Abstract

A novel, to our knowledge, approach to light-stripe triangulation configuration that allows for parallel, fast, real-time three-dimensional surface topography with an extremely large number of optically resolved depth steps is presented, analyzed, and experimentally demonstrated. The method is based on a color-coding and decoding arrangement that exploits polychromatic illumination and axially dispersing optical elements. This leads to an increase of the depth-measuring range without any decrease in the axial or the lateral resolution. Our experiments yield three-dimensional surface measurements with lateral and depth optical resolutions of <40 nm, for a depth of focus of 48 mm, resulting in 1.2 × 106 resolving depth steps.

© 2001 Optical Society of America

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References

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  1. T. Asakura, ed., International Trends in Optics and Photonics ICO IV: Part VI, Optical Metrology, Vol. 74 of Springer Series in Optical Sciences (Springer, New York, 1999), pp. 281–355.
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

1999 (2)

1994 (2)

D. W. Manthey, K. N. Knapp, D. Lee, “Calibration of a laser range-finding coordinate-measuring machine,” Opt. Eng. 33, 3372–3380 (1994).
[CrossRef]

R. G. Dorsch, G. Häusler, J. M. Herrmann, “Laser triangulation: fundamental uncertainty in distance measurement,” Appl. Opt. 33, 1306–1314 (1994).
[CrossRef] [PubMed]

1993 (1)

D. Mendlovic, “Three-dimensional imaging sensing based on a zone-plate array,” Opt. Commun. 95, 26–32 (1993).
[CrossRef]

1992 (3)

N. Davidson, A. A. Friesem, E. Hasman, “Efficient formation of non-diffracting beams with uniform intensity along the propagation direction,” Opt. Commun. 88, 326–330 (1992).
[CrossRef]

N. Davidson, R. Duer, A. A. Friesem, E. Hasman, “Blazed holographic gratings for polychromatic and multidirectional incidence light,” J. Opt. Soc. Am. A 9, 1196–1199 (1992).
[CrossRef]

E. Hasman, N. Davidson, A. A. Friesem, “Multifunctional holographic elements for surface measurements,” Opt. Eng. 31, 363–368 (1992).
[CrossRef]

1991 (4)

1989 (1)

1988 (1)

1987 (2)

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

J. A. Cox, “Point-source location using hexagonal arrays,” Opt. Eng. 26, 69–74 (1987).

1985 (1)

G. Bickel, G. Häusler, M. Maul, “Triangulation with expended range of depth,” Opt. Eng. 24, 975–977 (1985).

1984 (1)

Baribeau, R.

Bickel, G.

G. Bickel, G. Häusler, M. Maul, “Triangulation with expended range of depth,” Opt. Eng. 24, 975–977 (1985).

Cox, J. A.

J. A. Cox, “Point-source location using hexagonal arrays,” Opt. Eng. 26, 69–74 (1987).

Davidson, N.

Dorsch, R. G.

Duer, R.

Durnin, J.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Eberly, J. H.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Friberg, A. T.

Friesem, A. A.

Hasman, E.

Häusler, G.

Heckel, W.

Herrmann, J. M.

Keren, S.

Knapp, K. N.

D. W. Manthey, K. N. Knapp, D. Lee, “Calibration of a laser range-finding coordinate-measuring machine,” Opt. Eng. 33, 3372–3380 (1994).
[CrossRef]

Lee, C. H.

Lee, D.

D. W. Manthey, K. N. Knapp, D. Lee, “Calibration of a laser range-finding coordinate-measuring machine,” Opt. Eng. 33, 3372–3380 (1994).
[CrossRef]

Manthey, D. W.

D. W. Manthey, K. N. Knapp, D. Lee, “Calibration of a laser range-finding coordinate-measuring machine,” Opt. Eng. 33, 3372–3380 (1994).
[CrossRef]

Maul, M.

G. Bickel, G. Häusler, M. Maul, “Triangulation with expended range of depth,” Opt. Eng. 24, 975–977 (1985).

Mendlovic, D.

D. Mendlovic, “Three-dimensional imaging sensing based on a zone-plate array,” Opt. Commun. 95, 26–32 (1993).
[CrossRef]

Miceli, J. J.

