Abstract
Partial derivatives of displacement are optically determined by superimposing two shifted holographic reconstructions which correspond to single components of displacement. Two different methods are proposed, one of which involves shifting a holographic-moiré pattern on itself. A second method takes advantage of holographic multiplexing techniques to incorporate an initial pattern into the shifting process. The latter facilitates the formation of the moiré corresponding to strain information. This paper demonstrates that either method of obtaining derivatives is feasible by documenting an investigation of a disk subjected to diametral compression.
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Abbreviations
- d :
-
displacement vector
- e i :
-
propagation vector
- ê i :
-
unit vector in the direction of propagation
- n i :
-
fringe-order number
- p :
-
pitch
- x,y,z :
-
coordinates of the reference system
- u,v,w :
-
scalar components of the displacement
- z c :
-
coordinate of the center of rotation
- z p :
-
coordinate of the photographic plate
- D :
-
diameter of the disk
- P :
-
object point
- α:
-
sensitivity angle
- β:
-
angle of rotation of the photographic plate
- δ:
-
fringe spacing
- ɛ ij :
-
components of the strain tensor
- θr :
-
reference-beam angle
- Δ:
-
increment
- λ:
-
wavelength
- φβ :
-
phase change of the initial pattern
References
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Gilbert, J.A. Differentiation of holographic-moiré patterns. Experimental Mechanics 18, 436–440 (1978). https://doi.org/10.1007/BF02325061
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DOI: https://doi.org/10.1007/BF02325061