Theoretical study of three-dimensionally position-sensitive scintillation detector based on continuous crystal

In the field of nuclear imaging (PET, Compton camera, etc.) the application of detectors that are position sensitive in all the three dimensions could increase spatial resolution of images by avoiding the parallax error. In the present paper the viability of a three-dimensionally position-sensitive scintillation detector using continuous scintillator crystal is theoretically studied. The feasibility of building such a detector is based on the recognition that both the spatial position and the radiant flux of a point-like isotropic radiation source can be determined by performing flux density measurements at four appropriately selected points of the space. On the basis of this one can construct a position-sensitive scintillation detector where the scintillation crystal is surrounded with four or more photodetectors, supposing that the point of interaction (POI) of the gamma ray within the scintillator could be considered as a point-like isotropic light source. The POI coordinates can then be determined relying on the finding that the ratio of two arbitrary linear combinations of the photodetector responses is equal to the same ratio constructed from the solid angles subtended by the photodetectors as seen from the POI. The results of theoretical calculations describing the relations between the photodetector responses and the spatial coordinates of the POI are presented for three different photodetector–scintillator combinations.