Volume 29, number 1 OPTICS COMMUNICATIONS April 1979 SUBTRACTION AND ADDITION OF OPTICAL SIGNALS USING A DOUBLE-GRATING SHEARING INTERFEROMETER K. PATORSKI Warsaw Technical University, Precision Mechanics Department, Institute o f Design o f Precise and Optical Instruments, 02-525 Warsaw, Poland Received 20 December 1978 Revised manuscript received 22 January 1979 Realisation of real-time optical image addition and subtraction is proposed and experimentally verified by the use of a double grating shearing interferometer. Real-time superposition of processed signals, continuous change of their lateral separation, and independent control of the phase difference between the signals constitute attractive characteristics of the configuration proposed. 1. Introduction It is frequently required to compare photographical- ly encoded optical signals in order to detect the differ- ences between them. Many optical methods have been devised for this purpose; a review of these techniques has been given by Ebersole [1 ]. The purpose of this report is to describe the inter- ferometric technique for real time optical subtraction (and addition) based on a double-grating shearing in- terferometer. Two diffraction gratings are used to superimpose the image being compared, whereas in previously described real-time methods using two dif- fraction gratings [2,3] superposition was achieved in a Mach-Zehnder interferometer configuration. Lateral shift of one of the gratings serves for the adjustment of the proper phase relationship between the signals. The optical system proposed can be also regarded as a modification of a shearing interferometer recently proposed by Ebersole and Wyant [4]. 2. Principle The optical system of the instrument is shown schematically in fig. 1. Two identical diffraction grat- ings G1 and G2 are illuminated by a spatially coherent monochromatic collimated beam of interferometric quality. The signals in the form of photographic im- ages are placed in front of the first grating G1. Behind the second grating the imaging lens L1 is placed. Its main role is to image the signals P1 and P2 at the im- age plane I. Additionally, lens L1 enables a spatial fil- tering operation of the double-diffracted spectrum at the back focal plane. Of the beams emerging from the second grating on- Fig. 1. Schematic diagram of the optical system of the double grating shearing interferometer used for real-time addition and sub- traction. S - monochromatic point source, L - collimating optics, P1 and P2 - optical signals in form of photographic transpari- ences, G1 and G2 - linear diffraction gratings, L1 - imaging lens, F - spatial filter, I - image plane. 13