Abstract

A two-wavelength method for endoscopic topography reconstruction is introduced that can be applied to out-of-plane sensitive electronic-speckle-pattern interferometry systems based on rigid endoscope imaging systems. The surface measurement is performed by detection of the phase-difference distribution affected by a change in the applied laser wavelength. Furthermore, the off-axis endoscopic illumination geometry is taken into account by an approximation. Experimental results of the characterization of the endoscopic surface reconstruction technique and the measurement accuracy obtained are described and discussed. Finally, the applicability of the method is demonstrated with results from the topographic reconstruction of a free-form surface.

© 2004 Optical Society of America

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References

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  1. M.-A. Beeck, W. Hentschel, “Laser metrology—a diagnostic tool in automotive development processes,” Opt. Lasers Eng. 34, 101–120 (2000).
    [CrossRef]
  2. H. Steinbichler, G. Gehring, “TV-holography and holographic interferometry: industrial applications,” Opt. Lasers Eng. 24, 111–127 (1996).
    [CrossRef]
  3. S. Schedin, G. Pedrini, H. J. Tiziani, “Pulsed digital holography for deformation measurements on biological tissues,” Appl. Opt. 39, 2853–2857 (2000).
    [CrossRef]
  4. B. Kemper, W. Avenhaus, D. Dirksen, A. Merker, G. von Bally, “Endoscopic double-pulse electronic-speckle-pattern interferometer for technical and medical intracavity inspection,” Appl. Opt. 39, 3899–3905 (2000).
    [CrossRef]
  5. W. Avenhaus, B. Kemper, G. von Bally, “Gastric wall elasticity assessed by dynamic holographic endoscopy: ex vivo investigations on the porcine stomach,” Gastrointest. Endosc. 54, 496–500 (2001).
    [CrossRef] [PubMed]
  6. S. Schedin, G. Pedrini, H. J. Tiziani, A. K. Aggarwal, “Comparative study of various endoscopes for pulsed digital holographic interferometry,” Appl. Opt. 40, 2692–2697 (2001).
    [CrossRef]
  7. T. Kreis, Holographic Interferometry: Principles and Methods (Akademie-Verlag, Berlin, 1996).
  8. K. B. Atkinson, Close Range Photogrammetry and Machine Vision (Whittles, Caithness, UK, 1996).
  9. Y. Zou, G. Pedrini, H. J. Tiziani, “Surface contouring in a video frame by changing the wavelength of a diode laser,” Opt. Eng. 35, 1074–1079 (1996).
    [CrossRef]
  10. G. Pedrini, P. Fröning, H. J. Tiziani, M. Gusev, “Pulsed digital holography for high-speed contouring that uses a two-wavelength method,” Appl. Opt. 38, 3460–3467 (1999).
    [CrossRef]
  11. B. Kemper, D. Dirksen, J. Kandulla, G. von Bally, “Quantitative determination of out-of-plane displacements by endoscopic electronic-speckle-pattern interferometry,” Opt. Commun. 194, 75–82 (2001).
    [CrossRef]
  12. T. Bothe, J. Burke, H. Helmers, “Spatial phase shifting in electronic speckle pattern interferometry: minimization of phase reconstruction errors,” Appl. Opt. 36, 5310–5316 (1997).
    [CrossRef] [PubMed]
  13. B. Kemper, J. Kandulla, D. Dirksen, G. von Bally, “Optimization of spatial phase shifting in endoscopic electronic speckle pattern interferometry,” Opt. Commun. 217, 151–160 (2003).
    [CrossRef]

2003 (1)

B. Kemper, J. Kandulla, D. Dirksen, G. von Bally, “Optimization of spatial phase shifting in endoscopic electronic speckle pattern interferometry,” Opt. Commun. 217, 151–160 (2003).
[CrossRef]

2001 (3)

B. Kemper, D. Dirksen, J. Kandulla, G. von Bally, “Quantitative determination of out-of-plane displacements by endoscopic electronic-speckle-pattern interferometry,” Opt. Commun. 194, 75–82 (2001).
[CrossRef]

W. Avenhaus, B. Kemper, G. von Bally, “Gastric wall elasticity assessed by dynamic holographic endoscopy: ex vivo investigations on the porcine stomach,” Gastrointest. Endosc. 54, 496–500 (2001).
[CrossRef] [PubMed]

S. Schedin, G. Pedrini, H. J. Tiziani, A. K. Aggarwal, “Comparative study of various endoscopes for pulsed digital holographic interferometry,” Appl. Opt. 40, 2692–2697 (2001).
[CrossRef]

2000 (3)

1999 (1)

1997 (1)

1996 (2)

H. Steinbichler, G. Gehring, “TV-holography and holographic interferometry: industrial applications,” Opt. Lasers Eng. 24, 111–127 (1996).
[CrossRef]

Y. Zou, G. Pedrini, H. J. Tiziani, “Surface contouring in a video frame by changing the wavelength of a diode laser,” Opt. Eng. 35, 1074–1079 (1996).
[CrossRef]

Aggarwal, A. K.

