Abstract

We developed the parametric equations that are needed to quantify the modulations in the sensitivity vector that occur when the phase-displacement equation is applied to make panoramic interferometric measurements. The measurement system relies on two collinear panoramic annular lenses, one to illuminate and the other to image their surroundings. When a coherent light source is used and a reference beam is added, interference occurs over the region of interest defined by the illuminating and viewing lenses. A holographic system is used to demonstrate the approach and quantify the analysis. We obtained interference fringes in real time by comparing holograms recorded before and after a section of cylindrical pipe is displaced relative to the measurement system. The annular images and the holographic fringes are acquired and stored digitally in a computer system, and image transformation algorithms are applied to remove optical distortions in the holographic patterns. Excellent agreement is obtained when the fringe loci are compared with those predicted on the basis of theory.

© 2000 Optical Society of America

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References

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  1. D. R. Matthys, J. A. Gilbert, J. Puliparambil, “Panoramic holointerferometry,” Exp. Mech. 35, 83–88 (1995).
    [CrossRef]
  2. J. L. Lindner, J. A. Gilbert, “Modal analysis using time-average panoramic holointerferometry,” Int. J. Anal. Exp. Modal Anal. 10, 143–151 (1995).
  3. S. B. Fair, “A panoramic electronic speckle pattern interferometer,” Ph.D. dissertation (University of Alabama in Huntsville, Huntsville, Alabama, 1998).
  4. D. R. Matthys, J. A. Gilbert, J. Puliparambil, “Endoscopic inspection using a panoramic annular lens,” in Second International Conference on Photomechanics and Speckle Metrology: Moire Techniques, Holographic Interferometry, Optical NDT, and Applications to Fluid Mechanics, F. Chiang, ed., Proc. SPIE1554B, 736–742 (1991).

1995 (2)

D. R. Matthys, J. A. Gilbert, J. Puliparambil, “Panoramic holointerferometry,” Exp. Mech. 35, 83–88 (1995).
[CrossRef]

J. L. Lindner, J. A. Gilbert, “Modal analysis using time-average panoramic holointerferometry,” Int. J. Anal. Exp. Modal Anal. 10, 143–151 (1995).

Fair, S. B.

S. B. Fair, “A panoramic electronic speckle pattern interferometer,” Ph.D. dissertation (University of Alabama in Huntsville, Huntsville, Alabama, 1998).

Gilbert, J. A.

D. R. Matthys, J. A. Gilbert, J. Puliparambil, “Panoramic holointerferometry,” Exp. Mech. 35, 83–88 (1995).
[CrossRef]

J. L. Lindner, J. A. Gilbert, “Modal analysis using time-average panoramic holointerferometry,” Int. J. Anal. Exp. Modal Anal. 10, 143–151 (1995).

D. R. Matthys, J. A. Gilbert, J. Puliparambil, “Endoscopic inspection using a panoramic annular lens,” in Second International Conference on Photomechanics and Speckle Metrology: Moire Techniques, Holographic Interferometry, Optical NDT, and Applications to Fluid Mechanics, F. Chiang, ed., Proc. SPIE1554B, 736–742 (1991).

Lindner, J. L.

J. L. Lindner, J. A. Gilbert, “Modal analysis using time-average panoramic holointerferometry,” Int. J. Anal. Exp. Modal Anal. 10, 143–151 (1995).

Matthys, D. R.

D. R. Matthys, J. A. Gilbert, J. Puliparambil, “Panoramic holointerferometry,” Exp. Mech. 35, 83–88 (1995).
[CrossRef]

D. R. Matthys, J. A. Gilbert, J. Puliparambil, “Endoscopic inspection using a panoramic annular lens,” in Second International Conference on Photomechanics and Speckle Metrology: Moire Techniques, Holographic Interferometry, Optical NDT, and Applications to Fluid Mechanics, F. Chiang, ed., Proc. SPIE1554B, 736–742 (1991).

Puliparambil, J.

