Abstract

A novel uneven fringe projection technique is presented whereby nonuniformly spaced fringes are generated at a digital video projector to give evenly spaced fringes in the measurement volume. The proposed technique simplifies the relation between the measured phase and the object's depth independent of pixel position. This method needs just one coefficient set for calibration and depth calculation. With uneven fringe projection the shape data are referenced to a virtual plane instead of a physical reference plane, so an improved measurement with lower uncertainty is achieved. Further, the method can be combined with a radial lens distortion model. The theoretical foundation of the method is presented and experimentally validated to demonstrate the advantages of the uneven fringe projection approach compared with existing methods. Measurement results on a National Physical Laboratory (UK) “step standard” confirm the measurement uncertainty using the proposed method.

© 2007 Optical Society of America

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2006 (4)

2005 (5)

C. E. Towers, D. P. Towers, and J. D. C. Jones, "Absolute fringe order calculation using optimized multifrequency selection in full-field profilometry," Opt. Lasers Eng. 43, 788-800 (2005).
[CrossRef]

J. Mutsch and B. Breuckmann, "Qualitätskontrolle von Blechteilen mittels topometrischer 3D-Mess- und Prüftechnik," Qual. Eng. 4, 18-19 (2005).

L. C. Chen and C. C. Liao, "Calibration of 3-D surface profilometry using digital fringe projection," Meas. Sci. Technol. 16, 1554-1566 (2005).
[CrossRef]

H. W. Guo, H. T. He, Y. J. Yu, and M. Y. Chen, "Least-squares calibration method for fringe projection profilometry," Opt. Eng. 44, 033603 (2005).
[CrossRef]

B. A. Rajoub, D. R. Burton, and M. J. Lalor, "A new phase-to-height model for measuring object shape using collimated projections of structured light," J. Opt. A 7, s368-s375 (2005).
[CrossRef]

2004 (2)

Z. H. Zhang, D. P. Zhang, X. Peng, and X. T. Hu, "Performance analysis of a 3-D full-field sensor based on fringe projection," Opt. Lasers Eng. 42, 341-353 (2004).
[CrossRef]

D. Ganotra, J. Joseph, and K. Singh, "Object reconstruction in multilayer neural network based profilometry using grating structure comprising two regions with different spatial periods," Opt. Lasers Eng. 42, 179-192 (2004).
[CrossRef]

2003 (3)

L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, "Profilometry by fringe projection," Opt. Eng. 42, 3307-3314 (2003).
[CrossRef]

Q. Y. Hu, P. S. Huang, Q. L. Fu, and F. P. Chiang, "Calibration of a 3-D shape measurement system," Opt. Eng. 42, 487-493 (2003).
[CrossRef]

M. Muramatsu, P. Torroba, N. Cap, and H. Rabal, "The projection diagram," Appl. Opt. 42, 4765-4771 (2003).
[CrossRef] [PubMed]

2002 (2)

G. K. Knopf and J. Kofman, "Surface reconstruction using neural network mapping of range-sensor images to object space," J. Electron. Imaging 11, 187-194 (2002).
[CrossRef]

D. Ganotra, J. Joseph, and K. Singh, "Profilometry for the measurement of 3-D object shape using radial basis function and multilayer perception neural networks," Opt. Commun. 209, 291-301 (2002).
[CrossRef]

2000 (3)

F. Chen, G. M. Brown, and M. Song, "Overview of three-dimensional shape measurement using optical methods," Opt. Eng. 39, 10-22 (2000).
[CrossRef]

F. J. Cuevas, M. Servin, and O. N. Stavroudis, "Multilayer neural network applied to phase and depth recovery from fringe patterns," Opt. Commun. 181, 239-259 (2000).
[CrossRef]

G. Sansoni, M. Carocci, and R. Rodella, "Calibration and performance evaluation of a 3-D imaging sensor based on the projection of structured light," IEEE Trans. Instrum. Meas. 49, 628-636 (2000).
[CrossRef]

1999 (1)

