[CrossRef]

Cho, S.-W.

Cho, Y. J.

Dirckx, J. J. J.

Dong, G. Y.

Freeman, D. M.

J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, "Multibeam interferometric illumination as the primary source of resolution in optical microscopy," Appl. Phys. Lett. 88, 171112 (2006).
[CrossRef]

Gesualdi, M. R. R.

E. A. Barbosa, E. A. Lima, M. R. R. Gesualdi, and M. Muramatsu, "Enhanced multiwavelength holographic profilometry by laser mode selection," Opt. Eng. 46, 075601-075607 (2007).
[CrossRef]

Gu, Q.

Guan, C.

Hahn, J.

Hassebrook, L. G.

Ho, C. S.

M. Chang and C. S. Ho, "Phase measuring profilometry using sinusoidal grating," Exp. Mech. 33, 117-122 (1993).
[CrossRef]

Hong, S. S.

J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, "Multibeam interferometric illumination as the primary source of resolution in optical microscopy," Appl. Phys. Lett. 88, 171112 (2006).
[CrossRef]

Horn, B. K. P.

J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, "Multibeam interferometric illumination as the primary source of resolution in optical microscopy," Appl. Phys. Lett. 88, 171112 (2006).
[CrossRef]

Johnson, W. O.

Jones, J. D. C.

Kang, S.-J.

W.-J. Ryu, Y.-J. Kang, S.-H. Baik, and S.-J. Kang, "A study on the 3-D measurement by using digital projection Moiré method," Opt. Int. J. Light Electron. Opt. 119, 453-458 (2007).
[CrossRef]

Kang, Y.-J.

W.-J. Ryu, Y.-J. Kang, S.-H. Baik, and S.-J. Kang, "A study on the 3-D measurement by using digital projection Moiré method," Opt. Int. J. Light Electron. Opt. 119, 453-458 (2007).
[CrossRef]

Kim, D.

Kim, H.

Kinoshita, M.

Lagarde, A.

Lee, B.

Li, J.

Li, J.-L.

Lima, E. A.

E. A. Barbosa, E. A. Lima, M. R. R. Gesualdi, and M. Muramatsu, "Enhanced multiwavelength holographic profilometry by laser mode selection," Opt. Eng. 46, 075601-075607 (2007).
[CrossRef]

Liu, H.

Mauvoisin, G.

Meadows, D. M.

Meng, X. F.

Mermelstein, M. S.

J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, "Multibeam interferometric illumination as the primary source of resolution in optical microscopy," Appl. Phys. Lett. 88, 171112 (2006).
[CrossRef]

Moisson, E.

Mounier, D.

Muramatsu, M.

E. A. Barbosa, E. A. Lima, M. R. R. Gesualdi, and M. Muramatsu, "Enhanced multiwavelength holographic profilometry by laser mode selection," Opt. Eng. 46, 075601-075607 (2007).
[CrossRef]

Pagès, J.

J. Salvi, J. Pagès, and J. Batlle, "Pattern codification strategies in structured light systems," Pattern Recogn. 37, 827-849 (2004).
[CrossRef]

Picart, P.

Ryu, J.

J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, "Multibeam interferometric illumination as the primary source of resolution in optical microscopy," Appl. Phys. Lett. 88, 171112 (2006).
[CrossRef]

Ryu, W.-J.

W.-J. Ryu, Y.-J. Kang, S.-H. Baik, and S.-J. Kang, "A study on the 3-D measurement by using digital projection Moiré method," Opt. Int. J. Light Electron. Opt. 119, 453-458 (2007).
[CrossRef]

Salvi, J.

J. Salvi, J. Pagès, and J. Batlle, "Pattern codification strategies in structured light systems," Pattern Recogn. 37, 827-849 (2004).
[CrossRef]

Shen, X. X.

Song, Y.

Su, H.-J.

Su, W.

Su, X.-Y.

Takahashi, Y.

Takai, H.

Takasaki, H.

Takeda, M.

Towers, C. E.

Towers, D. P.

Wang, Y.

Wang, Y. R.

Xu, X. F.

Yang, X. L.

Zhang, X.

Zheng, R.

Appl. Opt. (8)

Appl. Phys. Lett. (1)

J. Ryu, S. S. Hong, B. K. P. Horn, D. M. Freeman, and M. S. Mermelstein, "Multibeam interferometric illumination as the primary source of resolution in optical microscopy," Appl. Phys. Lett. 88, 171112 (2006).
[CrossRef]

Exp. Mech. (1)

M. Chang and C. S. Ho, "Phase measuring profilometry using sinusoidal grating," Exp. Mech. 33, 117-122 (1993).
[CrossRef]

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

J. Opt. Soc. Korea (1)

Opt. Eng. (1)

E. A. Barbosa, E. A. Lima, M. R. R. Gesualdi, and M. Muramatsu, "Enhanced multiwavelength holographic profilometry by laser mode selection," Opt. Eng. 46, 075601-075607 (2007).
[CrossRef]

Opt. Express (2)

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

W.-J. Ryu, Y.-J. Kang, S.-H. Baik, and S.-J. Kang, "A study on the 3-D measurement by using digital projection Moiré method," Opt. Int. J. Light Electron. Opt. 119, 453-458 (2007).
[CrossRef]

