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= Photon Capture =
= Photon Capture and Detection =
[[Image:BCF10,20,98_comp.png|frame]]
[[Image:BCF10,20,98_comp.png|frame]]
Taking the accepted photon yield in plastic scintillator to be 8000γ/MeV, the following considerations control the total photon capture:
Taking the accepted photon yield in plastic scintillator to be 8000γ/MeV, the following considerations control the total photon capture and detection:
* taking the energy deposition in plastic (~1 <math>g/cm^3</math>) to saturate at ~2 MeV/cm with 2 cm length of scintillator yields 4 MeV
* taking the energy deposition in plastic (~1 <math>g/cm^3</math>) to saturate at ~2 MeV/cm with 2 cm length of scintillator yields 4 MeV
* The critical angle in multi-clad BCF scintillating fibers is 27.4<sup>o</sup> C resulting in forward capture of 5.6%
* The critical angle in multi-clad BCF scintillating fibers is 27.4<sup>o</sup> C resulting in forward capture of 5.6%
* Lastly, frequency-dependent efficiency functions must be taken into account. Using nominal efficiency specifications, SiPM PDE distribution weighted by scintillator (BCF-10 or BCF-20) emission and BCF-98 waveguide transmission spectra is integrated over all wavelengths. These distributions are shown in adjacent figures.
* Frequency-dependent efficiency functions must be taken into account. Using nominal efficiency specifications, SiPM PDE distribution weighted by scintillator (BCF-10 or BCF-20) emission and BCF-98 waveguide transmission spectra is integrated over all wavelengths. These distributions are shown in adjacent figures.
* Assuming for simplicity a uniform light beam profile emerging from the waveguide, the output is rescaled according to active area available on the SiPM (e.g. 1 mm<sup>2</sup> for Hamamatsu MPPC compared to 4 mm<sup>2</sup> waveguide cross-section)
* Correction introduced for the saturation effect of the firing pixel population. When an appreciable fraction of available pixels are firing, the possibility of a photon hitting a firing pixel can no longer be neglected. This can be expressed as hollows:
<p align="center"><math>N_{fired} = N_{total}\left(1 - e^{\frac{-N_\gamma \cdot PDE}{N_{total}}}\right)</math></p>
{| class="wikitable" style="text-align:center" border="1" cellspacing="0" cellpadding="4"
{|border="0"
|
{| class="wikitable" align="center" style="text-align:center" border="1" cellspacing="0" cellpadding="4"
|+ Actual number of pixels fired
|-
|-
! !! BCF-10 !! BCF-20
! !! BCF-10 !! BCF-20
|-
|-
|'''SSPM~06''' || 192 || 393
|'''SSPM~06''' || 192 || 393
|}
|
| style="text-align:center" |Leading to<br>time resolution:
|
|
{| class="wikitable" align="center" style="text-align:center" border="1" cellspacing="0" cellpadding="4"
|+ Time resolution (ps)
|-
! !! BCF-10 !! BCF-20
|-
|'''MPPC''' || 201 || 221
|-
|'''SSPM~06''' || 195 || 136
|}
|}
|}