Optical generation of random numbers: theory and experiments
Anthony J. Martino, G. Michael Morris
Simulation of physical processes and Monte Carlo solutions to numerical problems on digital computers require sources of random numbers that follow specified density functions. In our experiments, the spatial coordinates of detected photoevents are used as a fast source of true random numbers to solve numerical problems by the Monte Carlo method. The probability density function for the location of a photoevent on the detector surface is proportional to the irradiance. We have constructed an optical random number generator using a microchannel plate detector with a resistive anode. It can produce bivariate random deviates with any probability density and any correlation between the two variables. The numbers pass the standard tests for randomness and fit to the given distributions (chi-square, correlation, sequence tests). Nonuniform distributions can be obtained with no loss of speed by manipulating the irradiance distribution across the detector, e.g., by imaging a transparency onto it. In particular, we have produced uniformly distributed random numbers and normally distributed random numbers with various correlations between the variables. We have also used the optical random number generator to find approximate solutions to systems of large linear algebraic equations and approximations to the inverses of large matrices, with a maximum error of <5%.
Annual Meeting Optical Society of America•Jan 1, 1985•1 citation