A simple mathematical method to determine the efficiencies of log-conical detectors

A new type of photon detector, log-conical, is proposed. The average path length traveled by an incident photon of arbitrary energy as well as the geometrical solid angle are calculated in a mathematical expression to determine the efficiencies of this detector for an arbitrarily positioned isotropic radiating point source. The off-axis effect of the source position was analyzed to demonstrate the powerful capability of the proposed method. The results are compared with those obtained using a standard 3″×3″ cylindrical detector of the same volume in order to show the enhanced efficiency of the log-conical detector.