Noise limitations in optical linear algebra processors

Volterra series modeling of spatial light modulators

We present a multiple-input, single-output, weakly nonlinear model of spatial light modulators by use of a second-order Volterra series and describe an experimental method to measure the nonlinear transfer functions by means of sinusoidal perturbation and synchronous detection with a lock-in amplifier. We also present an application of this method to a liquid-crystal light valve.

Temporal intensity noise characteristics and discrete numeric accuracy of analog liquid-crystal-based spatial light modulators

We investigate the temporal intensity noise characteristics of analog liquid-crystal-based spatial light modulators and how they affect the device's achievable discrete numeric accuracies in an optical computing system. First we present an analytical development that defines the concept of precision in analog computing systems, then we define a noise metric and a precision-optimal quantizer for determining the discrete numeric characteristics of the devices. Second we present an experimental discussion in which a low-noise test facility constructed for this investigation is described, and the noise characteristics of three commercially available liquid-crystal-based modulators are measured and analyzed. The accuracy implications of this measured noise are then discussed within the context of the analytical model for each modulator.

Matrix-vector multiplication using digital partitioning for more accurate optical computing

Digital partitioning offers a flexible means of increasing the accuracy of an optical matrix-vector processor. This algorithm can be implemented with the same architecture required for a purely analog processor, which gives optical matrix-vector processors the ability to perform high-accuracy calculations at speeds comparable with or greater than electronic computers as well as the ability to perform analog operations at a much greater speed. Digital partitioning is compared with digital multiplication by analog convolution, residue number systems, and redundant number representation in terms of the size and the speed required for an equivalent throughput as well as in terms of the hardware requirements. Digital partitioning and digital multiplication by analog convolution are found to be the most efficient algorithms if coding time and hardware are considered, and the architecture for digital partitioning permits the use of analog computations to provide the greatest throughput for a single processor. To our knowledge this is the first study to propose the use of digital partitioning for optical matrix processing.