Abstract

A method for direct shape measurement with short laser light pulses and digital holography with a CCD array is proposed. An in-line holographic setup is used in which the reference beam is reflected from a blazed reflection grating, i.e., a Littrow setup. By this method a relatively large optical delay is created between the reference and the object beams even with a small object–reference angle, which is necessary because of the limited resolution of the CCD. The delay varies continuously across one axis of the CCD array. In this way different object sections are reconstructed from different parts of the CCD, which in turn correspond to a certain path length from the object. By putting the sections together, one can evaluate the three-dimensional shape. Theoretical as well as experimental results are presented.

© 1998 Optical Society of America

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References

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  1. N. Abramson, “Light-in-flight recording: high-speed holographic motion pictures of ultrafast phenomena,” Appl. Opt. 22, 215–231 (1983).
    [CrossRef] [PubMed]
  2. T. E. Carlsson, “Measurement of three-dimensional shapes using light-in-flight recording by holography,” Opt. Eng. 32, 2587–2592 (1993).
    [CrossRef]
  3. U. Schnars, W. P. O. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
    [CrossRef] [PubMed]
  4. U. Schnars, T. M. Kreis, W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. 35, 977–982 (1996).
    [CrossRef]
  5. J. Pomarico, U. Schnars, H.-J. Hartmann, W. Jüptner, “Digital recording and numerical reconstruction of holograms: a new method for displaying light in flight,” Appl. Opt. 34, 8095–8099 (1995).
    [CrossRef] [PubMed]
  6. S. Svanberg, “Atomic and molecular spectroscopy. Basic aspects and practical application,” Vol. 6 of Springer Series on Atoms and Plasmas (Springer-Verlag, Berlin, 1992), pp. 104–107, 215.
  7. T. M. Kreis, M. Adams, W. P. O. Jüptner, “Methods of digital holography: a comparison,” in Optical Inspection and Micromeasurements II, C. Gorick, ed., Proc. SPIE3098, 224–233 (1997).
    [CrossRef]
  8. Y. N. Denisyuk, D. I. Staselko, R. R. Herke, “On the effect of the time and spatial coherence of radiation source on the image produced by a hologram,” Nouv. Rev. Opt. Appl. 1, Suppl. 2, 4–5 (1970).
  9. T. M. Kreis, W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
    [CrossRef]
  10. T. E. Carlsson, “Holographic interferometry with ultra-short laser pulses,” in High-Speed Photography and Photonics: 21st International Congress, U. Kim, ed., Proc. SPIE2513, 392–402 (1995).
    [CrossRef]

1997 (1)

T. M. Kreis, W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

1996 (1)

U. Schnars, T. M. Kreis, W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. 35, 977–982 (1996).
[CrossRef]

1995 (1)

1994 (1)

1993 (1)

T. E. Carlsson, “Measurement of three-dimensional shapes using light-in-flight recording by holography,” Opt. Eng. 32, 2587–2592 (1993).
[CrossRef]

1983 (1)

1970 (1)

Y. N. Denisyuk, D. I. Staselko, R. R. Herke, “On the effect of the time and spatial coherence of radiation source on the image produced by a hologram,” Nouv. Rev. Opt. Appl. 1, Suppl. 2, 4–5 (1970).

Abramson, N.

Adams, M.

T. M. Kreis, M. Adams, W. P. O. Jüptner, “Methods of digital holography: a comparison,” in Optical Inspection and Micromeasurements II, C. Gorick, ed., Proc. SPIE3098, 224–233 (1997).
[CrossRef]

Carlsson, T. E.

T. E. Carlsson, “Measurement of three-dimensional shapes using light-in-flight recording by holography,” Opt. Eng. 32, 2587–2592 (1993).
[CrossRef]

T. E. Carlsson, “Holographic interferometry with ultra-short laser pulses,” in High-Speed Photography and Photonics: 21st International Congress, U. Kim, ed., Proc. SPIE2513, 392–402 (1995).
[CrossRef]

Denisyuk, Y. N.

Y. N. Denisyuk, D. I. Staselko, R. R. Herke, “On the effect of the time and spatial coherence of radiation source on the image produced by a hologram,” Nouv. Rev. Opt. Appl. 1, Suppl. 2, 4–5 (1970).

Hartmann, H.-J.

Herke, R. R.

