Abstract

We report a method for 3-D sensing by light sectioning. The specific goal is to demonstrate that high resolution and large depth can be achieved simultaneously, thus overcoming the major limitation of conventional light sectioning. We use the diffraction pattern of an axicon to generate a light knife with large depth of field (for example, 1700 mm) and high lateral resolution (for example, 55 μm). Illuminating an object with this light knife creates a profile on the object. We detect this profile with a CCD TV camera and evaluate the centroid of the profile by means of an interpolation algorithm.

© 1988 Optical Society of America

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References

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  1. G. Schmaltz, Technische Oberflächenkunde (Springer-Verlag, Berlin, 1936), p. 73.
  2. G. Bickel, G. Häusler, M. Maul, “Triangulation with Expanded Range of Depth,” Opt. Eng. 24, 975 (1985).
    [CrossRef]
  3. W. Dremel, G. Häusler, M. Maul, “Triangulation with Large Dynamical Range,” Proc. Soc. Photo-Opt. Instrum. Eng. 665, 182 (1986).
  4. J. H. McLeod, “Axicon: A New Type of Optical Element,” J. Opt. Soc. Am. 44, 592 (1954).
    [CrossRef]
  5. J. H. McLeod, “Axicons and Their Uses,” J. Opt. Soc. Am. 50, 166 (1960).
    [CrossRef]
  6. C. W. McCutchen, “Generalized Aperture and Three Dimensional Diffraction Images,” J. Opt. Soc. Am. 54, 240 (1964).
    [CrossRef]
  7. W. H. Steel, “Axicons with Spherical Surfaces,” in Optics in Metrology, X. Mollet, Ed. (Pergamon, London, 1960), p. 181.
  8. J. M. Burch, C. Forno, “The NPL Centrax—A New Lens for Photogrammetry,” Proc. Soc. Photo-Opt. Instrum. Eng. 399, 412 (1983).
  9. H. H. Barrett, W. Swindell, Radiological Imaging (Academic, New York, 1981), p. 384.
  10. A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).
  11. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980), p. 1147.
  12. M. T. Gale, P. Seitz, “High Resolution Optical Metrology and Edge Detection Using a PC-Controlled Smart CCD Camera,” Proc. Soc. Photo-Opt. Instrum. Eng. 701, 254 (1986).
  13. F. Buechli, E. Heeb, K. Knop, “Low Cost Smart Camera,” Proc. Soc. Photo-Opt. Instrum. Eng. 595, 278 (1985).
  14. I. A. Mikhaltsova, V. I. Nalivaiko, I. S. Soldatenkov, “Kinoform Axicons,” Optik 67, 267 (1984).

1986 (2)

W. Dremel, G. Häusler, M. Maul, “Triangulation with Large Dynamical Range,” Proc. Soc. Photo-Opt. Instrum. Eng. 665, 182 (1986).

M. T. Gale, P. Seitz, “High Resolution Optical Metrology and Edge Detection Using a PC-Controlled Smart CCD Camera,” Proc. Soc. Photo-Opt. Instrum. Eng. 701, 254 (1986).

1985 (2)

F. Buechli, E. Heeb, K. Knop, “Low Cost Smart Camera,” Proc. Soc. Photo-Opt. Instrum. Eng. 595, 278 (1985).

G. Bickel, G. Häusler, M. Maul, “Triangulation with Expanded Range of Depth,” Opt. Eng. 24, 975 (1985).
[CrossRef]

1984 (1)

I. A. Mikhaltsova, V. I. Nalivaiko, I. S. Soldatenkov, “Kinoform Axicons,” Optik 67, 267 (1984).

1983 (1)

J. M. Burch, C. Forno, “The NPL Centrax—A New Lens for Photogrammetry,” Proc. Soc. Photo-Opt. Instrum. Eng. 399, 412 (1983).

1964 (1)

1960 (1)

1954 (1)

Barrett, H. H.

H. H. Barrett, W. Swindell, Radiological Imaging (Academic, New York, 1981), p. 384.

Bickel, G.

