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This paper introduces a mathematical model to evaluate fast and cost-effective 3D image sensors based on single photon detectors. The model will help engineers evaluate design parameters based on operating conditions and system performance. Ranging is based on the time-of-flight principle using TCSPC techniques. Two scenarios are discussed: (i) short-distance range indoors and (ii) medium-distance range outdoors. The model predicts an accuracy of 0.25cm at 5m with 0.5W of illumination and 1klux of background light. In the medium-range scenario, a precision of 0.5cm is predicted at 50m with 20W of illumination and 20klux of background light.