Y. N. Denisyuk, D. I. Staselko, R. R. Herke, “On the effect of the time and spatial coherence of radiation source on the image produced by a hologram,” Nouv. Rev. Opt. Appl. 1, Suppl. 2, 4–5 (1970).

Jüptner, W.

Jüptner, W. P. O.

T. M. Kreis, W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

U. Schnars, T. M. Kreis, W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. 35, 977–982 (1996).
[CrossRef]

U. Schnars, W. P. O. Jüptner, “Direct recording of holograms by a CCD target and numerical reconstruction,” Appl. Opt. 33, 179–181 (1994).
[CrossRef] [PubMed]

T. M. Kreis, M. Adams, W. P. O. Jüptner, “Methods of digital holography: a comparison,” in Optical Inspection and Micromeasurements II, C. Gorick, ed., Proc. SPIE3098, 224–233 (1997).
[CrossRef]

Kreis, T. M.

T. M. Kreis, W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

U. Schnars, T. M. Kreis, W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. 35, 977–982 (1996).
[CrossRef]

T. M. Kreis, M. Adams, W. P. O. Jüptner, “Methods of digital holography: a comparison,” in Optical Inspection and Micromeasurements II, C. Gorick, ed., Proc. SPIE3098, 224–233 (1997).
[CrossRef]

Pomarico, J.

Schnars, U.

Staselko, D. I.

Y. N. Denisyuk, D. I. Staselko, R. R. Herke, “On the effect of the time and spatial coherence of radiation source on the image produced by a hologram,” Nouv. Rev. Opt. Appl. 1, Suppl. 2, 4–5 (1970).

Svanberg, S.

S. Svanberg, “Atomic and molecular spectroscopy. Basic aspects and practical application,” Vol. 6 of Springer Series on Atoms and Plasmas (Springer-Verlag, Berlin, 1992), pp. 104–107, 215.

Appl. Opt. (3)

Nouv. Rev. Opt. Appl. (1)

Y. N. Denisyuk, D. I. Staselko, R. R. Herke, “On the effect of the time and spatial coherence of radiation source on the image produced by a hologram,” Nouv. Rev. Opt. Appl. 1, Suppl. 2, 4–5 (1970).

Opt. Eng. (3)

T. M. Kreis, W. P. O. Jüptner, “Suppression of the dc term in digital holography,” Opt. Eng. 36, 2357–2360 (1997).
[CrossRef]

U. Schnars, T. M. Kreis, W. P. O. Jüptner, “Digital recording and numerical reconstruction of holograms: reduction of the spatial frequency spectrum,” Opt. Eng. 35, 977–982 (1996).
[CrossRef]

T. E. Carlsson, “Measurement of three-dimensional shapes using light-in-flight recording by holography,” Opt. Eng. 32, 2587–2592 (1993).
[CrossRef]

Other (3)

T. E. Carlsson, “Holographic interferometry with ultra-short laser pulses,” in High-Speed Photography and Photonics: 21st International Congress, U. Kim, ed., Proc. SPIE2513, 392–402 (1995).
[CrossRef]

S. Svanberg, “Atomic and molecular spectroscopy. Basic aspects and practical application,” Vol. 6 of Springer Series on Atoms and Plasmas (Springer-Verlag, Berlin, 1992), pp. 104–107, 215.

T. M. Kreis, M. Adams, W. P. O. Jüptner, “Methods of digital holography: a comparison,” in Optical Inspection and Micromeasurements II, C. Gorick, ed., Proc. SPIE3098, 224–233 (1997).
[CrossRef]

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Figures (5)

Fig. 1
Fig. 1

Principal setup. The reference beam is reflected from a blazed reflection grating that tilts the pulse front and makes the path length vary across the x axis of the CCD sensor.

Fig. 2
Fig. 2

Intersection between the object and the reference pulse front.

Fig. 3
Fig. 3

Recorded object.

Fig. 4
Fig. 4

Images reconstructed from the hologram are shown for different positions of the reference wave. The hologram of every 0.6 mm of a screw head is shown. Initially only intersections of the screw head are visible, and finally the bottom of the hole in the screw head is visible.

Fig. 5
Fig. 5

3-D plot of the screw head.

