Calibration of a PET detector module that measures depth of interaction

We investigate two in situ calibration techniques (using gamma rays incident from the patient side) for PET detector modules that measure interaction depth via an analog ratio. For each crystal element in the camera, we need to determine two unknowns: the gain ratio K of the two detector (PMT and PD) signals and the depth dependence α of the signals (defined as the ratio of the signal observed when the crystal is excited at the end closest to and furthest from the detector). The light collection is assumed to be linearly dependent on distance from the detector end, in agreement with experimental results. The first method extracts K and α using (a) the ratio of the PMT and PD signals for interactions that occur in the detector end closest to the patient (the most probable depth) and (b) the shape of the PMT pulse height distribution which reflects the exponential attenuation length in the detector. The second method utilizes the fact that E=PD+PMT (the total energy estimator) is independent of Γ=PD/(PD+PMT) (the depth estimator) when K is correct, with a distribution position that is α dependent. On simulated data, both the gain ratio and depth dependence are determined with errors of 3% rms and 2% rms respectively, resulting in minimal degradation of energy and depth resolution