Abstract

An endoscope is used in pulsed digital holography to simultaneously evaluate in-plane and out- of-plane transient and harmonic displacements on a flat metallic plate. The plate is illuminated from two different directions. The optical path for each illumination direction is matched to its corresponding reference beam, but also in such a way that each object–reference beam pair optical path is mismatched such that they are incoherent and can be stored in a single CCD frame. As is typical in these types of interferometric arrangement, two digital holograms are needed to compare two different states of the plate. Each hologram is Fourier transformed and due to the incoherence introduced, two separate spectra are readily identified, each belonging to an object–reference beam pair. On comparing by subtraction the phase obtained from the two pulsed digital holograms, it is possible to gather quantitative in-plane and out-of- plane results from transient and harmonic displacements.

© 2006 Optical Society of America

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References

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  1. D. Hadbawnik, "Holographische endoskopie," Optik 45, 21-38 (1976).
  2. H. I. Bjelkhagen, M. D. Friedman, and M. Epstein, "Holographic high resolution endoscopy through optical fiber," Proc. Laser Inst. Am. 64, 94-103 (1988).
  3. M. Yonemura, T. Nishisaka, and H. Machida, "Endoscopic hologram interferometry using fiber optics," Appl. Opt. 20, 1664-1667 (1981).
    [CrossRef] [PubMed]
  4. B. Kemper, D. Dirksen, W. Avenhaus, A. Merker, and G. Von Bally, "Endoscopic double-pulse electronic-speckle-pattern interferometer for technical and medical intracavity inspection," Appl. Opt. 39, 3899-3905 (2000).
    [CrossRef]
  5. G. Pedrini, S. Schedin, I. Alexeenko, and H. J. Tiziani, "Use of endoscopes in pulsed digital holographic interferometry," in Optical Measurement Systems for Industrial Inspection II: Applications in Production Engineering, P. Hoefling, W. P. O. Jueptner, and M. Kujawinska, eds., Proc. SPIE 4399, 1-8 (2001).
    [CrossRef]
  6. O. Coquoz, R. Conde, R. Taleblou, and C. Depeursinge, "Performance of endoscopy holography with a multicore optical fiber," Appl. Opt. 34, 7186-7193 (1995).
    [CrossRef] [PubMed]
  7. G. Pedrini, H. J. Tiziani, and Yunlu Zou, "Digital double pulse-TV-holography," Opt. Laser Eng. 26, 199-219 (1997).
    [CrossRef]
  8. G. Pedrini and H. J. Tiziani, "Quantitative evaluation of two-dimensional dynamic deformation using digital holography," Opt. Laser Eng. 29, 249-256 (1997).
    [CrossRef]

2001

G. Pedrini, S. Schedin, I. Alexeenko, and H. J. Tiziani, "Use of endoscopes in pulsed digital holographic interferometry," in Optical Measurement Systems for Industrial Inspection II: Applications in Production Engineering, P. Hoefling, W. P. O. Jueptner, and M. Kujawinska, eds., Proc. SPIE 4399, 1-8 (2001).
[CrossRef]

2000

1997

G. Pedrini, H. J. Tiziani, and Yunlu Zou, "Digital double pulse-TV-holography," Opt. Laser Eng. 26, 199-219 (1997).
[CrossRef]

G. Pedrini and H. J. Tiziani, "Quantitative evaluation of two-dimensional dynamic deformation using digital holography," Opt. Laser Eng. 29, 249-256 (1997).
[CrossRef]

1995

1988

H. I. Bjelkhagen, M. D. Friedman, and M. Epstein, "Holographic high resolution endoscopy through optical fiber," Proc. Laser Inst. Am. 64, 94-103 (1988).

1981

1976

D. Hadbawnik, "Holographische endoskopie," Optik 45, 21-38 (1976).

Alexeenko, I.

G. Pedrini, S. Schedin, I. Alexeenko, and H. J. Tiziani, "Use of endoscopes in pulsed digital holographic interferometry," in Optical Measurement Systems for Industrial Inspection II: Applications in Production Engineering, P. Hoefling, W. P. O. Jueptner, and M. Kujawinska, eds., Proc. SPIE 4399, 1-8 (2001).
[CrossRef]

Avenhaus, W.

Bjelkhagen, H. I.

H. I. Bjelkhagen, M. D. Friedman, and M. Epstein, "Holographic high resolution endoscopy through optical fiber," Proc. Laser Inst. Am. 64, 94-103 (1988).

Conde, R.

Coquoz, O.

Depeursinge, C.

Dirksen, D.

Epstein, M.

H. I. Bjelkhagen, M. D. Friedman, and M. Epstein, "Holographic high resolution endoscopy through optical fiber," Proc. Laser Inst. Am. 64, 94-103 (1988).

