Optoelectronic implementation of a 256-channel sonar adaptive-array processor.

We present an optoelectronic implementation of an adaptive-array processor that is capable of performing beam forming and jammer nulling in signals of wide fractional bandwidth that are detected by an array of arbitrary topology. The optical system makes use of a two-dimensional scrolling spatial light modulator to represent an array of input signals in 256 tapped delay lines, two acousto-optic modulators for modulating the feedback error signal, and a photorefractive crystal for representing the adaptive weights as holographic gratings. Gradient-descent learning is used to dynamically adapt the holographic weights to optimally form multiple beams and to null out multiple interference sources, either in the near field or in the far field. Space-integration followed by differential heterodyne detection is used for generating the system's output. The processor is analyzed to show the effects of exponential weight decay on the optimum solution and on the convergence conditions. Several experimental results are presented that validate the system's capacity for broadband beam forming and jammer nulling for linear and circular arrays.

Spatio-temporal operator formalism for holographic recording and diffraction in a photorefractive-based true-time-delay phased-array processor.

We present a spatio-temporal operator formalism and beam propagation simulations that describe the broadband efficient adaptive method for a true-time-delay array processing (BEAMTAP) algorithm for an optical beamformer by use of a photorefractive crystal. The optical system consists of a tapped-delay line implemented with an acoustooptic Bragg cell, an accumulating scrolling time-delay detector achieved with a traveling-fringes detector, and a photorefractive crystal to store the adaptive spatio-temporal weights as volume holographic gratings. In this analysis, linear shift-invariant integral operators are used to describe the propagation, interference, grating accumulation, and volume holographic diffraction of the spatio-temporally modulated optical fields in the system to compute the adaptive array processing operation. In addition, it is shown that the random fluctuation in time and phase delays of the optically modulated and transmitted array signals produced by fiber perturbations (temperature fluctuations, vibrations, or bending) are dynamically compensated for through the process of holographic wavefront reconstruction as a byproduct of the adaptive beam-forming and jammer-excision operation. The complexity of the cascaded spatial-temporal integrals describing the holographic formation, and subsequent readout processes, is shown to collapse to a simple imaging condition through standard operator manipulation. We also present spatio-temporal beam propagation simulation results as an illustrative demonstration of our analysis and the operation of a BEAMTAP beamformer.