Abstract

Volume holograms provide the possibility for very high density storage of the interconnecting weights in an optical neural computer. The number of connections that can be stored in a hologram of volume V can approach N³ = O(V/λ³). We have shown previously how N^3/2 out of N² pixels can be selected as fractal sampling grids at the input and output planes so that all connections can be independently implemented by the volume hologram. We derive the sampling grids for arbitrary N^d→N^3–dmappings for any 1 ⪯ d ⪯ 2, and we extend these ideas to the use of volume holograms for the implementation of local connectivity. If each pixel in a 2-D array of M units is to be arbitrarily interconnected to its C neighbors, the total number of connections is MC. We show that the volume required for the implementation of the local connectivity scheme we describe is O(MC).

© 1988 Optical Society of America