D. R. Matthys, J. A. Gilbert, J. Puliparambil, “Panoramic holointerferometry,” Exp. Mech. 35, 83–88 (1995).
[CrossRef]

D. R. Matthys, J. A. Gilbert, J. Puliparambil, “Endoscopic inspection using a panoramic annular lens,” in Second International Conference on Photomechanics and Speckle Metrology: Moire Techniques, Holographic Interferometry, Optical NDT, and Applications to Fluid Mechanics, F. Chiang, ed., Proc. SPIE1554B, 736–742 (1991).

Exp. Mech. (1)

D. R. Matthys, J. A. Gilbert, J. Puliparambil, “Panoramic holointerferometry,” Exp. Mech. 35, 83–88 (1995).
[CrossRef]

Int. J. Anal. Exp. Modal Anal. (1)

J. L. Lindner, J. A. Gilbert, “Modal analysis using time-average panoramic holointerferometry,” Int. J. Anal. Exp. Modal Anal. 10, 143–151 (1995).

Other (2)

S. B. Fair, “A panoramic electronic speckle pattern interferometer,” Ph.D. dissertation (University of Alabama in Huntsville, Huntsville, Alabama, 1998).

D. R. Matthys, J. A. Gilbert, J. Puliparambil, “Endoscopic inspection using a panoramic annular lens,” in Second International Conference on Photomechanics and Speckle Metrology: Moire Techniques, Holographic Interferometry, Optical NDT, and Applications to Fluid Mechanics, F. Chiang, ed., Proc. SPIE1554B, 736–742 (1991).

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Figures (11)

Fig. 1
Fig. 1

Annular image captured by a PAL.

Fig. 2
Fig. 2

Optical characteristics of an illuminating lens.

Fig. 3
Fig. 3

Coordinate systems used in the derivation of the governing equations for a dual PAL interferometric measurement system.

Fig. 4
Fig. 4

Schematic of the sensitivity vector C having an out-of-plane (radial) component C y and an in-plane (longitudinal) component C z .

Fig. 5
Fig. 5

Experimental setup for recording real-time holograms: 1, laser; 2, mirror; 3, beam splitter; 4, spatial filter; 5, collimating lens; 6, illuminating PAL; 7, pipe section; 8, imaging PAL; 9, transfer lens; 10, polarizer; 11, mask; 12, thermoplastic holocamera; 13, CCD camera.

Fig. 6
Fig. 6

Out-of-plane (radial) sensitivity coefficient.

Fig. 7
Fig. 7

In-plane (longitudinal) sensitivity coefficient.

Fig. 8
Fig. 8

Holointerferometric fringe pattern for a pipe section translated along the X axis.

Fig. 9
Fig. 9

Holointerferometric fringe pattern for a pipe section translated along the Z axis.

Fig. 10
Fig. 10

Second quadrant of the image shown in Fig. 8 is linearized and compared with theory.

Fig. 11
Fig. 11

First quadrant of the image shown in Fig. 9 is linearized and compared with theory.

Equations (17)

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FOV=R-yetan 26.6°+tan 18.8°.
γi=1.00417 ϕi-0.2978,
η1, ξ1=dy tan ϕImax, dy=R-yetan ϕImax, R-ye,
η2, ξ2=dz-2ze-dy tan ϕImax, dy=dz-2ze-R-yetan ϕImax, R-ye,
ϕImin=tan-1dz-2ze-R-yetan ϕImaxR-ye.
ROI=2 tan ϕImaxR-ye-dz-2ze2 tan ϕImax.
γI=1.00417 ϕI-0.2978,
γV=1.00417 ϕV-0.2978.
ϕV=tan-1dz-2ze-R-yetan ϕIR-ye.
γV=1.00417 tan-1dz-2ze-R-yetan ϕIR-ye-0.2978.
δ=nλ=eˆI-eˆV·d=C·d,
eˆI=cos γIj+sin γIk,
eˆV=-cos γVj+sin γVk,
C=Cyj+Czk=cos γI+cos γVj+sin γI-sin γVk.
d=ui+vj+wk.
δ=nλ=Cyv+Czw=cos γI+cos γV×d cos γd+sin γI-sin γVd sin γd,
δ=nλ=cos1.00417ϕI-0.2978+cos1.00417ϕV-0.2978d cos γd+sin1.00417ϕI-0.2978+sin1.00417ϕV-0.2978d sin γd,

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