In what cases we need external position estimation ? Alexandre Chekhtman NRL/GMU

1. Gamma-ray Large Area Space Telescope In what cases we need external position estimation ? Alexandre Chekhtman NRL/GMU

2. “Normal” single crystal energy reconstruction • We have the measured adc signal for both ends of crystal: • adcP and adcM • We subtract pedestals and correct for nonlinearity by converting to DAC scale (using charge injection calibration): • dacP=adc2dac(adcP-pedP) • dacM=adc2dac(adcM-pedM) • We calculate the energy estimator based on the data from each crystal end, considering that energy is deposited in the crystal center: • ctrEneP=MeVperDac*dacP • ctrEneM=MeVperDac*dacM • We calculate “geomeric mean” of two ends, which doesn’t depend on position along the crystal: • Ene = sqrt(ctrEneP*ctrEneM) • We do not need to know the position along the crystal for energy reconstruction.

3. Sometimes this scheme doesn’t work • If one end of crystal has a dead channel • In case of direct energy deposition to one diode • Energy deposition is closer than 1 cm to a diode : • Energy measurement by this diode is affected by light collection non-uniformity • In all these cases we should use only the energy measurement from one diode and the external position estimation, to correct for light attenuation. For example, if we know only ctrEneM, then using ext_pos we can find ctrEneP: • Asym = pos2asym(ext_pos) • ctrEneP = ctrEneM*exp(asym) • Then we calculate energy like in normal case (see previous slide)

4. Non-uniformity near the diode up to 20% • This effect could be significant only for narrow energy depositions: muons, protons, heavy ions, first few X0’s of high energy showers (>100 GeV). • For high energy shower near and after the maximum and for low energy showers the effect of this non-uniformity will be small.

5. Direct energy deposition in a diode • The signal from direct energy deposition by MIP in a big diode is close to the MIP scintillation signal • For small diode direct energy deposition will be ~6 times bigger than from scintillation. • In this case of direct energy deposition the position is known ( it is near the end of the crystal), but to decide that there is a direct energy deposition we need an external position estimation. • “external” means “not from this crystal” – it could be from the fit, based on position measurements in other CAL layers

6. Requirements to external position estimation • we do not need very good precision • Asymmetry is ~0.3 at 15 cm from crystal center => ratio of two ends changes by 2% per 1cm => error of 1 cm in the external position estimation contributes 1% to the energy measurement in this crystal. • We can use the linear fit to the transversal positions of the hit crystals (“hodoscopic” position) • precision is ~1 cm • Always correct, while longitudinal position measurement could be wrong or unavailable • Provides information about the width of the energy deposition • Probably we need 2nd pass in CAL reconstruction • Calculate rough energies in all crystals • Make a “hodoscopic” fit to get rough position estimation • Refine enegy calculation in the crystals with narrow energy deposition close to the crystal end • Make “full” position fit – including longitudinal position measurements where they are available

7. Conclusion • The are situations when only one end of crystal could be used for energy measurement • in these cases we need “external” position estimation to calculate the crystal energy • Hodoscopic fit could be used for this purpose: requires modification in CalRecon sequence