Friedman, M. D.

H. I. Bjelkhagen, M. D. Friedman, and M. Epstein, "Holographic high resolution endoscopy through optical fiber," Proc. Laser Inst. Am. 64, 94-103 (1988).

Hadbawnik, D.

D. Hadbawnik, "Holographische endoskopie," Optik 45, 21-38 (1976).

Hoefling, P.

G. Pedrini, S. Schedin, I. Alexeenko, and H. J. Tiziani, "Use of endoscopes in pulsed digital holographic interferometry," in Optical Measurement Systems for Industrial Inspection II: Applications in Production Engineering, P. Hoefling, W. P. O. Jueptner, and M. Kujawinska, eds., Proc. SPIE 4399, 1-8 (2001).
[CrossRef]

Jueptner, W. P. O.

G. Pedrini, S. Schedin, I. Alexeenko, and H. J. Tiziani, "Use of endoscopes in pulsed digital holographic interferometry," in Optical Measurement Systems for Industrial Inspection II: Applications in Production Engineering, P. Hoefling, W. P. O. Jueptner, and M. Kujawinska, eds., Proc. SPIE 4399, 1-8 (2001).
[CrossRef]

Kemper, B.

Kujawinska, M.

G. Pedrini, S. Schedin, I. Alexeenko, and H. J. Tiziani, "Use of endoscopes in pulsed digital holographic interferometry," in Optical Measurement Systems for Industrial Inspection II: Applications in Production Engineering, P. Hoefling, W. P. O. Jueptner, and M. Kujawinska, eds., Proc. SPIE 4399, 1-8 (2001).
[CrossRef]

Machida, H.

Merker, A.

Nishisaka, T.

Pedrini, G.

G. Pedrini, S. Schedin, I. Alexeenko, and H. J. Tiziani, "Use of endoscopes in pulsed digital holographic interferometry," in Optical Measurement Systems for Industrial Inspection II: Applications in Production Engineering, P. Hoefling, W. P. O. Jueptner, and M. Kujawinska, eds., Proc. SPIE 4399, 1-8 (2001).
[CrossRef]

G. Pedrini, H. J. Tiziani, and Yunlu Zou, "Digital double pulse-TV-holography," Opt. Laser Eng. 26, 199-219 (1997).
[CrossRef]

G. Pedrini and H. J. Tiziani, "Quantitative evaluation of two-dimensional dynamic deformation using digital holography," Opt. Laser Eng. 29, 249-256 (1997).
[CrossRef]

Schedin, S.

G. Pedrini, S. Schedin, I. Alexeenko, and H. J. Tiziani, "Use of endoscopes in pulsed digital holographic interferometry," in Optical Measurement Systems for Industrial Inspection II: Applications in Production Engineering, P. Hoefling, W. P. O. Jueptner, and M. Kujawinska, eds., Proc. SPIE 4399, 1-8 (2001).
[CrossRef]

Taleblou, R.

Tiziani, H. J.

G. Pedrini, S. Schedin, I. Alexeenko, and H. J. Tiziani, "Use of endoscopes in pulsed digital holographic interferometry," in Optical Measurement Systems for Industrial Inspection II: Applications in Production Engineering, P. Hoefling, W. P. O. Jueptner, and M. Kujawinska, eds., Proc. SPIE 4399, 1-8 (2001).
[CrossRef]

G. Pedrini, H. J. Tiziani, and Yunlu Zou, "Digital double pulse-TV-holography," Opt. Laser Eng. 26, 199-219 (1997).
[CrossRef]

G. Pedrini and H. J. Tiziani, "Quantitative evaluation of two-dimensional dynamic deformation using digital holography," Opt. Laser Eng. 29, 249-256 (1997).
[CrossRef]

Von Bally, G.

Yonemura, M.

Zou, Yunlu

G. Pedrini, H. J. Tiziani, and Yunlu Zou, "Digital double pulse-TV-holography," Opt. Laser Eng. 26, 199-219 (1997).
[CrossRef]

Appl. Opt.

Opt. Laser Eng.

G. Pedrini, H. J. Tiziani, and Yunlu Zou, "Digital double pulse-TV-holography," Opt. Laser Eng. 26, 199-219 (1997).
[CrossRef]

G. Pedrini and H. J. Tiziani, "Quantitative evaluation of two-dimensional dynamic deformation using digital holography," Opt. Laser Eng. 29, 249-256 (1997).
[CrossRef]

Optik

D. Hadbawnik, "Holographische endoskopie," Optik 45, 21-38 (1976).

Proc. Laser Inst. Am.

