Positron Detection: LYSO screens

Potential Upgraded LYSO (0.5mm x 0.5mm pixel; 10mm long)

light-collection efficiency and SNR for single ~GeV positron light_collection.pdf
ATTENTION: the formula for the light-collection efficiency is wrong:
I assumed 1.1 x 10^-3 for the light-collection efficiency:
- move the camera closer (500 mm instead of 760mm)
- use a lens with f=0.95 (Navitar)
- assume that the light is reflected from the back side due to ESR (2pi instead of 4pi emission)
- pi (0.95*50mm/2)^2 / (2pi* (500mm)^2) = 1.1 x 10^-3

Camera: Hamamatsu Orca Flash 4.0 camera (https://www.hamamatsu.com/eu/en/product/cameras/cmos-cameras/C13440-20CU.html)
Lens specifications: 50mm focal length
Magnification factor: lower end of ruler (pixel 1864) 140mm marker: (pixel 345): 1 pixel (6.5 micrometer) ↔ (140 mm / (1864-345)): M = 140 mm / ((1864-345) * 6.5 micrometer) = 14.18
Distance screen to lens: s; distance lens to sensor: s': thin-lens formula: 1/s + 1/s' = 1/f
Magnification: M = s/s' = (s/f - 1) → s = 50mm (14.18 + 1) = 760 mm
LYSO dimensions: 2mm x 2mm → imaged to (2mm / (14.18*6.5 micrometer))^2 ~ 471 pixel
We gain a factor of 16 if we reduce the crystal size to 0.5mm x 0.5mm
Light collection efficiency (lower estimate; doesn't take directionality of the emission into account; f-number: 1.2): pi (50mm / (2*1.2))^2 / (2 pi * (760 mm)^2) ~ 3.8 x 10^-4

LYSO1 seems to have a defect around some pixels, so only LYSO2 was used for analysis.

Experimental setup (all measurements made in tunnel):

dy = 67.36mm; obtained by using distance from PDC downstream pipe center and zero dispersion axis from PDC CAD model
d_nom = 24.81 mm; obtained from d_nom at DTOTR1 (Spectrometer Energy Calibration) linearly scaled to LYSO2 z-position

Positron energy spectrum calculation steps:

Images of LYSO screens were collected by camera and averaged over shots (3000 shots for 0.1mm Al foil, 100 shots for 1mm Pb glass)
For background subtraction details, see presentation above
Images are projected along non-dispersion (x) axis to give plot of y position [px] vs counts per px
px is converted to mm on both axes using resolution ~5.63 px/mm (calculated by comparing screen size on image to physical measurements made in tunnel)
Horizontal axis is converted from mm to GeV using the formula:

(All energies are in GeV)

Vertical axis is converted from counts per mm (dN/dy) to counts per GeV by chain rule:

GEANT4 simulation for Al used to calibrate from counts per GeV to positrons per GeV (Pb simulation is linearly scaled up by 3x to match data).

(dotted lines represent part of spectrum where significant number of positrons are obstructed by the ceiling of the dipole exit window)

For 0.1mm Al foil data in the 2.5 GeV to 3.5 GeV range, total camera counts (14889 counts) are compared with the number of positrons from the simulation (1048 positrons) to give experimental calibration value of ~14 counts/positron.
Assuming dy is accurate to +/-1cm and d_nom is accurate to +/-7%, calibration value is accurate to +/- 2 counts per positron

Final experimental sensitivity: 14 +/- 2 counts per positron.