Atkinson, K. B.

K. B. Atkinson, Close Range Photogrammetry and Machine Vision (Whittles, Caithness, UK, 1996).

Avenhaus, W.

W. Avenhaus, B. Kemper, G. von Bally, “Gastric wall elasticity assessed by dynamic holographic endoscopy: ex vivo investigations on the porcine stomach,” Gastrointest. Endosc. 54, 496–500 (2001).
[CrossRef] [PubMed]

B. Kemper, W. Avenhaus, D. Dirksen, A. Merker, G. von Bally, “Endoscopic double-pulse electronic-speckle-pattern interferometer for technical and medical intracavity inspection,” Appl. Opt. 39, 3899–3905 (2000).
[CrossRef]

Beeck, M.-A.

M.-A. Beeck, W. Hentschel, “Laser metrology—a diagnostic tool in automotive development processes,” Opt. Lasers Eng. 34, 101–120 (2000).
[CrossRef]

Bothe, T.

Burke, J.

Dirksen, D.

B. Kemper, J. Kandulla, D. Dirksen, G. von Bally, “Optimization of spatial phase shifting in endoscopic electronic speckle pattern interferometry,” Opt. Commun. 217, 151–160 (2003).
[CrossRef]

B. Kemper, D. Dirksen, J. Kandulla, G. von Bally, “Quantitative determination of out-of-plane displacements by endoscopic electronic-speckle-pattern interferometry,” Opt. Commun. 194, 75–82 (2001).
[CrossRef]

B. Kemper, W. Avenhaus, D. Dirksen, A. Merker, G. von Bally, “Endoscopic double-pulse electronic-speckle-pattern interferometer for technical and medical intracavity inspection,” Appl. Opt. 39, 3899–3905 (2000).
[CrossRef]

Fröning, P.

Gehring, G.

H. Steinbichler, G. Gehring, “TV-holography and holographic interferometry: industrial applications,” Opt. Lasers Eng. 24, 111–127 (1996).
[CrossRef]

Gusev, M.

Helmers, H.

Hentschel, W.

M.-A. Beeck, W. Hentschel, “Laser metrology—a diagnostic tool in automotive development processes,” Opt. Lasers Eng. 34, 101–120 (2000).
[CrossRef]

Kandulla, J.

B. Kemper, J. Kandulla, D. Dirksen, G. von Bally, “Optimization of spatial phase shifting in endoscopic electronic speckle pattern interferometry,” Opt. Commun. 217, 151–160 (2003).
[CrossRef]

B. Kemper, D. Dirksen, J. Kandulla, G. von Bally, “Quantitative determination of out-of-plane displacements by endoscopic electronic-speckle-pattern interferometry,” Opt. Commun. 194, 75–82 (2001).
[CrossRef]

Kemper, B.

B. Kemper, J. Kandulla, D. Dirksen, G. von Bally, “Optimization of spatial phase shifting in endoscopic electronic speckle pattern interferometry,” Opt. Commun. 217, 151–160 (2003).
[CrossRef]

B. Kemper, D. Dirksen, J. Kandulla, G. von Bally, “Quantitative determination of out-of-plane displacements by endoscopic electronic-speckle-pattern interferometry,” Opt. Commun. 194, 75–82 (2001).
[CrossRef]

W. Avenhaus, B. Kemper, G. von Bally, “Gastric wall elasticity assessed by dynamic holographic endoscopy: ex vivo investigations on the porcine stomach,” Gastrointest. Endosc. 54, 496–500 (2001).
[CrossRef] [PubMed]

B. Kemper, W. Avenhaus, D. Dirksen, A. Merker, G. von Bally, “Endoscopic double-pulse electronic-speckle-pattern interferometer for technical and medical intracavity inspection,” Appl. Opt. 39, 3899–3905 (2000).
[CrossRef]

Kreis, T.

