Measurement of three-dimensional rigid body motion by multiple exposure speckle photography: use of uncollimated beam illumination in free space geometry

Abstract

A theoretical and experimental analysis is carried out showing the effect of multiple exposures on fringes in the case of three-dimensional motion of a diffuse object illuminated by a diverging beam from a laser point source. Experimental conditions are such that the speckle patterns remain fully correlated in spite of the object moving in three-dimensional space in a direction that makes an angle with the optical axis. Owing to the in-plane component of the three-dimensional displacement the point of null-speckle displacement shifts either in the direction of the in-plane component of the motion or in the opposite direction depending upon the direction of the out-of-plane displacement component. This modifies the fringe profile as compared with the case of pure out-of-plane motion. The intensity distribution at the Fresnel plane of a specklegram is investigated after filtering by a converging beam for double exposure and multiple exposures. Good agreement is found between the theoretical and experimental results.