We analyze the performance of a novel detector array for detecting and localizing particle emitting sources. The array is spherically shaped and consists of multiple "eyelets," each having a conical shape with a lens on top and a particle detectors subarray inside. The array's configuration is inspired by and generalizes the biological compound eye: it has a global spherical shape and allows a large number of detectors in each eyelet. The array can be used to detect particles including photons (e.g. visible light, <i>X</i> or γ rays), electrons, protons, neutrons, or α particles. We analyze the performance of the array by computing statistical Cramer-Rao bounds on the errors in estimating the direction of arrival (DOA) of the incident particles. In numerical examples, we first show the influence of the array parameters on its performance bound on the mean-square angular error (MSAE). Then we optimize the array's configuration according to a min-max criterion, i.e. minimize the worst case lower bound of the MSAE. Finally we introduce two estimators of the source direction using the proposed array and analyze their performance, thereby showing that the performance bound is attainable in practice. Potential applications include artificial vision, astronomy, and security.