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Rioux, M.

Tsai, C. W.

Turunen, J.

Vasara, A.

Wang, J.

Appl. Opt. (5)

J. Opt. Soc. Am. A (2)

Opt. Commun. (2)

D. Mendlovic, “Three-dimensional imaging sensing based on a zone-plate array,” Opt. Commun. 95, 26–32 (1993).
[CrossRef]

N. Davidson, A. A. Friesem, E. Hasman, “Efficient formation of non-diffracting beams with uniform intensity along the propagation direction,” Opt. Commun. 88, 326–330 (1992).
[CrossRef]

Opt. Eng. (4)

G. Bickel, G. Häusler, M. Maul, “Triangulation with expended range of depth,” Opt. Eng. 24, 975–977 (1985).

D. W. Manthey, K. N. Knapp, D. Lee, “Calibration of a laser range-finding coordinate-measuring machine,” Opt. Eng. 33, 3372–3380 (1994).
[CrossRef]

J. A. Cox, “Point-source location using hexagonal arrays,” Opt. Eng. 26, 69–74 (1987).

E. Hasman, N. Davidson, A. A. Friesem, “Multifunctional holographic elements for surface measurements,” Opt. Eng. 31, 363–368 (1992).
[CrossRef]

Opt. Lett. (4)

Phys. Rev. Lett. (1)

J. Durnin, J. J. Miceli, J. H. Eberly, “Diffraction-free beams,” Phys. Rev. Lett. 58, 1499–1501 (1987).
[CrossRef] [PubMed]

Other (1)

T. Asakura, ed., International Trends in Optics and Photonics ICO IV: Part VI, Optical Metrology, Vol. 74 of Springer Series in Optical Sciences (Springer, New York, 1999), pp. 281–355.

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Figures (8)

Fig. 1
Fig. 1

Color-coded light-stripe triangulation system.

Fig. 2
Fig. 2

ADO; hybrid diffractive–refractive optical element.

Fig. 3
Fig. 3

Measured and calculated dispersion of the cylindrical lenses (λ0 = 529 nm); refractive lens, measured (crosses) and calculated (dotted–dashed curve); diffractive lens, measured (pluses) and calculated (dashed curve); combined diffractive–refractive lens, measured (circles) and calculated (solid curve).

Fig. 4
Fig. 4

Measured (crosses) and calculated (solid curve) diffraction efficiency of the DOE as a function of the wavelength.

Fig. 5
Fig. 5

Measured sections of the imaged light-intensity distributions of the intersection between the rainbow light sheet and a flat object: (a) without VWF and (b) with VWF.

Fig. 6
Fig. 6

Intensity cross sections at three positions along the focal range, without the VWF: (a) measured and (b) calculated. Dashed curve, z = 299 mm; solid curve, z = 323 mm; dotted–dashed curve, z = 347 mm.

Fig. 7
Fig. 7

Measured (dots) and calculated (solid curves) intensity cross sections at three positions along the focal range for (a) z = 299 mm, (b) z = 323 mm, (c) z = 347 mm.

Fig. 8
Fig. 8

Section of a measured profile of a flat object (pluses). Also shown is the expected linear object (dashed curve).

Equations (16)

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

δF=κΔx2/λ0,
tx=expiϕx=exp-i πx2λ0f0,
fdλ=f0λ0/λ.
ΔF=Δz=f0Δλ/λo,
ΔFF0f0F0Δλλ0,
Mo=ΔFδFΔλλ0D24λ0f0=Δλλ0 NDOE,
NDOEλ0δλDL,
Mf=Δλδλf,
δz=δximgsin θ,
NRD=ΔFδz=MoδFδz.
nλ=b1λ2λ2-c1+b2λ2λ2-c2+b3λ2λ2-c3,
frλ=frλ0nλ0-1nλ-1.
Fλ=fdλfrλ-dfrλ+fdλ-d.
η1=sinπNπN2 sinπλd-λλN sinπNλd-λλ2,
Ix0, z , λ=1λz2expiϕLx1, λ×expi πλzx0-x12dx12,
Ipxo, z=SλRVWFλIx0, z, λdλ,

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