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In this paper, the problem of detecting far-field particle sources, such as nuclear, radioactive, optical, or cosmic, is considered. This problem arises in applications including security, surveillance, visual systems, and astronomy. The authors propose a mean-difference test (MDT) with cubic and spherical detector arrays, assuming Poisson distributed measurement models. Through performance analysis, including computing the probability of detection for a given probability of false alarm, the authors show that the MDT has a number of advantages over the generalized likelihood-ratio test (GLRT), such as computational efficiency, higher probability of detection, asymptotic constant false-alarm rate (CFAR), and applicability to low signal-to-noise ratio (SNR). For each array, the authors also present an estimator to find the source direction. Finally, Monte Carlo numerical examples are conducted that confirm the analytical results.