Real-time processing of the multiple matrix product using an incoherent optical system

Dammann gratings-based truly parallel optical matrix multiplication accelerator

Matrix multiplication (MM) is a fundamental operation in various scientific and engineering computations, as well as in artificial intelligence algorithms. Efficient implementation of MM is crucial for speeding up numerous applications. Photonics presents an opportunity for efficient acceleration of dense matrix computation, owing to its intrinsic advantages, such as huge parallelism, low latency, and low power consumption. However, most optical matrix computing architectures have been limited to realizing single-channel vector-matrix multiplication or using complex configurations to expand the number of channels, which does not fully exploit the parallelism of optics. In this study, we propose a novel, to the best of our knowledge, scheme for the implementation of large-scale two-dimensional optical MM with truly massive parallelism based on a specially designed Dammann grating. We demonstrate a sequence of MMs of 50 pairs of randomly generated 4 × 8 and 8 × 4 matrices in our proof-of-principle experiment. The results indicate that the mean relative error is approximately 0.048, thereby demonstrating optical robustness and high accuracy.

Cross-talk analysis and reduction in fully parallel matrix-matrix multipliers

Analog optical processors that calculate a product of two matrices in a single clock cycle are analyzed for cross talk. It is determined that the sidelobes from the sinc function corresponding to the individual pixels of the spatial light modulator that encodes the first matrix are the main source of the cross talk. This cross talk can be reduced substantially by the use of an apodizing function for individual pixels of the spatial light modulator. This scheme for cross-talk reduction is verified by computer simulation. Initial experimental results are presented that demonstrate the gray-scale performance of the matrix-matrix multiplier as well as sidelobe suppression with apodization.

Modified direct twos-complement parallel array multiplication algorithm for complex matrix operation

A direct twos-complement parallel array multiplication algorithm is introduced and modified for digital optical numerical computation. The modified version overcomes the problems encountered in the conventional optical twos-complement algorithm. In the array, all the summands are generated in parallel, and the relevant summands having the same weights are added simultaneously without carries, resulting in the product expressed in a mixed twos-complement system. In a two-stage array, complex multiplication is possible with using four real subarrays. Furthermore, with a three-stage array architecture, complex matrix operation is straightforwardly accomplished. In the experiment, parallel two-stage array complex multiplication with liquid-crystal panels is demonstrated.

Fully parallel analog optical calculation of multiple outer products

An analog optical processor for evaluating weighted sums of outer products in parallel is described. It uses a linear array of light sources oriented along the diagonal, two-dimensional spatial light modulators to encode input vectors, a two-dimensional detector array to generate the output, and conventional spherical and cylindrical lenses. This system can be used to multiply two matrices as well as to evaluate a weighted rank-1 synthesis of images in a single clock cycle of the processor. Initial experimental results are presented, and factors limiting the performance are described. Implications of this architecture to optical signal- and image-processing systems are discussed.

Parallel multiple matrix multiplication using an orthogonal shadow-casting and imaging system

A novel orthogonal shadow-casting and imaging optical system is proposed for performing multiple matrix multiplication. An analysis is given for describing the construction of a matrix processor. Preliminary experiments of matrix multiplication are demonstrated.

Optical system for real-time multiplication of the multiple matrix with a 2-D light source array

An optical system for real-time multiplication of the multiple matrix is proposed. A 2-D light source array enables this system to perform a triple matrix multiplication without the unidirectional diffuser that was essential in the former system we proposed. The performance of this system is discussed based on a simplified model to show the guidelines for designing the system. The preliminary experiments of multiplying three 3 x 3 matrices are successfully carried out with a mean error of 2.0%. A method to multiply the multiple matrix with binary elements using our system is also shown.