Detection efficiencies of parallel, fan and cone beam collimators for source distributions in an attenuating medium

Fan-beam (FB) and cone-beam (CB) collimators have been applied in SPECT due to their improved trade-off between spatial resolution and detection efficiency when compared with conventional parallel-hole (PH) collimators. However, the advantages have usually been evaluated in the absence of attenuation and scatter. In this study, the authors studied the detection efficiencies of the three collimator geometries in more realistic imaging situations. Theoretical formulations were derived for the detection efficiencies of the three collimators for point and line sources placed in air and inside attenuating media with attenuation effect only. The effects of scatter were investigated using Monte Carlo simulation methods. For primary photons with and without attenuation effect, theoretical predictions agreed with results from Monte Carlo simulations. They indicate that for a point source, the relative detection efficiencies of FB and CB with respect to PH collimator at different depths in an attenuating medium are the same as those without attenuation. For a line source placed along the central axes of the collimators, the relative detection efficiencies of the FB and CB collimators are lower with attenuation than without. This is due to the increased attenuation effect at greater depths outweighing the increase in geometric efficiency. The addition of scatter does not significantly change the relative efficiencies for a line source. Finally, the signal-to-noise ratios of the FB and CB are higher than that of the PH collimator and the differences increase with source depth. The understanding of the relative detection efficiencies is important in evaluating potential clinical applications of the FB and CB collimators