Optical implementation of an iterative algorithm formatrix inversion.

A confocal Fabry-Perot processor, with coherent image amplification provided by a photorefractive BaTiO(3) crystal in the feedback path, is analyzed and implemented to perform the iterative algorithm based on the relation B(-1) = (I - A)(-1) = (infinity)Sigma(k=0) A(k), where B is the matrix to be inverted and I is the identity matrix. Both A and B are large size matrices. When the feedback loop contains a coherent matrix-vector multiplier (AX) and the input vector is sequentially scanned from one element to another, the columns of B(-1) can be sequentially generated at the output. The photorefractive BaTiO(3) amplifier provides loss compensation and coherence restoration of the feedback signal, thereby increasing the effective number of iterations in the algorithm. Thus it becomes possible to use this technique to implement slowly (as well as rapidly) converging algorithms. Experimental verification of the matrix inversion algorithm is presented, along with an analysis of possible real-time operations.

[1]  J W Goodman,et al.  Performance limitations of an analog method for solving simultaneous linear equations. , 1982, Applied optics.

[2]  Sing H. Lee,et al.  Two-stage injection-locked ring dye laser/amplifier for coherent image amplification , 1984 .

[3]  Jack N. Cederquist,et al.  Coherent optical feedback for the analog solution of partial differential equations , 1980 .

[4]  Sing H. Lee,et al.  The use of feedback in optical information processing , 1979 .

[5]  J. Cederquist.  Integral-equation solution using coherent optical feedback , 1981 .

[6]  Y. Fainman,et al.  Optimal coherent image amplification by two-wave coupling in photorefractive BaTiO3 , 1986 .

[7]  James R. Leger,et al.  A Microcomputer-Based Hybrid Processor At The University Of California, San Diego , 1982 .

[8]  I. Ledoux,et al.  Two-wave mixing and energy transfer in BaTiO3 application to laser beamsteering , 1984 .

[9]  S. H. Lee,et al.  Solution of linear and nonlinear equations by optical methods. , 1984, Applied optics.

[10]  Marvin B. Klein,et al.  Optimal Properties Of Photorefractive Materials For Optical Data Processing , 1983 .

[11]  Jack Feinberg,et al.  Asymmetric self-defocusing of an optical beam from the photorefractive effect , 1982 .

[12]  N. Bojarski.  The far field in terms of the spatial Fourier transform of the sources and its implications on the inverse problem , 1985 .

[13]  Henri Rajbenbach,et al.  Two‐beam coupling in photorefractive Bi12SiO20 crystals with moving grating: Theory and experiments , 1985 .