Multi-layer opto-electronic neural network

A method for storing (K) Fourier-space holograms within a volume holographic medium, comprising the steps of, for K Fourier-space holograms .nu..sup.(k,i) (k=1,2, . . . , N):

• loading a weight vector .nu..sup.(k,n) into a spatial light modulator means using a predetermined and fixed lexicographic ordering scheme;
• spatially modulating a first plane-wave laser beam in accordance with the loaded weight vector;
• multiplying a light pattern transmitted by the spatial light modulator means in accordance with a random, two-dimensional phase encoding function;
• applying the phase-encoded light pattern, with a first Fourier transform lens means, to approximately a midpoint of the volume holographic medium so as to generate, at the midpoint, a Fourier transform of the phase-encoded light pattern while simultaneously applying a second plane-wave laser beam, which is temporally coherent with the first plane-wave laser beam, so as to illuminate the medium at an angle .psi..sub.k to a z.sub.2 -axis of the medium and within a x.sub.2-z.sub.2 plane;
• forming a weight vector hologram .nu..sup.(k) within the medium;
• changing the angle .psi..sub.k to an angle .psi..sub.(k+1) ;
• and
• repeating the preceding loading, spatially modulating, multiplying, applying, forming, and changing steps for each k=1,2, . . . , K until all .nu..sup.(k) have been stored in the medium.

A method for generating vector inner products (.function..sub.k.sup.(i)) for accomplishing pattern recognition, comprising the steps of:

• loading an unknown pattern vector .sigma..sup.(i) (i=1,2, . . . , N) into a spatial light modulator means using a same pre-determined and fixed lexicographic ordering scheme that was initially employed to store a weight vector .nu..sup.(k,i) (k=1,2, . . . , K;
• i=1,2, . . . , N) template into a volume holographic medium;
• spatially modulating a first plane-wave laser beam in accordance with the unknown pattern vector;
• employing a phase encoder means to multiply the spatially modulated first plane-wave laser beam by a random, two-dimensional phase encoding function;
• transmitting a phase encoded light pattern representative of the multiplied spatially modulated first plane-wave laser beam from the phase encoder means to a first Fourier transform lens means;
• generating within the volume holographic medium, with the first Fourier transform lens means, a Fourier transform of the phase encoded light pattern;
• generating, within the volume holographic medium, an angular spectrum of plane waves having amplitudes proportional to vector inner products .sigma..sup.(i) .cndot..nu..sup.(k,i) (k=1,2, . . . , K;
• i=1,2, . . . , N) and propagation angles of .psi..sub.k (k=1,2, . . . , K) which correspond to reference angles .psi..sub.k of a plane-wave coherent optical signal;
• focusing onto a detector means, with a second Fourier transform lens means, plane waves of the angular spectrum of plane waves generated within the volume holographic medium;
• reading out, from the detector means, signals representing vector inner products corresponding to the plane waves focused upon the detector means;
• serially and nonlinearly processing the output of the detector means;
• temporarily storing the nonlinearly processed output of the detector means;
• feeding the temporarily stored output of the detector means back into the spatial modulating means for further neural network processing as input signals of a next pattern vector .sigma..sup.(i+1) and reading out the temporarily stored output of the detector means as pattern recognition results.