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THE SET-UP: The air-shower detector array made out of six detectors. The detectors are composed of a scintillator and a SiPM (Sillicon Photomultiplier) each. Depending on the shower size, one or more detectors can be passed by a shower front, and hence these respective detectors would register signals each. The data of a single signal from one detector is 1024 entries of voltage and time.

To calculate the total energy of a single event, the first step should be to get the energy of a single detector for that event, so we have to integrate the voltage over time. Then, since the energy is proportional to the voltage E = q*U, one should get the total energy of a single detector. But should we add up all the energies from the detectors to get the total energy of that event? Or should we perhaps do something else?

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First of all: I do not know how well you can properly estimate the energy of detector the size of yours, but I guess that you would have very large uncertainties. But I can try to answer the first part of your question, how do you get the total energy of an event for a detetor array.

You can read in detail about the energy reconstruction of a large array here. The general idea is that you first reconstruct the direction of the shower, or more importantly, the zenith angle. At a given point in time, an air shower consist of a convex plane of secondaries traveling roughly along the axis of the shower. When this shower front hits your detectors, and you can use the timing information of your detectors to reconstruct the shape of the shower front which in turn will give you the direction of the shower axis.

Now that you have shower axis, you can reconstruct the so-called lateral distribution function (LDF). Here you basically plot the energy of each detector versus the distance from the shower axis. At experiments like the Pierre Auger Observatory or IceTop, one fits the LDF and uses it to determine the LDF at a standard benchmark value, e.g. at a distance of 125m to the shower axis (IceTop) or 1000m (PAO). This energy value as well as the zenith are then used to estimate the energy. The energy estimation is usually based on shower simulation, or, in the case of PAO, a calibration using another energy estimator (the Pierre Auger Observatory has additional fluorescence telescopes that can estimate shower energy independently, but only for at night and thus for as smaller subset of showers. But these showers can be used to calibrate the surface detector energy estimation).

I hope this helps and gives you a general overview.

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