dinate z, the source was placed at the centre of the AFOV(zsrc =0 mm), or at the distance of three-eights of the AFOVlength from the centre of the scanner(zsrc = 187.5 mm). For the transverse direction, x coordinate was defned at xsrc = 10 mm, 100 mm and 200 mm with y always at ysrc =0 mm. Only subsample of simulated events (pairs of hits) was selected for the re-construction, fulflling selection criteria requiredfor true coincidences, which include scattering flters and energy thresholds applied (see detailed description in Refs.[6, 16]).At least 150000 eventswere used for the reconstruc

tion, for each sourceposition. The data include coordinates and times of hits inside the strips for each photon pair, i.e. (x1,y1,z1,t1,x2,y2,z2,t2). The tests, described in this article, encompasses three cases (for the smearing applied): assuming the spatial resolution in axial direction to be σz =2 mm, 5 mm or 10 mm, whilst for the time of hit being fxed at σt = 80 ps (corresponding to σz = 10 mm[7]). The latter was chosen intentionally to test the worst possible case of time of fight (TOF) taken into account. Thus3D sinogram couldbe composed, collecting linesof response (LOR) with TOF information optionally used for each event[20]. 3. Reconstruction procedure The reconstruction of the 3D image of the source, selectedfor the simulations, is essential for the estimation of spatial resolution of PET detectors, which is characterized by the so-called Point Spread Function (PSF). It is defnedasthe widthofthe reconstructed profleofapoint source, measured similarly to FWHM along three principal axes[20]. 3.1. FBP algorithm Fora general2D case, FBP algorithm, based on theinverse Radontransformation[21], canbe defned as mapping fltered sinogram pF(s, φ) by an operator X∗, which returns an image f(x, y) Zπ F f(x, y)= � X ∗ p (x, y)= dφpF(s = x cos φ + y sin φ, φ) , (1) 0 where pF(s, φ) is obtainedbyapplying an apodized ramp flter h(s) on the initial sinogram p(s, φ) [20] ZRF �� 00 p F(s, φ)= dsp s 0,φ h s − s. (2) −RF Here, RF denotes the radius of the feld of view (FOV). In reality, scanner geometry requires sinogram variables (displacement s and angle φ)tobe mapped onto discrete pairs(si,φi). Furthermore, it trans- F forms(1)intoa sum, containing functionspi (s = x cos φ+y sin φ, φi). Here, F pi (s, φi) canbe derived foranyarbitrary Cartesian pair (x, y) that defnes unmapped s, usinglinear interpolationbetween pF(sk,φi) and pF(sk+1,φi), calculated for two “known” neighbours sk and sk+1 (sk