General method to determine the position-charge relationship for position-sensitive detectors with variously shaped resistive anodes

A new approach using the Green function instead of the method of Fourier expansion is presented to determine the position-charge relationship for radiation detectors employing a charge division on the resistive anode bordered by an additional resistive line. The resistive anode with a polygonal shape is considered as a general case. Theoretical consideration shows that the position of radiation incidence in the position-sensitive detectors is represented in the integral form containing the Green function if the total charge generated in the detector is assumed to be collected over an infinite time. Anodes with the geometries of a triangle, square, circle or spherical triangle are described as practical shapes. It is shown that, when the shape of the anode is (spherical) triangular or square, the relationship between the position and charge is determined by a harmonic function obtained from a simple geometric consideration. (author)