Abstract

A rigid endoscope and three different object illumination source positions are used in pulsed digital holography to measure the three orthogonal displacement components from hidden areas of a harmonically vibrating metallic cylinder. In order to obtain simultaneous 3D information from the optical set up, it is necessary to match the optical paths of each of the reference object beam pairs, but to incoherently mismatch the three reference object beam pairs, such that three pulsed digital holograms are incoherently recorded within a single frame of the CCD sensor. The phase difference is obtained using the Fourier method and by subtracting two digital holograms captured for two different object positions.

© 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 (1999).
    [CrossRef]
  5. G. Pedrini, S. Schedin, and H. J. Tiziani, "Use of endoscopes in pulsed digital holographic interferometry," in Optical Measurement System for Industrial Inspection II: Applications in productions Engineering, R. Holfling, W. Jupter 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. C. M. Vest, Holography Interferometry, (Wyle, New York, 1979).
  8. Staffan Schedin, G. Pedrini, H. J. Tiziani, and Fernando Mendoza Santoyo, "Simultaneous three-dimensional dynamic deformation measurement with pulsed digital holography," Appl. Opt. 38, 7056-7062 (1999).
    [CrossRef]
  9. G. Pedrini and I , Alexeenko,"Miniaturized optical system based on digital holography," Sixth International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, Proc. SPIE, 5503, 423-498 (2004).
  10. Ervin Kolenovic, Wolfgang Osten, Reiner Klattenhoff, Songcan Lai, Chritoph Von Kopylow, and Werner Juptner. "Miniaturized digital holography sensor for distal three-dimensional endoscopy," Appl. Opt. 42, 5167-5172 (2003).
    [CrossRef] [PubMed]

2003

1999

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).

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).

Kemper, B.

Machida, H.

Merker, A.

Nishisaka, T.

Staffan Schedin,

Taleblou, R.

Von Bally, G.

Yonemura, M.

Appl. Opt.

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).

Other

G. Pedrini, S. Schedin, and H. J. Tiziani, "Use of endoscopes in pulsed digital holographic interferometry," in Optical Measurement System for Industrial Inspection II: Applications in productions Engineering, R. Holfling, W. Jupter and M. Kujawinska, eds. Proc. SPIE 4399, 1-8 (2001).
[CrossRef]

C. M. Vest, Holography Interferometry, (Wyle, New York, 1979).

G. Pedrini and I , Alexeenko,"Miniaturized optical system based on digital holography," Sixth International Conference on Vibration Measurements by Laser Techniques: Advances and Applications, Proc. SPIE, 5503, 423-498 (2004).

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Figures (6)

Fig. 1.
Fig. 1.

Experimental set up for the 3D endoscopic pulsed digital holography with simultaneous recording of three digital holograms. BS, Beam splitters; CB, Cube beam splitters; M, mirrors; O, object illumination beams; R reference beams.

Fig. 2.
Fig. 2.

Fourier spectrum consisting of three incoherently added digital holograms.

Fig. 3.
Fig. 3.

Geometry of the illuminating beams, showing the unitary vectors of illumination.

Figs. 4.
Figs. 4.

(a), (b) and (c) are wrapped phase map of three illumination directions, i1, i2 and i3 respectively.

Fig. 5.
Fig. 5.

The component of the resultant deformation normal to the cylinder surface.

Fig. 6.
Fig. 6.

The component of the resultant deformation tangent to the cylinder surface.

Equations (16)

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I ( ξ , η ) = k = 1 3 I k ( ξ , η )
= k = 1 3 [ R k ( ξ , η ) + O k ( ξ , η ) 2 ]
O k ( ξ , η ) = o 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 )
I ( ξ , η ) = k = 1 3 { 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 ) = o k 2 ( ξ , η ) + r k 2 ( ξ , η )
c k ( ξ , η ) = o k ( ξ , η ) r k ( ξ , η ) exp [ i ϕ k ( ξ , η ) ]
FT { I } = k = 1 2 [ A k ( f ξ , f n )
+ C k ( f ξ f k ξ , f n f kn )
+ C k * ( f ξ f k ξ , f n f kn ) ]
ϕ k ( ξ , η ) = arctan Im [ c k ( ξ , η ) ] Re [ c k ( ξ , η ) ] , k = 1,2,3
Δ ϕ k ( ξ , η ) = ϕ k ( ξ , η ) ϕ k ( ξ , η ) , k = 1,2,3
Δ ϕ k = ( 2 π λ ) u s k
s k = n ̂ k n ̂ o , k = 1,2,3

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