Volume 34, number 1 OPTICS COMMUNICATIONS July 1980 OPTICAL IMAGE SUBTRACTION THROUGH SPECKLE MODULATED BY YOUNG FRINGES H.J. RABAL, N. BOLOGNINI *, E. SICRE and M. GARAVAGLIA Centro de Investigaciones Opticas (ClOp) (CONICET- UNLP - LEMIT) 1900 La Plata, Argentina Received 26 March 1980 A new method for subtracting images is proposed. It is based on assigning complementary Young's fringes to the speckles of the common parts of two images. In this way, carrier frequency is cancelled, and "a-posteriori" spatial filtering shows only noncommon parts. Suggestions on applications of the method are briefly commented. The importance is well known of developing sim- ple and fast techniques for extracting the differences between two 2- and 3-dimensional scenes. In the last few years several methods have been proposed [1-4]. A review of the most important ones can be found in r'ef. [51. The purpose of this paper is to propose a new ap- proach, similar in some extent to the technique de- veloped by Debrus et al. [3]. In its first step, the in- formation contained in a transparency, modulated by a very fine speckle pattern, is photographically record- ed. Afterwards, the photographic plate is slightly moved in-plane and then, a second transparency, modulated by the same speckle pattern, is recorded on the same plate. The developed plate contains pairs of equally spaced speckle grains for identical parts of the transparencies, and of unpaired speckles for differ- ent ones. If the transmittance of this plate is Fourier transformed in a conventional way [6], the paired speckles give raise to Young's fringes, while the spec- trum of the unpaired ones spread all over the Fourier plane. If a slit filter is located in the nulls of the Young's fringes, it will only pass the light coming from the unpaired speckles, and the subsequent Fourier transform will depict a picture of the differ- ences between the two transparencies. The method we propose also has two steps. In the first one, a transparency modulated by speckles that * Fellow of the Comisi6n de Investigaciones Cientfficas de la Provincia de Buenos Aires, Argentina (C1C). are themselves modulated by Young's fringes, is re- corded on a photographic plate. These speckles are obtained from the image of a diffuser by a lens whose pupil consists of two round holes, as suggested in ref. [7]. Then, Young's fringes are shifted by half a period, and the second transparency is recorded. If the two exposures are equal, the Young's fringes of the speckle of identical parts of both transparencies are added to a constant background, while the contrast of the Young's fringes of the speckle corresponding to non- identical parts increases in accordance with their mis- match. When the developed plate is Fourier transform- ed as before, the non-cancelled Young's fringes give raise to two diffracted orders in the Fourier plane. If a filter is placed in this plane, in order to observe only one diffracted order, and this order is again Fourier transforlned, an image of the differences between the transparencies will be obtained. The same principle can be applied for subtracting images of diffusing three-dimensional objects. Young's fringe shifting can be performed by moving in-plane the photographic plate in the direction per- pendicular to the fringes. In this case, the cancellation of Young's fringes is exact in the whole plane. How- ever, in some cases it is more practical to produce the n-phase-shift by rotating a plane-parallel plate placed behind one of the holes, in spite of the fact that can- cellation of Young's fringes is not complete all over the plane. Fig. 1 shows the experimental set-up used for obtain- ing the differences between two scenes. The necessary