Abstract

An optical system based on in-line digital holography for the evaluation of deformations is described. In-line holograms are recorded on a CCD chip. The problem of overlapping twin images typical for the in-line arrangement is solved by digital reconstruction and filtering of the unwanted wave fronts. Two separate interferograms of an object under test in its undeformed and deformed states are recorded each on a CCD chip. The phases of the two wave fronts are obtained from the complex amplitudes of the digital reconstructed wave fronts, and the deformation is calculated from the phase differences. Experimental results are presented.

© 1998 Optical Society of America

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References

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  1. C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).
  2. R. Jones, C. Wikes, Holographic and Speckle Interferometry, 2nd ed., Vol. 6 of Cambridge Studies in Modern Optics (Cambridge U. Press, Cambridge, 1989).
  3. G. Pedrini, H. Tiziani, Y. Zou, “Digital double-pulse TV-holography,” Opt. Laser Eng. 26, 199–219 (1997).
    [CrossRef]
  4. M. Takeda, I. Hideki, S. Kobayashi, “Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry,” J. Opt. Soc. Am. 72, 156–160 (1982).
    [CrossRef]
  5. U. Schnars, “Direct phase determination in hologram interferometry with use of digitally recorded holograms,” J. Opt. Soc. Am. A 11, 2011–2015 (1994).
    [CrossRef]
  6. G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital double-pulse holographic interferometry for vibration analysis,” J. Mod. Opt. 42, 367–374 (1995).
    [CrossRef]
  7. R. J. Collier, C. B. Burckhard, L. H. Lin, Optical Holography (Academic, New York, 1971).
  8. M. Adams, T. Kreis, W. Juptner, “Particle size and position measurement with digital holography,” in Optical Inspection and Measurements II, C. Gorecki, ed., Proc. SPIE3098, 234–240 (1997).
    [CrossRef]
  9. L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
    [CrossRef]

1997

G. Pedrini, H. Tiziani, Y. Zou, “Digital double-pulse TV-holography,” Opt. Laser Eng. 26, 199–219 (1997).
[CrossRef]

1995

G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital double-pulse holographic interferometry for vibration analysis,” J. Mod. Opt. 42, 367–374 (1995).
[CrossRef]

1994

1987

L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[CrossRef]

1982

Adams, M.

M. Adams, T. Kreis, W. Juptner, “Particle size and position measurement with digital holography,” in Optical Inspection and Measurements II, C. Gorecki, ed., Proc. SPIE3098, 234–240 (1997).
[CrossRef]

Burckhard, C. B.

R. J. Collier, C. B. Burckhard, L. H. Lin, Optical Holography (Academic, New York, 1971).

Collier, R. J.

R. J. Collier, C. B. Burckhard, L. H. Lin, Optical Holography (Academic, New York, 1971).

Hideki, I.

Jones, R.

R. Jones, C. Wikes, Holographic and Speckle Interferometry, 2nd ed., Vol. 6 of Cambridge Studies in Modern Optics (Cambridge U. Press, Cambridge, 1989).

Juptner, W.

M. Adams, T. Kreis, W. Juptner, “Particle size and position measurement with digital holography,” in Optical Inspection and Measurements II, C. Gorecki, ed., Proc. SPIE3098, 234–240 (1997).
[CrossRef]

Kobayashi, S.

Kreis, T.

M. Adams, T. Kreis, W. Juptner, “Particle size and position measurement with digital holography,” in Optical Inspection and Measurements II, C. Gorecki, ed., Proc. SPIE3098, 234–240 (1997).
[CrossRef]

Lin, L. H.

R. J. Collier, C. B. Burckhard, L. H. Lin, Optical Holography (Academic, New York, 1971).

Onural, L.

L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[CrossRef]

Pedrini, G.

G. Pedrini, H. Tiziani, Y. Zou, “Digital double-pulse TV-holography,” Opt. Laser Eng. 26, 199–219 (1997).
[CrossRef]

G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital double-pulse holographic interferometry for vibration analysis,” J. Mod. Opt. 42, 367–374 (1995).
[CrossRef]

Schnars, U.

Scott, P. D.

L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[CrossRef]

Takeda, M.

Tiziani, H.

G. Pedrini, H. Tiziani, Y. Zou, “Digital double-pulse TV-holography,” Opt. Laser Eng. 26, 199–219 (1997).
[CrossRef]

Tiziani, H. J.

