Calculation of single detector efficiencies and extension of the normalization sinogram in PET

A fast iterative method is presented for calculating single detector efficiencies for positron emission tomographs. These efficiencies can be used to extend the normalization scan to areas outside that covered by the normalization source. The root mean square (rms) error of the calculated single detector efficiencies decreases exponentially with the number of iterations. Thirty iterations per normalization image are sufficient and take about 1 s on a SUN Classic. The geometry factors are composed of factors which only depend on the distance from the centre of the field-of-view (FOV) and of factors which show a more complex pattern over the normalization sinogram. The geometry factors are specific to each scanner. On the ECAT 931 scanner the complex part of the geometry factors showed a diamond shaped pattern (caused by the varying sensitivity of single detectors in a detector block with varying angle of incidence) and S-shaped curves (representing attenuation caused by supporting rods for the ring source). The coefficient of variation of the diamond-shaped pattern was 4% for detectors farthest from the centre of the FOV. Extensions of the normalization scan may, therefore, contain a relative rms error of about 4% if the applied geometry factors only take the distance from the centre of the FOV into account.