Abstract
A symmetrical double-beam illumination is used in conjunction with a fictitious fringe system to obtain a moiré pattern which represents the projection of the displacement vector into a single plane. The fictitious system of fringes is generated by a rotation of the photographic plate. This additional degree of freedom makes it possible to optically superimpose holograms, to apply spatial filtering techniques, and to control fringe localization. The method is applicable for displacement determination throughout the entire holographic range. A disk subjected to diametral compression is used to demonstrate that displacements and strains on the order of magnitude of those found in real engineering problems can be determined very accurately.
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Abbreviations
- \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{d} \) :
-
displacement vector
- d x :
-
scalar component of the displacement
- f(u) :
-
function of the fictitious displacement
- \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{g} \) :
-
sensitivity vector
- \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{i} , \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{j} , \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{k} \) :
-
basis of unit vectors
- \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{k} _1 , \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{k} _1 ^\prime , \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{k} _2 , \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{k} _2 ^\prime \) :
-
propagation vectors
- \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\thicksim}$}}{n} ,n\mathop p\limits_ \sim ,n\mathop {p'}\limits_ \sim \) :
-
normal vectors
- n 1 ,n 2 ,n R :
-
fringe-order numbers
- u,v :
-
scalar components of the displacement
- x,y,z :
-
coordinates of reference system
- z c :
-
z coordinate of the center of rotation
- C :
-
rotation axis
- D :
-
distance from the localization surface to the hologram; diameter of the disk
- D′ :
-
distance between the object and the holographic plate
- H~ :
-
rotation vector
- P :
-
point on object surface
- P′ :
-
point on localization surface
- P 1 ,P 1 ′,P 2 :
-
points on the photographic plate
- R~ :
-
position vector from the center of rotation to a point on the photographic plate
- α:
-
angle between the illumination beams and the normal to the object surface
- β,βx, βy :
-
angles of rotation of the photographic plate
- δ,δ' :
-
phase changes
- δ, δm :
-
fringe spacing
- ∈x, ∈y :
-
components of strain
- θ :
-
angle between observation or illume nation directions and the normal the object surface
- θp :
-
angle between a scattered ray and the normal to the photographic plate
- θR :
-
angle between the reference beam and the normal to the photographic plate
- Δθp,Δθp',ΔθR :
-
changes in angle
- λ:
-
wavelength of the laser light
- φ, φ1, φ2, φ R :
-
phase relations
References
Wilson, A. D., “Holographically Observed Torsion in a Cylindrical Shaft,” Ap. Opt.,9 (9) (1970).
Wilson, A. D., “In-Plane Displacement of a Stressed Membrane with a Hole Measured by Holographic Interferometry,” Ap. Opt.,10 (4) (1971).
Ennos, A. E., “Measurement of In-Plane Surface Strains by Hologram Interferometry,” J. of Phys. E., Sci. Instr. (1) (1968).
Butters, J. N., “Application of Holography to Instrument Diaphragm Deformations and Associated Topics,”The Engineering Uses of Holography, Cambridge Univ. Press, London, New York (1970).
Boone, P. M., “Holographic Determination of In-Plane Deformation,” Opt. Technol.,2 (1970).
Abranson, N., “The Holo-Diagram VI: Practical Device in Coherent Optics”,Ap. Opt.,11 (11) (1972).
Sciammarella, C. A., “Holographic Interferometry Analyzed from the Point of View of Moiré Patterns,” Exp. Mech. in Res. and Dev., Proc. of Int. Symp. on Exp. Mech., Univ. of Waterloo, June 12–16, 1972.
Viénot, J., et al, “Hologram Interferometry: Surface Displacement Fringe Analysis as an Approach to the Study of Mechanical Strains and other Application to the Determination of Anisotropy in Transparent Objects,”The Engineering Uses of Holography, Cambridge Univ. Press, London, New York (1970).
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Sciammarella, C.A., Gilbert, J.A. A holographic-moiré technique to obtain separate patterns for components of displacement. Experimental Mechanics 16, 215–220 (1976). https://doi.org/10.1007/BF02329271
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DOI: https://doi.org/10.1007/BF02329271