Opt. Lett. (2)

Pattern Recogn. (1)

J. Salvi, J. Pagès, and J. Batlle, "Pattern codification strategies in structured light systems," Pattern Recogn. 37, 827-849 (2004).
[CrossRef]

Other (2)

E. Stoykova, J. Harizanova, and V. Sainov, "Pattern projection profilometry for 3D coordinates measurement of dynamic scenes," in Three-Dimensional Television: Capture, Transmission, Display, H. M. Ozaktas and L. Onural, ed. (Springer, 2008), pp. 85-164.
[CrossRef]

I. Yamaguchi, "Phase-shifting digital holography," in Digital Holography and Three-Dimensional Display, T.-C. Poon, ed. (Springer, 2007), pp. 145-172.

Supplementary Material (1)

» Media 1: AVI (2321 KB)     

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Figures (10)

Fig. 1.
Fig. 1.

Geometry of the proposed profilometry system

Fig. 2.
Fig. 2.

Intersectional region with field of views by both a CCD camera and a projector.

Fig. 3.
Fig. 3.

Spatial resolution in the intersectional region: (a) the relation between spatial resolution and angular resolutions of both a CCD camera and a projector and (b) the contour map of resolvable voxel in the intersectional region.

Fig. 4.
Fig. 4.

Schematic of 3D profilometry with multi-frequency and four-step phase shift sinusoidal fringe projection.

Fig. 5.
Fig. 5.

Composite local illumination functions of multi-frequency sinusoidal fringe patterns of (a) a single spatial frequency of n = 10, (b) two spatial frequencies of n = 5 and 10, (c) two spatial frequencies of n = 9 and 10, and (d) nine spatial frequencies of n = 2, 3,…,and 10. The shift parameter s is set to s = 512.

Fig. 6.
Fig. 6.

The peak-shaped response by the overlapped patterns with the composition of multi-frequency sine waves at (a) s = 256, (b) s = 512 , and (c) s = 768 .

Fig. 7.
Fig. 7.

Experiment setup of the proposed profilometry.

Fig. 8.
Fig. 8.

Images of the target objects (a) illuminated by low spatial frequency fringe pattern (n=10) and (b) high spatial frequency fringe pattern (n=10). (c) Synthesized image of the object illuminated by the local illuminated function and (d) the movie of scanning the local illumination (Media 1).

Fig. 9.
Fig. 9.

Depth profiles obtained using multi-frequency fringe composite (a) with a single frequency n = 10, (b) with two frequencies in the case of n = 5 and 10, (c) with n = 9 and 10, and (d) with nine frequencies n = 2,3,…, and 10.

Fig. 10.
Fig. 10.

Experimental results of depth extraction of spatially separated 20 balls; (a) camera image, (b) measured depth profile, and (c) perspective view of measured depth profile.

Tables (1)

Tables Icon

Table 1. Comparison between the actual depth of the center points of 20 balls and the extracted depth of the center points.

Equations (20)

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zzCCD=cotθDetect(xxCCD).
(xxCCDzzCCD)=(cosφCCDsinφCCDsinφCCDcosφCCD) (xxCCDzzCCD) .
zOBJzCCD=cot(φCCD+θDetect) (xOBJxCCD) ,
zOBJzPRJ=cot(φPRJ+θLocal) (xOBJxPRJ) .
zOBJ=(xCCDxPRJ)tan(φPRJ+θLocal)(zCCDzPRJ)tan(φPRJ+θLocal)tan(φCCD+θDetect)+zCCD,
xOBJ=(zCCDzPRJ)cot(φPRJ+θLocal)(xCCDxPRJ)cot(φPRJ+θLocal)cot(φCCD+θDetect)+xCCD.
Sresolution=S(xmn,zmn;xm+1n;zm+1n;xmn+1,zmn+1)
+S(xm+1n+1,zm+1n+1;xm+1n,zm+1n;xmn+1,zmn+1) .
S(x1,y1;x2,y2;x3,y3)=12[(x1·y2)+(x2·y3)+(x3·y2)][(x2·y1)+(x3·y2)+(x1·y3)].
Pn,p(ξ)=1+cos(2πfnξ+p),
p=0,π/2,π,and3π/2,
fn=2n .
cos(2πfnξ)=[Pn,0(ξ)Pn,π(ξ)]/2 ,
sin(2πfnξ)=[Pn,3π/2(ξ)Pn,π/2(ξ)]/2 .
exp(j2πfnξ)=[Pn,0(ξ)Pn,π(ξ)] / 2+j [Pn,3π/2(ξ)Pn,π/2(ξ)] / 2 .
PLocal(ξ;s)=real{nFr[h(ξs)]fξ=fnexp(j2πfnξ)} ,
h=(ξs) =δ(ξs).
PLocal(ξ;s)=real{nexp[j2πfn(ξs)]}
=real{nexp(j2πfns){[Pn,0(ξ)Pn,π(ξ)]+j[Pn,3π/2(ξ)Pn,π/2(ξ)]}/2}.
ILocal(s)=real{nexp(j2πfns){[In,0In,π]+j[In,3π/2In,π/2]}/2} .

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