T. Kreis, Holographic Interferometry: Principles and Methods (Akademie-Verlag, Berlin, 1996).

Merker, A.

Pedrini, G.

Schedin, S.

Steinbichler, H.

H. Steinbichler, G. Gehring, “TV-holography and holographic interferometry: industrial applications,” Opt. Lasers Eng. 24, 111–127 (1996).
[CrossRef]

Tiziani, H. J.

von Bally, G.

B. Kemper, J. Kandulla, D. Dirksen, G. von Bally, “Optimization of spatial phase shifting in endoscopic electronic speckle pattern interferometry,” Opt. Commun. 217, 151–160 (2003).
[CrossRef]

B. Kemper, D. Dirksen, J. Kandulla, G. von Bally, “Quantitative determination of out-of-plane displacements by endoscopic electronic-speckle-pattern interferometry,” Opt. Commun. 194, 75–82 (2001).
[CrossRef]

W. Avenhaus, B. Kemper, G. von Bally, “Gastric wall elasticity assessed by dynamic holographic endoscopy: ex vivo investigations on the porcine stomach,” Gastrointest. Endosc. 54, 496–500 (2001).
[CrossRef] [PubMed]

B. Kemper, W. Avenhaus, D. Dirksen, A. Merker, G. von Bally, “Endoscopic double-pulse electronic-speckle-pattern interferometer for technical and medical intracavity inspection,” Appl. Opt. 39, 3899–3905 (2000).
[CrossRef]

Zou, Y.

Y. Zou, G. Pedrini, H. J. Tiziani, “Surface contouring in a video frame by changing the wavelength of a diode laser,” Opt. Eng. 35, 1074–1079 (1996).
[CrossRef]

Appl. Opt. (5)

Gastrointest. Endosc. (1)

W. Avenhaus, B. Kemper, G. von Bally, “Gastric wall elasticity assessed by dynamic holographic endoscopy: ex vivo investigations on the porcine stomach,” Gastrointest. Endosc. 54, 496–500 (2001).
[CrossRef] [PubMed]

Opt. Commun. (2)

B. Kemper, D. Dirksen, J. Kandulla, G. von Bally, “Quantitative determination of out-of-plane displacements by endoscopic electronic-speckle-pattern interferometry,” Opt. Commun. 194, 75–82 (2001).
[CrossRef]

B. Kemper, J. Kandulla, D. Dirksen, G. von Bally, “Optimization of spatial phase shifting in endoscopic electronic speckle pattern interferometry,” Opt. Commun. 217, 151–160 (2003).
[CrossRef]

Opt. Eng. (1)

Y. Zou, G. Pedrini, H. J. Tiziani, “Surface contouring in a video frame by changing the wavelength of a diode laser,” Opt. Eng. 35, 1074–1079 (1996).
[CrossRef]

Opt. Lasers Eng. (2)

M.-A. Beeck, W. Hentschel, “Laser metrology—a diagnostic tool in automotive development processes,” Opt. Lasers Eng. 34, 101–120 (2000).
[CrossRef]

H. Steinbichler, G. Gehring, “TV-holography and holographic interferometry: industrial applications,” Opt. Lasers Eng. 24, 111–127 (1996).
[CrossRef]

Other (2)

T. Kreis, Holographic Interferometry: Principles and Methods (Akademie-Verlag, Berlin, 1996).

K. B. Atkinson, Close Range Photogrammetry and Machine Vision (Whittles, Caithness, UK, 1996).

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Figures (9)

Fig. 1
Fig. 1

Schematic of an endoscope ESPI system: OB, object; EN, endoscope; ML, microlens; BS, beam splitter; SMF(O) and SMF(R), single-mode fibers for an object wave (O) and a reference wave (R); FKs, fiber couplers; P’s, polarizers; L, lens; AOM, acousto-optic modulator; DPG, double-pulse generator; CCD, CCD camera; PC/IP, computer with a digital image processing system; MO, monitor.

Fig. 2
Fig. 2

Sketch of sensitivity vector S for an endoscope ESPI system: EN, endoscope; F, illumination fiber; o.A., optical axis; a, distance between the object’s surface and the endoscope’s tip along the optical axis; Δx, Δy, and Δz, distances of the illumination fiber in the x, y, and z directions from the endoscope’s tip; P(x, y, z), point on the object’s surface, k Q and k B , directions of illumination and observation, respectively, in P(x, y, z); d obj, topographic vector.

