In dual-plate speckle photography, the images corresponding to both deformation states are recorded on separate photographic plates. In this way, two major limitations of speckle photography, large rigid body displacements of the specimen and the 180-deg displacement direction ambiguity, can be overcome. When both photographic plates are placed with the glass base of one of them between the emulsions and they are illuminated by a narrow laser beam, a pattern of circular fringes is generated. Displacements can be measured by evaluating the distance between the center of the fringe pattern and the undiffracted laser beam, A new algorithm for the fully automatic analysis of such fringe patterns is presented. Its performance is tested using computersimulated fringes and compared with performance obtained using a previously developed algorithm.