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Extension to three dimensions of a holographic-moiré technique to separate patterns corresponding to components of displacement

A combination of dual-beam holographic interferometry and moiré provides a practical solution to the problem of the optical separation of displacement components

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Abstract

The holographic-moiré technique to obtain separate patterns for the Cartesian components of the displacement vector is extended to curved surfaces. An initial pattern which is often required for the observation of the displacement fringes is analyzed for this case. Criteria are established for the localization of this initial pattern to follow close to the contour of the object surface. A PVC pipe subjected to torsion demonstrates the proposed technique and, when analytical arguments are checked experimentally, a close correlation is observed.

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Abbreviations

a :

distance between points P and M on object surface

d, d′ :

displacement magnitudes

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{d} , \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{d} ', \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{d} _1\) :

displacement vectors

d o :

outer diameter of the pipe

d i :

inner diameter of the pipe

e 1 ,e′ 1 e 2 ,e r :

propagation vector

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{g}\) :

sensitivity vector

n :

fringe-order number

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{n} _p\) :

plate normal

\(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{n} _s\) :

unit vector

C :

rotation center

D :

distance between model and photographic plate

E :

Young’s modulus

L :

length of pipe

M, O, P, P′, P1, P′1, P2, Q, Q′:

points under consideration

M t :

applied torque

\((R_p , \theta _p ,), (R_{\bar p} , \theta _{\bar p} ), (R_{\bar c} , \theta _c )\) :

polar coordinates

(U, V, W), (U r ,U θ ,U z ):

displacement components

(X, Y, Z), (r, θ, z) :

coordinates

Z c :

distance between photographic plate and rotation center

α:

sensitivity angle

β:

angle of rotation of photographic plate

δ, δ′:

angular phase change

\(\delta _M\) :

fringe spacing

\(\theta ^*\) :

angle of twist per unit length

\(\theta _T , \theta _R , \theta _P\) :

angles

λ:

wavelength of laser light

ν:

Poisson’s ratio

ϕ (z):

angle of twist

\(\Delta \theta _P , \Delta \theta _M\) :

incremental angles

References

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  4. Hung, Y.Y. and Taylor, C.E., “Measurement of Surface Displacements Normal to the Line of Sight by Holo-Moiré Interferometry,” J. Appl. Mech.,42 (1975).

  5. Sciammarella, C.A. andGilbert, J.A., “A Holographic-moiré Technique to Obtain Separate Patterns for Components of Displacement,”Experimental Mechanics,16 (6),215–220 (Jun. 1976).

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  10. Vienot, J. CH. et al., “Hologram Interferometry: Surface Displacement Fringe Analysis as an Approach to the Study of Mechanical Strains and other Applications to the Determinations of Anisotropy in Transparent Objects,”The Engineering Uses of Holography, E.R. Robertson andJ.M. Harvey, eds., Cambridge Univ. Press, London, New York (1970).

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Author information

Authors and Affiliations

  1. College of Engineering and Applied Science, University of Wisconsin, 53201, Milwaukee, WI

    J. A. Gilbert (Professor)

  2. Illinois Institute of Technology, 60616, Chicago, IL

    C. A. Sciammarella & S. K. Chawla

Authors
  1. J. A. Gilbert
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  2. C. A. Sciammarella
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  3. S. K. Chawla
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Gilbert, J.A., Sciammarella, C.A. & Chawla, S.K. Extension to three dimensions of a holographic-moiré technique to separate patterns corresponding to components of displacement. Experimental Mechanics 18, 321–327 (1978). https://doi.org/10.1007/BF02324926

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  • DOI: https://doi.org/10.1007/BF02324926

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