The application of Berry-Gibbs theory to phase objects, using interferometry, holography or schlieren methods

Berry and Gibbs show how to obtain the `density function' ρ of a three-dimensional object from measurements of the `opacity function' F. This is the line integral of ρ along rays passing through the object, which are recorded on photographic plates. The present paper shows that this theory may be applied to results obtained by interferometry (holographic or otherwise) or schlieren measurements of phase objects, as are commonly used in fluid mechanics investigations. The most serious practical difficulty arises from the apparent need to vary the view angle over a 180° range. This reduces the apparent advantage of `three-dimensional' holography. It may be shown, however, that for elongated objects, the angles of view should be concentrated around the direction of elongation, and that a considerably reduced range of view angles may then be adequate.