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Double Images in Copy Holograms D. B. Brumm Institute of Science and Technology, The University of Michi- gan, Ann Arbor, Michigan 48107. Received 29 December 1966. It has been demonstrated 1 that a hologram can be copied or duplicated without having the two emulsions in contact by re- cording the interference pattern between the undiffracted wave passing through the hologram and one of the first-order diffracted waves. In this letter we demonstrate that such a copy hologram can be made to reconstruct a double image of the original object under certain conditions. These double images are easily avoided if desired. Consider the instance where we assume that the emulsion of the original hologram H 1 (see Fig. 1) is infinitely thin, and that the copy hologram H 2 is exposed while in contact with H 1 . When H 1 is illuminated with a monochromatic plane wave, the transmitted light has three components of interest: the undif- fracted or zero-order wave, and two first-order diffracted waves which are complex conjugates of one another. These three component waves interfere in pairs to produce the three components of the total fringe system recorded by H 2 . Only two of these components are of interest, those formed by the interference of the undiffracted wave with each of the first- order waves. Each component of the resulting fringe pattern reconstructs two waves; one wave produces a virtual image while the other focuses to a real image. Thus, the two component fringe patterns reconstruct a total of four images: two are real and two are virtual. For the conditions assumed, however (the two emulsions coincident during the exposure of H 2 ), the two virtual images coincide as do their conjugates. A different situation arises if H 2 is exposed when separated from H 1 , as shown in Fig. 1. If H 1 is illuminated with a mono- chromatic plane wave, a virtual image of the original object is re- constructed at a certain distance Z 0 from H 1 . A real or conjugate image is also reconstructed; its location is determined by reflect- 588 APPLIED OPTICS / Vol. 6, No. 3 / March 1967 Fig. 1. Exposure of copy hologram H 2 by the transmitted and diffracted fields of original hologram H 1 . The reconstructed images of H 1 are shown. Fig. 2. Locations of images reconstructed by the copy hologram H 2 . Fig. 3. Double real image of the copy hologram. The two holograms were about 6 mm apart during the exposure of H 2 . ing the virtual image about H 1 Thus, both images are equidis- tant from H 1 . If H 2 is exposed in a plane parallel to H 1 , but at a distance d away (d < z 0 ), it intercepts the undiffracted wave and both reconstructed waves. Both virtual and real images have the same effect at H 2 ; each produces, by interference with the reference beam, a fringe system that will reconstruct both a virtual and a real image equidistant from H 2 . The two component fringe systems reconstruct images at different distances from H 2 , however. The component of H 2 generated by the virtual image of H 1 reconstructs virtual and real images at distances of z 0 + d from H 2 ; the component due to the real image of H 1 reconstructs images at distances of Z 0 - d. When illuminated with a plane wave, H 2 then reconstructs double images (both virtual and real), with the images of each pair being 2d apart, as shown in Fig. 2. A photograph of the real image reconstructed by a hologram pro- duced as described above is shown in Fig. 3. The double image appears as predicted.
