Streamlining ICI Transformed as a Nonnegative System - David Hyland (Photonics)
More than seventy-five years ago, R. Hanbury Brown and R. Q. Twiss performed the first experiments in quantum optics. At the outset, their results showed great promise for the field of astronomical science, featuring inexpensive hardware, immunity to atmospheric turbulence, and enormous interferometry baselines. This was put to good use for the determination of stellar diameters up to the present time. However, for two-dimensional imaging with faint objects, the integration times are prohibitive. Recently, in a sequence of papers, the present author developed a stochastic search algorithm to remove this roadblock, reducing millions of hours to minutes or seconds. Also, the author’s paper entitled “The Rise of the Brown-Twiss Effect” summarized the search algorithm and emphasized the mathematical proofs of the algorithm. The current algorithm is a sequence of six lines of code. The goal of the present article is to streamline the algorithm in the form of a discrete-time dynamic system and to reduce the size of the state space. The previous algorithm used initial conditions that were randomly assorted pixel intensities. The intensities were mutually statistically independent and uniformly distributed over the range <semantics><mfenced close=")" open="[">0,δ</mfenced></semantics>, where <semantics>δ</semantics> is a (very small) positive constant. The present formulation employs a transformation requiring the uniformly distributed phase of the fast Fourier transform of the cross correlations of the data as initial conditions. We shall see that this strategy results in the simplest discrete-time dynamic system capable for exploring the alternate features and benefits of compartmental nonnegative dynamic systems.