A review of mathematical operations by optical data processing

The article describes the basic principles involved in spatial filting along with a particular application of it in mathematical operations. Laser played the important role in the development of optical-data-processing. Starting from the well-known results in diffraction theory that a lens forms in its back focal plane, the Fourier-transform of the field distribution in the front plane, some spatial filters may be used to modify the Fourier-transform so formed and consequently the image. Many problems such as pattern recognition in aerial photography, machine reading of documents, tracing bubble and spark chamber tracks in photographs, air traffic control, processing of satellite photographs, inspection of integrated circuits, photomasks character recognition and the problems in geophysics, radar engineering, biology and astronomy can be solved easily. Many recent advances have been made in this field with a view to improve and develop the techniques for the above problems. In this article it has been shown that it is possible to add, subtract, differentiate, integrate, multiply, divide, convolute and cross-correlate the functions by means of spatial filtering. Grating as a spatial filter has been used to perform the various mathematical operations.