G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital double-pulse holographic interferometry for vibration analysis,” J. Mod. Opt. 42, 367–374 (1995).
[CrossRef]

Vest, C. M.

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).

Wikes, C.

R. Jones, C. Wikes, Holographic and Speckle Interferometry, 2nd ed., Vol. 6 of Cambridge Studies in Modern Optics (Cambridge U. Press, Cambridge, 1989).

Zou, Y.

G. Pedrini, H. Tiziani, Y. Zou, “Digital double-pulse TV-holography,” Opt. Laser Eng. 26, 199–219 (1997).
[CrossRef]

Zou, Y. L.

G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital double-pulse holographic interferometry for vibration analysis,” J. Mod. Opt. 42, 367–374 (1995).
[CrossRef]

J. Mod. Opt.

G. Pedrini, Y. L. Zou, H. J. Tiziani, “Digital double-pulse holographic interferometry for vibration analysis,” J. Mod. Opt. 42, 367–374 (1995).
[CrossRef]

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Opt. Eng.

L. Onural, P. D. Scott, “Digital decoding of in-line holograms,” Opt. Eng. 26, 1124–1132 (1987).
[CrossRef]

Opt. Laser Eng.

G. Pedrini, H. Tiziani, Y. Zou, “Digital double-pulse TV-holography,” Opt. Laser Eng. 26, 199–219 (1997).
[CrossRef]

Other

R. J. Collier, C. B. Burckhard, L. H. Lin, Optical Holography (Academic, New York, 1971).

M. Adams, T. Kreis, W. Juptner, “Particle size and position measurement with digital holography,” in Optical Inspection and Measurements II, C. Gorecki, ed., Proc. SPIE3098, 234–240 (1997).
[CrossRef]

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).

R. Jones, C. Wikes, Holographic and Speckle Interferometry, 2nd ed., Vol. 6 of Cambridge Studies in Modern Optics (Cambridge U. Press, Cambridge, 1989).

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Figures (4)

Fig. 1
Fig. 1

Schematic of the experimental arrangements for in-line digital holographic interferometry. The reference beam is coupled into the interferometer by use of (a) fiber or (b) a beam splitter.

Fig. 2
Fig. 2

Method used for the suppression of the unwanted reconstruction: (a) digitally sampled in-line hologram recorded on a CCD, (b) absolute value of the Fourier transform of a hologram with a high-pass filter for the suppression of the dc term, (c) digital reconstruction of the image of the aperture, (d) filtering of the image to remove the noise, and (e) phase of the wave front.

Fig. 3
Fig. 3

Experimental results obtained by the deformation of a metallic plate: (a) Fringes obtained by subtraction the intensities of the two holograms. Phase maps obtained by (b) primary reconstruction and (c) conjugated reconstruction.

Fig. 4
Fig. 4

Plate vibrating with a frequency of 1295 Hz. (a) Digital reconstruction of the image of the aperture. (b) Phase maps obtained by primary reconstruction. (c) Phase maps obtained by conjugated reconstruction. (d) Pseudo 3-D representation of the deformation.

Equations (14)

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r x ,   y = A   exp i ϕ R ,     | r x ,   y | = A = const ,
u x ,   y = | u x ,   y | exp [ i ϕ x ,   y ] .
I = | r x ,   y | 2 + | u x ,   y | 2 + r x ,   y u * x ,   y + r * x ,   y u x ,   y
= A 2 + | u x ,   y | 2 + 2 A | u x ,   y | cos ϕ x ,   y - ϕ R ,
u x ,   y = B   exp -   π i λ x 2 + y 2 d - b ,
I x ,   y = A 2 + B 2 + 2 AB   cos π λ x 2 + y 2 d - b ,
π λ 1 d - b N x + 1 Δ 2 + N y + 1 Δ 2 - N x Δ 2 + N y Δ 2 < π ,
d - b 1 λ 2 N x + 2 N y + 2 Δ 2 .
H x ,   y = v x ,   y + Au * x ,   y + Au x ,   y ,
H 1 x ,   y = v x ,   y + w x ,   y + Au x ,   y .
ϕ x ,   y = arctan Im u x ,   y Re u x ,   y arctan Im H 1 x ,   y Re H 1 x ,   y .
H 2 x ,   y = v x ,   y + Au r * x ,   y .
ϕ r x ,   y = arctan Im u r * x ,   y Re u r * x ,   y arctan Im H 2 x ,   y Re H 2 x ,   y .
Δ ϕ u = 2 π λ ds ,

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