site 30 and the first stricken crystal 34 shown in the figure as u201c a u201d fig4 shows the projection of the lever on the axial plane the projection of the lever length is shown as u201c a u2032 u201d and the distance between the annihilation site 30 and the first stricken crystal 34 is shown as u201c a u2032 u201d the axial projection of the lever arm fraction which will also be referred to as the u201c lever arm projection u201d is defined as f a u2032 a u2032 the axial conditional probability for the geometry shown in fig3 and 4 is determinable on the basis of a single geometric parameter namely f the axial projection of the lever arm fraction this parameter is shared by all voxels that are in a particular voxel column 29 recognition of this symmetry significantly reduces the computational and storage burden associated with obtaining the axial conditional probability for all the voxels in the region of interest as a result of this symmetry it is possible to obtain for each pair of crystal columns 26 28 an axial conditional probability associated with every voxel in a particular voxel column 29 the elements of the three dimensional geometric system response matrix can thus be viewed as solid angles each of which is a product of an axial angle and a trans axial angle the trans axial angle is the corresponding element of the two dimensional geometric system response matrix the axial angle depends only on f and on a scale factor that corresponds to the apparent size of the scintillation crystal as viewed from the annihilation site a particular element g ij 3d of the three dimensional geometric system response.