Position Error Correction Using Homography in Discretized Positioning Circuit for Gamma-Ray Imaging Detection System

A discretized positioning circuit (DPC) based on a resistive network has been developed to reduce the size of a gamma-ray detection system using multi-anode photomultiplier tubes (MA-PMT) in an array, because it can drastically decrease the number of output channels. The output signal from the gamma-ray detection system is a current pulse generated in each tube that contains information about the gamma-ray energy and detecting position in the array. The output current pulse is distributed to four outputs according to the resistance ratio of the resistive network in the DPC, and the detected position is estimated using the height values of the four distributed current pulses. However, owing to parasitic capacitors of MA-PMT connected in parallel to resistors in the resistive network, the four output pulses are affected by the RC time constants. In particular, when the duration of the input signal is not long enough, the height values of the distributed pulses are reduced, and thereby the position error increases significantly. In this paper, we present a new distortion correction method that considers the pulse duration and the RC time constant. In order to correct the position error, we employed homography, which is a coordinate transformation method. The ideal grid was mapped to a new grid for the distorted position. Using this method, error correction was completely achieved, even for short current pulses.