6533b82afe1ef96bd128cb30

RESEARCH PRODUCT

Multiple Matched Spatial Filter Performed With Nonsymmetrical Fourier Transformers

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MULTIPLE MATCHED SPATIAL FILTER PERFORMED WITH NONSYMMETRICAL FOURIER TRANSFORMERSCARLOS FERREIRA and CARMEN VAZQUEZDepartamento de Optica. Universitat de Valencia.C/ Dr. Moliner, 50. 46100 Burjassot, Spain.1. INTRODUCTIONClassical matched spatial filters (CMSF) have been successfully employed for optical pattern recog-nition. To detect different signals, multiple matched spatial filters can be synthesized and several me-thods to perform the filters have been developed. Based on the sensitivity to input orientation of CMSF,we proposed a filter [1] where the signals to be detected were rotated by different angles when recordingthe hologram. Thus, the recognition of a signal is only achieved when the input in the filtering systemhas been suitably rotated. The number of signals simultaneously recorded was limited by the angular tole-rance of symmetrical correlators, of the order of ten degrees [2] for CMSF.In a recent paper [3], we presented a nonsymmetrical Fourier correlator, composed of two nonsymme-trical Fourier transformers (NFT) [4] in cascade, that reduces the angular tolerance shown by the symme-trical correlators, working with CMSF, to the order of four degrees depending, as in the previous case,on the structure and complexity of the input.The aim of this paper is to combine the NFTs with the method to perform the multiple matched filterdescribed in Ref[1] in order to increase, at least in a certain angular region, the number of signals towhich the filter can be matched. As the angular tolerance in nonsymmetrical systems is smaller than insymmetrical ones, the number of signals to be recorded with the filter proposed in this work can be in-creased in an angular sector of superresolved spatial frequencies.2. BASIC THEORYLet us suppose that we want to record a multiple filter matched to n characters si(xo,yo), rotatedto the angles Bi(i= 1,2,...,n). To perform that filter, the Fourier hologram of a transparency with thetransparent characters on dark background is recorded. The input can be written