We derive the response of a volume grating to arbitrary small deformations, using a perturbative approach. This result is of interest for two applications: (a) when a deformation is undesirable and one seeks to minimize the diffracted field's sensitivity to it and (b) when the deformation itself is the quantity of interest and the diffracted field is used as a probe into the deformed volume where the hologram was originally recorded. We show that our result is consistent with previous derivations motivated by the phenomenon of shrinkage in photopolymer holographic materials. We also present the analysis of the grating's response to deformation due to a point indenter and present experimental results consistent with theory.
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