The speckles of the image plane of an object are radially shifted and decorrelated when the object is axially translated . It will be shown that the radial shift of the corresponding speckles is removed when the pupil of the optical system is placed in the back focal plane of the imaging lens . A photographic plate twice exposed to the irradiance of image plane and laterally shifted between the exposures , exhibits , after processing , a system of Young's fringes in its Fourier plane . The contrast of these fringes , which represents the correlation degree of the recorded speckle patterns , is only a function of the relative value of the axial shift of the object in camparison with the depth of focus of the imaging lens . If the pupil of the optical system is placed in the plane of the imaging lens , the contrast of the fringes generated in the same way as above , depends on the maximum value of the radial shift suffered by the speckles with respect to their mean size in image plane .
"Detection Of Axial Displacements Of A Diffusing Object", Proc. SPIE 0136, 1st European Conf on Optics Applied to Metrology, (18 April 1978); doi: 10.1117/12.956167; https://doi.org/10.1117/12.956167