Relative displacement determination of surfaces of two objects by means of speckle-field dynamic interference in the image plane

The interference of two speckle-modulated waves reflected from two three-dimensional deformable objects and passed through the image-forming lens system is theoretically considered. The equation connecting a vector of relative displacement of surfaces of two objects and the change of interference order in the region of their images overlapping is obtained. In the case of the coincidence of the objects illumination and observation, the equation precisely concurs with the similar equation in holographic interferometry. For verification of the validity of this theory, the experiment, in which deformation of the membrane was studied by a new method and by a method of real time holographic interferometry, was carried out. It is demonstrated the good correlation of results obtained by both methods.