G. Bickel, G. Häusler, M. Maul, “Triangulation with Expanded Range of Depth,” Opt. Eng. 24, 975 (1985).
[CrossRef]

Buechli, F.

F. Buechli, E. Heeb, K. Knop, “Low Cost Smart Camera,” Proc. Soc. Photo-Opt. Instrum. Eng. 595, 278 (1985).

Burch, J. M.

J. M. Burch, C. Forno, “The NPL Centrax—A New Lens for Photogrammetry,” Proc. Soc. Photo-Opt. Instrum. Eng. 399, 412 (1983).

Dremel, W.

W. Dremel, G. Häusler, M. Maul, “Triangulation with Large Dynamical Range,” Proc. Soc. Photo-Opt. Instrum. Eng. 665, 182 (1986).

Forno, C.

J. M. Burch, C. Forno, “The NPL Centrax—A New Lens for Photogrammetry,” Proc. Soc. Photo-Opt. Instrum. Eng. 399, 412 (1983).

Gale, M. T.

M. T. Gale, P. Seitz, “High Resolution Optical Metrology and Edge Detection Using a PC-Controlled Smart CCD Camera,” Proc. Soc. Photo-Opt. Instrum. Eng. 701, 254 (1986).

Gradshteyn, I. S.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980), p. 1147.

Häusler, G.

W. Dremel, G. Häusler, M. Maul, “Triangulation with Large Dynamical Range,” Proc. Soc. Photo-Opt. Instrum. Eng. 665, 182 (1986).

G. Bickel, G. Häusler, M. Maul, “Triangulation with Expanded Range of Depth,” Opt. Eng. 24, 975 (1985).
[CrossRef]

Heeb, E.

F. Buechli, E. Heeb, K. Knop, “Low Cost Smart Camera,” Proc. Soc. Photo-Opt. Instrum. Eng. 595, 278 (1985).

Knop, K.

F. Buechli, E. Heeb, K. Knop, “Low Cost Smart Camera,” Proc. Soc. Photo-Opt. Instrum. Eng. 595, 278 (1985).

Maul, M.

W. Dremel, G. Häusler, M. Maul, “Triangulation with Large Dynamical Range,” Proc. Soc. Photo-Opt. Instrum. Eng. 665, 182 (1986).

G. Bickel, G. Häusler, M. Maul, “Triangulation with Expanded Range of Depth,” Opt. Eng. 24, 975 (1985).
[CrossRef]

McCutchen, C. W.

McLeod, J. H.

Mikhaltsova, I. A.

I. A. Mikhaltsova, V. I. Nalivaiko, I. S. Soldatenkov, “Kinoform Axicons,” Optik 67, 267 (1984).

Nalivaiko, V. I.

I. A. Mikhaltsova, V. I. Nalivaiko, I. S. Soldatenkov, “Kinoform Axicons,” Optik 67, 267 (1984).

Papoulis, A.

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).

Ryzhik, I. M.

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980), p. 1147.

Schmaltz, G.

G. Schmaltz, Technische Oberflächenkunde (Springer-Verlag, Berlin, 1936), p. 73.

Seitz, P.

M. T. Gale, P. Seitz, “High Resolution Optical Metrology and Edge Detection Using a PC-Controlled Smart CCD Camera,” Proc. Soc. Photo-Opt. Instrum. Eng. 701, 254 (1986).

Soldatenkov, I. S.

I. A. Mikhaltsova, V. I. Nalivaiko, I. S. Soldatenkov, “Kinoform Axicons,” Optik 67, 267 (1984).

Steel, W. H.

W. H. Steel, “Axicons with Spherical Surfaces,” in Optics in Metrology, X. Mollet, Ed. (Pergamon, London, 1960), p. 181.

Swindell, W.

