Phase-object detection by use of double-exposure fringe-modulated speckle patterns

We study the properties of a double-exposure image specklegram of a diffuse object obtained by use of a doubleaperture pupil. A phase object is placed in front of one aperture during the first or the second exposure. Also, it is assumed that a uniform displacement of the diffuser between exposures is produced. The recorded specklegram is coherently illuminated and analyzed by Fourier transform operations. The average intensity distribution and the interference fringe visibility in the Fourier plane are investigated. On this basis, an alternative interference technique to detect phase objects is proposed