Optical correlation and convolution of real 2-D inputs and real 2-D filters

Frequently in character recognition, there is a need to correlate or convolve purely real 2-D inputs and real 2-D filters. We propose two optical correlators. The first, basic real-input-real-filter optical correlator, adds x and y mirror images adjacent to the image to generate real and even images. This avoids the need for an offset reference to capture phase. Therefore, we have greater diffraction efficiency and a reduction in filter LCD pixel size. The second, Hilbert transform basic real-input-real-filter optical correlator, uses a Hilbert transform by masking in the filter plane to reduce the number elements in the filter LCD to that of the number of pixels in a filter image. An optical system can generate the mirror images in real time so that both the input LCD and the filter LCD can have only the same number of elements as their respective number of image pixels. Pile show how a spatial filter can be used to remove the intensity offset produced in the Hilbert transform and restore shift invariance if required. Finally, if desired, some rotation invariance can be achieved by overlapping the mirror images with the basic correlator. Advantages and disadvantages of the proposed correlators are discussed.