Determination of displacements from holograms using simply applied methods that are comparable to speckle techniques

A system of equations is developed which relates the general displacement field from usual and image-plane double exposure holograms of objects illuminated by collimated or point light sources. By defining a coordinate system in the direction of the holographic plate and requiring that the object be several plate diameters from the plate, certain simplifications in the system of equations can be made to decouple the displacement components. As a result, the in-plane components can be independently determined from the apparent fringe shift observed from the holographic plate. The out-or-plane component can then be solved from a linear equation using the in-plane components. All three components of displacement can be simultaneously determined from a single film plate, regardless of the proportion of in- to out-of-plane components. The method is validated by comparisons with speckle results and theoretical analyses.