  Aim: Investigate whether a time walk assessment derived from crystal light
sharing and multi-photon time stamps can improved the TOF resolution.
  Method: Monte Carlo simulations were performed for SiPM (FBK-NUV-HD) coupled
to conventional 4x4 mm2 pixelated LSO (0.2%Ca:Ce ) and also coupled to 8x4 mm2
pixelated LSO in which a triangular optical window allows light sharing between
the two 4x4 mm2 sub-pixels depending on the DOI. A time walk estimation was
modelled as a DOI dependent weighted sum of the time differences within the
photons detection sequence. The DOI dependent weights were optimized in order
to get the best TOF resolution.
  Results: A strong linear DOI dependence of the light sharing between the two
4x4 mm2 sub-pixels was observed. The TOF resolutions for a 4x4x20 mm3 LSO were
99.7, 81.2, 66.4 ps-fwhm without any correction, with DOI correction and with
DOI dependent time walk correction, respectively. The time walk correction was
derived from the 7 time stamps of the (2**k )th photons in the sequence, with k
within[0,6].
  Conclusion: photon time walk can be estimated from the photon time detection
series and can be advantageously combined with the DOI assessment to improve
TOF resolution.
