An analysis on fringe formation in holographic interferometry

Formation of interference fringes in the holographic measurement of displacement distribution on a rough surface or flow-velocity distribution on a section plane in a fluid is analyzed using the concept of random process and the stationary-phase method. The displacement or velocity is assumed to vary slowly on the surface. Restrictions are not severe in other respects: the rough surface may be curved; the illumination wave need not be plane; the entrance pupil of the observing optical system may be located at a finite distance from the object. Many types of holographic interferometry, such as multiple-exposure or time-average method, are taken into consideration. The analysis is made for two cases: where the observation point is far from the rough surface and where it is far from the entrance pupil of the observing system, including the observation near the rough surface. In the former case the resultant intensity at the observation point can be considered as the superposition of the constituent fringe intensity arising from the displacement of each contributing point on the rough surface. In the latter the intensity can be obtained as the integral of the contributing part of the constituent fringe intensity over the entrance pupil.