Equations (20)

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dU O x ,   y = γ kr O - ω t r O   α O ξ ,   η exp i kr O - ω t d ξ d η , r O = z 2 + x - ξ 2 + y - η 2 1 / 2 ,
U R x ,   y = γ kr R - ω t α R   exp i ϕ - ω t , r R = 2 x - m x tan   β + 2 z R ,
dI x ,   y = U R + dU O × U R + dU O * = U R 2 + dU O 2 + U R dU O * + U R * dU O ,
dE H x ,   y = τ C   dI H x ,   y d t = τ C   U R * dU O d t = τ C   α R   exp - i ϕ - ω t γ kr R - ω t × γ kr O - ω t r O   α ξ ,   η × exp i kr O - ω t d ξ d η d t = α R   exp - i ϕ r O   Γ Δ r α ξ ,   η exp ikr O d ξ d η ,
r O = z 2 + x - ξ 2 + y - η 2 1 / 2 z + x - ξ 2 + y - η 2 2 z = z + x 2 + y 2 2 z + ξ 2 + η 2 2 z - x ξ + y η z .
E H x ,   y = A O   dE H = A O α R   exp - i ϕ r O   Γ Δ r α ξ ,   η × exp ikr O d ξ d η 1 r O   α R   exp i z - ϕ exp ik x 2 + y 2 2 z ×   A O   Γ Δ r α ξ ,   η exp ik ξ 2 + η 2 2 z × exp ik x ξ + y η z d ξ d η ,
I E x ,   y = U E E H = 1 k 2   α R z   exp i z - ϕ exp ik x 2 + y 2 2 z × A O   Γ Δ r α ω ξ ,   ω η exp i   z 2 k ω ξ 2 + ω η 2 × exp - i ω ξ x + ω η y d ω ξ d ω η ,
I E x ,   y = α R z   exp i z - ϕ exp i   k 2 z x 2 + y 2 k 2 × Γ Δ r α ω ξ ,   ω η × exp i   z 2 k ω ξ 2 + ω η 2 , Γ Δ r α ω ξ ,   ω η = k 2 exp i ϕ - z exp i   z 2 k ω ξ 2 + ω η 2 α R z × - 1 I E x ,   y exp - i   k 2 z x 2 + y 2 ,
U E x ,   x E = exp - x - x E 2 2 Λ 2 ,
Δ r = r R - r O = 0     r O = 2 x E - m x tan   β + 2 z R .
r O = R + z O = 2 x E - m x tan   β + 2 z R x O = x E + R   sin   θ   cos   ϕ y O = y E + R   sin   θ   sin   ϕ   R = 2 x E - m x tan   β + 2 z R 1 + cos   θ z O = R   cos   θ sin   θ = x O - x E 2 + y O - y E 2 1 / 2 R .
B ω ξ ,   ω η ,   x E = - 1 exp - x - x E 2 2 Λ 2 E H x ,   y × exp - i   k 2 z x 2 + y 2 .
P ω ξ ,   ω η ,   τ = B ω ξ ,   ω η ,   x E B ω ξ ,   ω η ,   x E * ,
B ω ξ ,   ω η ,   x E = x - 1 exp - x - x E 2 2 Λ 2 exp - i   kx 2 2 z × y - 1 E H x ,   y exp - i   ky 2 2 z = x - 1 exp - x - x E 2 2 Λ 2 H x ,   ω η , H x ,   ω η = exp - i   kx 2 2 z y - 1 E H x ,   y exp - i   ky 2 2 z ,
max Δ x ,   Δ y < λ 4   sin θ / 2 λ 2 θ min λ z 2 d ,
Δ ξ = λ z N x Δ x ,   Δ η = λ z N y Δ y ,
Δ ξ = λ z N C Δ x 2 λ z   tan   β L C = λ z Λ ,
δ z = 2 Δ x   tan   β .
λ = 610 × 10 - 9   m Δ y = 8 × 10 - 6   m z = 0.64   m N y = 572     Δ η = 610 × 10 - 9 × 0.64 572 × 8 × 10 - 6 = 85.3   μ m , λ = 610 × 10 - 9   m Δ x = 8 × 10 - 6   m z = 0.64   m N τ = Λ Δ x = L C 2 Δ x   tan   β = 309     Δ ξ = 610 × 10 - 9 × 0.64 309 × 8 × 10 - 6 = 157   μ m .
Δ x = 8 × 10 - 6   m β = 22 °     δ z = 2   tan 22 ° × 8 × 10 - 6   m = 6.5   μ m .

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