H. I. Bjelkhagen, M. D. Friedman, and M. Epstein, "Holographic high resolution endoscopy through optical fiber," Proc. Laser Inst. Am. 64, 94-103 (1988).

Proc. SPIE

G. Pedrini, S. Schedin, I. Alexeenko, and H. J. Tiziani, "Use of endoscopes in pulsed digital holographic interferometry," in Optical Measurement Systems for Industrial Inspection II: Applications in Production Engineering, P. Hoefling, W. P. O. Jueptner, and M. Kujawinska, eds., Proc. SPIE 4399, 1-8 (2001).
[CrossRef]

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Figures (8)

Fig. 1
Fig. 1

Experimental setup for in-plane and out-of-plane pulsed digital holographic endoscopy with simultaneous recording of two digital holograms corresponding to illumination directions n ^ 1 and n ^ 2 . BS, beam splitters; CB, cube beam splitters; M, mirrors; O1, O2, illumination beams; R1, R2 reference beams.

Fig. 2
Fig. 2

Fourier spectrum of the simultaneous pulsed digital hologram consisting of two incoherently added interference patterns.

Fig. 3
Fig. 3

(a) and (b) Wrapped phase maps for the two illumination directions, η1 and η2, respectively. The pulse separation was 80 μs.

Fig. 4
Fig. 4

(a) and (b) x and z displacement maps from Figs. 3(a) and 3(b), respectively. (c) The vector resultant of the x and z displacements along the line shown.

Fig. 5
Fig. 5

Distribution of the displacement vector resultant x and z on the xz plane.

Fig. 6
Fig. 6

(a) and (b) Wrapped phase maps for the two illumination directions, η1 and η2, respectively. The pulse separation was 80 μs.

Fig. 7
Fig. 7

(s) and (b) x and z displacement maps from Figs. 6(a) and 6(b), respectively. (c) The vector resultant of the x and z displacements along the line shown.

Fig. 8
Fig. 8

Distribution of the displacement vector resultant x and z on the xz plane.

Equations (66)

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I ( ξ , η ) = k = 1 2 I k ( ξ , η ) = k = 1 2 [ | R k ( ξ , η ) + U k ( ξ , η ) | 2 ] ,
U k ( ξ , η ) = u k ( ξ , η ) exp [ i ϕ k ( ξ , η ) ] ,
R k ( ξ , η ) = r k ( ξ , η ) exp 2 π i ( f k ξ ξ + f k η η ) ,
f k ξ
f k η
I ( ξ , η ) = k = 1 2 { a k ( ξ , η ) + c k ( ξ , η ) exp 2 π i ( f k ξ ξ + f k η η ) + c k * ( ξ , η ) exp [ 2 π i ( f k ξ ξ + f k η η ) ] } ,
a k ( ξ , η ) = u k     2 ( ξ , η ) + r k     2 ( ξ , η ) ,
c k ( ξ , η ) = u k ( ξ , η ) r k ( ξ , η ) exp [ i ϕ k ( ξ , η ) ] .
f k ξ
f k η
ϕ k ( ξ , η )
F T { I } = k = 1 2 [ A k ( f ξ , f n ) + C k ( f ξ f k ξ , f n f k n ) + C k * ( f ξ f k ξ , f n f k n ) ] ,
C k
C k *
ϕ k ( ξ , η )
C k
C k *
C k
C k *
( f k ξ , f k η ) = 0
ϕ k ( ξ , η ) = arctan Im [ C k ( ξ , η ) ] Re [ C k ( ξ , η ) ] , k = 1 , 2 .
t i = 0
t i = 0
ϕ k ( ξ , η )
t i
Δ ϕ k ( ξ , η ) = ϕ k ( ξ , η ) ϕ k ( ξ , η ) , k = 1 , 2 ,
Δ ϕ k = ( 2 π λ ) u s k ,
u
s k
s k = n ^ k n ^ o , k = 1 , 2 .
n ^ k
n ^ o
s ^ 1 = ( sin α , 0 , 1 + cos α ) ,     s ^ 2 = ( sin α , 0 , 1 + cos α ) .
α
( n ^ 1  and   n ^ 2 )
( n ^ o )
Δ ϕ k
u
s k
1024 × 1024
Δ x × Δ y = 9 μm 2
12   mm
2 5   mm
λ = 532   nm
5   cm
n ^ 1
n ^ 2
± α
n ^ o
t i
5   cm
2 .5   cm × 4 .0   cm
0 .5   mm
t i = 0
Δ ϕ k
n ^ 1
n ^ 2
12   mm
25   mm
Δ ϕ k
4   mm
12   mm
25   mm
2160   Hz
n ^ 1
n ^ 2

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