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The current trend in positron emission tomography (PET) towards very high spatial resolution tomographs raises the problem of detecting high energy gamma-rays with a high spatial accuracy while preserving the overall sensitivity of the camera. It is the purpose of this paper to investigate the effects of some geometrical parameters on the detection efficiency and intrinsic spatial resolution of a circular array of narrow closely packed detectors. Two approaches were employed: the first one uses the Monte-Carlo technique to simulate the interactions of gamma-rays in the detectors; the second one is based on the linear attenuation on a beam of gamma-rays impinging on a detector array. Aperture functions and modulation transfer functions were obtained for various configurations of the detectors and septas. Expressions for the resolution and the spectral signal-to-noise ratio were derived. It is shown that minor modifications to the geometry can improve both the efficiency and intrinsic resolution of the detector array.