Detection of small displacements of diffuse objects illuminated by a speckle pattern

The detection of axial displacements of an object imaged with a laser beam on to a photographic plate is not easy because the aperture of the imaging system is not generally large and the variation of its impulse response with the defect of focus is then relatively slow. We propose here a double-exposure method in which the object is illuminated under a large angle of incidence θ by a random beam which is generated by a laser-illuminated ground glass. After the first exposure, the object undergoes an axial translation ? and the photographic plate is laterally displaced. ? is small and we can assume that this axial translation results only in a lateral displacement ? tg θ of the incident amplitude from the ground glass. Under these conditions, the two intensity distributions recorded by the photographic plate are no more identical and the contrast of the Young's fringes observed in the Fourier plane of the photographic plate is a decreasing function of ?.