H. H. Barrett, W. Swindell, Radiological Imaging (Academic, New York, 1981), p. 384.

J. Opt. Soc. Am. (3)

Opt. Eng. (1)

G. Bickel, G. Häusler, M. Maul, “Triangulation with Expanded Range of Depth,” Opt. Eng. 24, 975 (1985).
[CrossRef]

Optik (1)

I. A. Mikhaltsova, V. I. Nalivaiko, I. S. Soldatenkov, “Kinoform Axicons,” Optik 67, 267 (1984).

Proc. Soc. Photo-Opt. Instrum. Eng. (4)

W. Dremel, G. Häusler, M. Maul, “Triangulation with Large Dynamical Range,” Proc. Soc. Photo-Opt. Instrum. Eng. 665, 182 (1986).

M. T. Gale, P. Seitz, “High Resolution Optical Metrology and Edge Detection Using a PC-Controlled Smart CCD Camera,” Proc. Soc. Photo-Opt. Instrum. Eng. 701, 254 (1986).

F. Buechli, E. Heeb, K. Knop, “Low Cost Smart Camera,” Proc. Soc. Photo-Opt. Instrum. Eng. 595, 278 (1985).

J. M. Burch, C. Forno, “The NPL Centrax—A New Lens for Photogrammetry,” Proc. Soc. Photo-Opt. Instrum. Eng. 399, 412 (1983).

Other (5)

H. H. Barrett, W. Swindell, Radiological Imaging (Academic, New York, 1981), p. 384.

A. Papoulis, Systems and Transforms with Applications in Optics (McGraw-Hill, New York, 1968).

I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series and Products (Academic, New York, 1980), p. 1147.

W. H. Steel, “Axicons with Spherical Surfaces,” in Optics in Metrology, X. Mollet, Ed. (Pergamon, London, 1960), p. 181.

G. Schmaltz, Technische Oberflächenkunde (Springer-Verlag, Berlin, 1936), p. 73.

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Figures (10)

Fig. 1
Fig. 1

Principle of conventional light sectioning.

Fig. 2
Fig. 2

Generation of light patterns with large depth of field: (a) light pencil by an axicon and (b) light knife by scanning axicon diffraction patterns.

Fig. 3
Fig. 3

Intensity cross section of a light knife generated with a large axicon (solid line). For comparison, a cross section of a light pencil is also shown (dashed line).

Fig. 4
Fig. 4

Cross section of an experimentally generated light knife (enlarged photograph). The width of the central lobe is 55 μm.

Fig. 5
Fig. 5

Cross section of a light knife generated with a small axicon. The contrast (maximum vs first minimum of the intensity) is larger than in Fig. 3 (where a larger axicon was used).

Fig. 6
Fig. 6

Contrast of the light knife vs radial extension of the axicon pattern. The latter is measured by the number of Bessel rings contained within the pattern.

Fig. 7
Fig. 7

Principle of light sectioning with large depth and high resolution.

Fig. 8
Fig. 8

How to avoid focusing problems in the imaging step: Scheimpflug condition.

Fig. 9
Fig. 9

Experimental results: (a) profile of an object step of 1.4-mm height and (b) computer evaluation of the profile in (a).

Fig. 10
Fig. 10

Shape of the object is evident after the evaluation of several profiles.

Equations (12)

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Δ z = 4 δ x 2 / λ             ( λ = wavelength ) .
I ( y ) = - + J 0 2 ( a r ) · circ ( 2 r / R ) d x ,
circ ( r / R ) = { 1 if r < R 0 if r > R and r = x 2 + y 2 .
a = 2 π λ · ( n - 1 ) · tan α .
- + J 0 2 ( a r ) · exp [ - 2 π i ( ν x + μ y ] d x d y ν = 0 = 2 μ · 2 4 a 2 - μ 2 .
I ( y ) = 1 π · y * J 0 ( 2 a y ) .
Δ z = R ( n - 1 ) · α .
δ x = 2.40 a = 2.40 · λ 2 π · ( n - 1 ) · tan α .
Δ z = 2 π 2.40 · λ · R · δ x .
δ z = δ x c tan θ ,
δ z = Δ x N · S · tan θ ,
Δ z N · S · δ z .

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