Vectorial measurements of speckle displacement by the 2-D electronic correlation method

It is shown that the 2-D cross-correlation function between the level-crossing maps obtained from two speckle patterns before and after displacement is equal to the occurrence-rate histogram of the distances between the level-crossing points. On the basis of this fact, the displacement vectors of speckles produced in both diffraction and image planes are successfully measured. The analysis for measurements of the speckle displacement in a vectorial form is performed on line using digital processing by means of a TV–computer system.