F. J. Cuevas, M. Servin, and R. Rodriguez-Vera, "Depth object recovery using radial basis functions," Opt. Commun. 163, 270-277 (1999).
[CrossRef]

1997 (1)

H. O. Saldner and J. M. Huntley, "Shape measurement by temporal phase unwrapping: comparison of unwrapping algorithms," Meas. Sci. Technol. 8, 986-992 (1997).
[CrossRef]

1996 (1)

G. K. Knopf and J. Kofman, "Neural network mapping of image-to-object coordinates for 3-D shape reconstruction," Proc. SPIE 2904, 129-137 (1996).
[CrossRef]

1994 (1)

W. S. Zhou and X. Y. Su, "A direct mapping algorithm for phase-measuring profilometry," J. Mod. Opt. 41, 89-94 (1994).
[CrossRef]

1992 (1)

J. Weng, P. Cohen, and M. Herniou, "Camera calibration with distortion models and accuracy evaluation," IEEE Trans. Pattern Anal. Mach. Intell. 14, 965-980 (1992).
[CrossRef]

1983 (1)

Appl. Opt. (3)

IEEE Trans. Instrum. Meas. (1)

G. Sansoni, M. Carocci, and R. Rodella, "Calibration and performance evaluation of a 3-D imaging sensor based on the projection of structured light," IEEE Trans. Instrum. Meas. 49, 628-636 (2000).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

J. Weng, P. Cohen, and M. Herniou, "Camera calibration with distortion models and accuracy evaluation," IEEE Trans. Pattern Anal. Mach. Intell. 14, 965-980 (1992).
[CrossRef]

J. Electron. Imaging (1)

G. K. Knopf and J. Kofman, "Surface reconstruction using neural network mapping of range-sensor images to object space," J. Electron. Imaging 11, 187-194 (2002).
[CrossRef]

J. Mod. Opt. (1)

W. S. Zhou and X. Y. Su, "A direct mapping algorithm for phase-measuring profilometry," J. Mod. Opt. 41, 89-94 (1994).
[CrossRef]

J. Opt. A (1)

B. A. Rajoub, D. R. Burton, and M. J. Lalor, "A new phase-to-height model for measuring object shape using collimated projections of structured light," J. Opt. A 7, s368-s375 (2005).
[CrossRef]

Meas. Sci. Technol. (2)

H. O. Saldner and J. M. Huntley, "Shape measurement by temporal phase unwrapping: comparison of unwrapping algorithms," Meas. Sci. Technol. 8, 986-992 (1997).
[CrossRef]

L. C. Chen and C. C. Liao, "Calibration of 3-D surface profilometry using digital fringe projection," Meas. Sci. Technol. 16, 1554-1566 (2005).
[CrossRef]

Opt. Commun. (3)

D. Ganotra, J. Joseph, and K. Singh, "Profilometry for the measurement of 3-D object shape using radial basis function and multilayer perception neural networks," Opt. Commun. 209, 291-301 (2002).
[CrossRef]

F. J. Cuevas, M. Servin, and R. Rodriguez-Vera, "Depth object recovery using radial basis functions," Opt. Commun. 163, 270-277 (1999).
[CrossRef]

F. J. Cuevas, M. Servin, and O. N. Stavroudis, "Multilayer neural network applied to phase and depth recovery from fringe patterns," Opt. Commun. 181, 239-259 (2000).
[CrossRef]

Opt. Eng. (5)

D. Xu, Y. Li, and M. Tan, "Method for calibrating cameras with large lens distortion," Opt. Eng. 45, 043602 (2006).
[CrossRef]

F. Chen, G. M. Brown, and M. Song, "Overview of three-dimensional shape measurement using optical methods," Opt. Eng. 39, 10-22 (2000).
[CrossRef]

L. Salas, E. Luna, J. Salinas, V. Garcia, and M. Servin, "Profilometry by fringe projection," Opt. Eng. 42, 3307-3314 (2003).
[CrossRef]

H. W. Guo, H. T. He, Y. J. Yu, and M. Y. Chen, "Least-squares calibration method for fringe projection profilometry," Opt. Eng. 44, 033603 (2005).
[CrossRef]