Fig. 3
Fig. 3

Recording parameters for determination of topography by the two-wavelength method with central illumination: EN, endoscope; F, illumination fiber; o.A., optical axis; a, distance between the object’s surface and the endoscope’s tip along the optical axis; SF, surface affected by inverse sensitivity vector S; NF, surface resulting from normalization; m, n, pixel coordinates in the horizontal (m) and vertical (n) directions; S x (m), ϑ y (m, n)), length of S in direction (ϑ x (m), ϑ y (m, n)); d′ (ϑ x (m), ϑ y (m, n)), distance between NF and the object’s surface in the direction (ϑ x (m), ϑ y (m, n)).

Fig. 4
Fig. 4

Schematic depiction of the recording parameters for determination of topography by the two-wavelength method with off-axis illumination. For explanations of EN, F, o.A., a, SF, NF, m, and n, see Fig. 3. Δx, Δy, and Δz, distances of the illumination fiber in the x, y, and z directions from the endoscope’s tip; k Q and k B , illumination and observation directions; S, sensitivity vector; S x (m), ϑ y (m, n)), length of S in the direction (ϑ x (m), ϑ y (m, n)); d″ (ϑ x (m), ϑ y (m, n)), distance between NF′ and the object’s surface. For a better illustration of the change of NF′, surface NF is also shown (dashed curve).

Fig. 5
Fig. 5

Approximation with which to determine surface topographies by endoscopic ESPI. For definitions of EN, F, o.A., a, NF, NF′, m, n, Δx, Δy, and Δz see Fig. 4. SE, calculated plane in distance a; d‴ (ϑ x (m), ϑ y (m, n)), distance of SE and object surface in the direction ϑ x (m), ϑ y (m, n).

Fig. 6
Fig. 6

Comparison of (a) the experimentally obtained phase difference with (b) the corresponding analytically calculated data of a metal plate positioned perpendicular to the endoscope’s optical axis (a = 9 mm, Δλ = 0.25 nm, Δx = 1.2 mm, Δy = 1.3 mm, Δz = 2.0 mm). (c) Central horizontal cross section through the unwrapped phase-difference distribution in (a) and (b).

Fig. 7
Fig. 7

Comparison of (a) experimentally determined phase-difference data with (b) related analytical data of a metal plate tilted 20° to the normal of the optical interferometer axis (a = 10 mm, Δλ = 0.33 nm, Δx = 1.2 mm, Δy = 1.3 mm, Δz = 2.0 mm). (c) Central horizontal cross section through unwrapped phase-difference distributions (a) and (b). (d), (e) Three-dimensional representations of the object’s surface reconstructed from the unwrapped experimental data in (a) and the unwrapped analytical data in (b). (f) Pseudo-three-dimensional plot of the difference between (d) and (e).

Fig. 8
Fig. 8

Horizontal cross sections through corrected and uncorrected analytical surface reconstructions of a tilted plane: (a) section at 1/6 of the image height, a = 8 mm, ω = 15°; (b) section at 1/2 of the image height, a = 8 mm, ω = 15°; (c) section at 5/6 of the image height, a = 8 mm, ω = 15°; (d) section at 1/2 of the image height, a = 5 mm, ω = 15°; (e) section at 1/2 of the image height, a = 11 mm, ω = 15°; (f) section at 1/2 of the image height, a = 8 mm, ω = 30°.

Fig. 9
Fig. 9

Reconstruction of the topography of a free-form surface (bottle cap; distance to the endoscope’s tip, a = 8 mm). (a) Experimentally obtained filtered phase-difference distribution Δϕ modulo 2π for Δλ = 0.25 nm. (b) Calculated phase-difference data of a synthetic plane perpendicular to the endoscope’s optical axis for a = 8 mm. (c) Subtraction of (b) from (a) modulo 2π. (d) Enlarged part of the object surface investigated, superimposed upon contour lines of the reconstructed topography. (e) Horizontal cross section through the topographic reconstruction [dashed white line in (d)]. (f) Vertical cross section through the topographic reconstruction [dashed white line in (d)].

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

S=kQ|kQ|+kB|kB|,
ϕi=2πλidobj · S+C,
Δϕ=ϕ1-ϕ2=2π1λ1-1λ2dobj · S=2πΛdobj · S,
Λ=λ1λ2λ2-λ1,
Δϕm, n=2πΛ dobjϑxm, ϑym, n×Sϑxm, ϑym, n.
Δϕm, n=4πΛ dϑxm, ϑym, n.

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