A biologically inspired compound-eye detector array - Part I: Modeling and fundamental limits

This is the first part of a two-part paper. In this paper, we propose a detector array for detecting and localizing sources that emit particles including photons, neutrons, or charged particles. The array consists of multiple "eyelets." Each eyelet has a conical module with a lens on its top and an inner subarray containing multiple particle detectors. The array configuration is inspired by and generalizes the biological compound eye: it is spherically shaped and has a larger number of detectors in each individual eyelet. Potential applications of this biomimetic array include artificial vision in medicine (e.g., artificial eyes for the blind) or robotics (e.g., for industry or space missions), astronomy and astrophysics, security (e.g., for radioactive materials), and particle communications. In this part, we assume Poisson distribution for each detector's measurement within the observation time window. Then we construct a general parametric model for the detection rate of the Poisson-distributed measurements illustrated by a circular Gaussian lens-shaping function (LSF) approximation, which is commonly used in optical and biological disciplines. To illustrate how this "prototype" model fits practical cases, we apply it to an example of localizing a candle from 20 miles away and estimating the parameters under this circumstance. In addition, we also discuss the hardware setup and performance measure of the proposed array, as well as its fundamental constraints. Part I forms the theoretical basis for Part II, in which we analyze the performance of the array, both analytically and numerically.