Q. Y. Hu, P. S. Huang, Q. L. Fu, and F. P. Chiang, "Calibration of a 3-D shape measurement system," Opt. Eng. 42, 487-493 (2003).
[CrossRef]

Opt. Express (1)

Opt. Lasers Eng. (3)

Z. H. Zhang, D. P. Zhang, X. Peng, and X. T. Hu, "Performance analysis of a 3-D full-field sensor based on fringe projection," Opt. Lasers Eng. 42, 341-353 (2004).
[CrossRef]

C. E. Towers, D. P. Towers, and J. D. C. Jones, "Absolute fringe order calculation using optimized multifrequency selection in full-field profilometry," Opt. Lasers Eng. 43, 788-800 (2005).
[CrossRef]

D. Ganotra, J. Joseph, and K. Singh, "Object reconstruction in multilayer neural network based profilometry using grating structure comprising two regions with different spatial periods," Opt. Lasers Eng. 42, 179-192 (2004).
[CrossRef]

Opt. Lett. (1)

Proc. SPIE (1)

G. K. Knopf and J. Kofman, "Neural network mapping of image-to-object coordinates for 3-D shape reconstruction," Proc. SPIE 2904, 129-137 (1996).
[CrossRef]

Qual. Eng. (1)

J. Mutsch and B. Breuckmann, "Qualitätskontrolle von Blechteilen mittels topometrischer 3D-Mess- und Prüftechnik," Qual. Eng. 4, 18-19 (2005).

Other (2)

K. Creath, "Phase measurement interferometry techniques," in Progress in Optics, E. Wolf, ed. (North-Holland, 1988), Vol. 26.
[CrossRef]

G. Rodger, D. Flack, and M. McCarthy, A review of industrial capabilities to measure free-form surfaces, Report DEPC-EM 014, p. 22 (National Physical Laboratory, 2007).

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Figures (9)

Fig. 1
Fig. 1

Schematic of the 3D imaging system.

Fig. 2
Fig. 2

Plan view of the relationship between fringe projector with the digital micromirror device along AN, CCD camera chip plane, and the reference.

Fig. 3
Fig. 3

Schematic illustration for measuring N / u .

Fig. 4
Fig. 4

Geometry of the imaging system (2D) for deriving the relation between phase and depth.

Fig. 5
Fig. 5

Measured depth by use of uneven and even fringe projection for the middle row with the plate positioned at z = 5   mm . X axis represents the pixel positions along row direction with a range 1 , 2 , 3 , … ,  1024 ; the vertical axis is the depth of the surface in millimeters.

Fig. 6
Fig. 6

(Color online) Illustration of the designed and measured distances between steps of the NPL standard step. (a) Design dimensions and (b) measured distances with respect to datum B.

Fig. 7
Fig. 7

Wrapped phase maps and a section of the phase profiles from the measured objects. Projected fringe numbers are (a) 100, (b) 99, (c) 90, and (d) their profiles from columns 462 to 562 along row 580.

Fig. 8
Fig. 8

Obtained absolute phase map of the measured objects by using the optimum three-frequency selection method.

Fig. 9
Fig. 9

(Color online) Three-dimensional representation of the captured objects from a single view by gradient shading.

Tables (2)

Tables Icon

Table 1 Calibration Results for Depth with Even and Uneven Fringe Projection

Tables Icon

Table 2 Comparison of Measurement Results with Designed and NPL CMM Data (mm)

Equations (8)

Equations on this page are rendered with MathJax. Learn more.

P A C = A C B Q P I ,
B Q = u E p C A C .
P n = n B Q P I .
P n = P I ( cos α n / u sin α ) .
N / u = ( d 2 d 1 ) / l .
D F L = Δ z L 0 Δ z ,
Δ z = Δ ϕ P 0 L 0 2 π L + Δ ϕ P 0 = L 0 / ( 1 + 2 π L Δ ϕ P 0 ) .
P A = ( cos α n ( 1 + k r 2 ) sin α / u ) P I .

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