Our Monte Carlo simulation code was then used to model gamma interactions occurring at different depths in the scintillator and to generate light pulses to be recorded by a photodetector. In this work, all parameters were chosen to simulate a LSO crystal as employed in the experimental setup used for validation. The bulk LSO material was modelled with an index of refraction of 1.82, an absorption length of 300 mm and a scattering length of 256 mm (Rothfuss et al., 2004 ). For each gamma interaction, the energy of the interaction was randomly selected following a distribution derived from an energy spectrum measured with a 2 × 2 × 20 mm3 LSO polished (Figure 2 ).
The corresponding number of scintillation photons was then calculated assuming a light yield of 25 photons/keV (Moszynski et al., 1997 ). The measured energy distribution accounts for the statistical variation introduced by the light yield of the scintillator and the quantum efficiency of the detector. We considered only photoelectric effect and Compton scattering. For each gamma interaction visible photons were emitted isotropically, creating a light pulse. The fate of these individual photons was tracked. Appropriate wavelength and time of emission for each photon were assigned based on scintillator properties. Scintillators produce light pulses with an exponential decay (~40 ns for LSO)(Melcher and Schweitzer, 1992 ), thus the emission times assigned to individual photons followed an exponential distribution with a 40 ns decay. Scintillator rise time was ignored. The emission spectrum of LSO was measured on crystals from the same bulk material as that used for experiments with time resolved fluorescence spectroscopy (TRFS) (Yang et al., 2009 (link)). The wavelength of the photons generated was selected by randomly sampling the measured emission spectrum.
On encountering the edges of the scintillator, photons may be reflected or transmitted (Figure 3a ). If a photon reaches the scintillator/photodetector boundary, it may be transmitted and detected, or reflected. A fraction of photons also escapes the crystal. The photodetector was modelled by its quantum efficiency spectrum. For the simulations presented here, the quantum efficiency (QE) of a Hamamatsu R6231 PMT was used. The size of the photodetector was set to match the size of the crystal. The reflection properties of the crystal surfaces were modelled using the LUTs computed from the AFM surface measurements. One end of the crystal was modelled as a polished surface in contact with optical grease (index of refraction 1.5) whereas all the other faces were modelled in contact with air (both in the case of an external reflector such as Teflon tape and no reflector) and either polished or rough depending on the type of crystal simulated. In some simulations, an external diffuse reflector was modelled by its reflection coefficient of 0.97, corresponding to a diffuse reflector such as Teflon tape. This reflector was assumed to be Lambertian and so the direction of reflected photons followed a Lambertian distribution. Photons were refracted when they re-entered the crystal. Arrival times and wavelengths of detected photons were recorded and used to generate simulated light pulses and spectra.
Different configurations were investigated: 2 × 2 × 20 mm3 and 5 × 5 × 20 mm3 “rough” crystals (ground finish surfaces) were simulated without and with reflector using the LUTs computed from the “rough” surface samples measured on such crystals. 2 × 2 × 20 mm3 LSO polished crystals were also simulated. For each crystal, 500 light pulses were generated in 1.5 mm bins at five different depths every 4 mm starting 2 mm away from the photodetector face that is at 0 mm. At each depth, the energies were histogrammed and the photopeak positions were extracted from the energy spectra to characterize the light output variation with depth. The maximum light output was defined as the photopeak position at the irradiation depth closest to the photodetector, 2 mm. All maximum light output values were normalized by the maximum light output of the polished crystal with reflector (expected to be the highest).
The corresponding number of scintillation photons was then calculated assuming a light yield of 25 photons/keV (Moszynski et al., 1997 ). The measured energy distribution accounts for the statistical variation introduced by the light yield of the scintillator and the quantum efficiency of the detector. We considered only photoelectric effect and Compton scattering. For each gamma interaction visible photons were emitted isotropically, creating a light pulse. The fate of these individual photons was tracked. Appropriate wavelength and time of emission for each photon were assigned based on scintillator properties. Scintillators produce light pulses with an exponential decay (~40 ns for LSO)(Melcher and Schweitzer, 1992 ), thus the emission times assigned to individual photons followed an exponential distribution with a 40 ns decay. Scintillator rise time was ignored. The emission spectrum of LSO was measured on crystals from the same bulk material as that used for experiments with time resolved fluorescence spectroscopy (TRFS) (Yang et al., 2009 (link)). The wavelength of the photons generated was selected by randomly sampling the measured emission spectrum.
On encountering the edges of the scintillator, photons may be reflected or transmitted (
Different configurations were investigated: 2 × 2 × 20 mm3 and 5 × 5 × 20 mm3 “rough” crystals (ground finish surfaces) were simulated without and with reflector using the LUTs computed from the “rough” surface samples measured on such crystals. 2 × 2 × 20 mm3 LSO polished crystals were also simulated. For each crystal, 500 light pulses were generated in 1.5 mm bins at five different depths every 4 mm starting 2 mm away from the photodetector face that is at 0 mm. At each depth, the energies were histogrammed and the photopeak positions were extracted from the energy spectra to characterize the light output variation with depth. The maximum light output was defined as the photopeak position at the irradiation depth closest to the photodetector, 2 mm. All maximum light output values were normalized by the maximum light output of the polished crystal with reflector (expected to be the highest).
