Abstract
The GRAPES-3 (Gamma Ray Astronomy at PeV EnergieS-3) experiment has been designed to study the composition and energy spectrum of primary cosmic rays (PCRs) over TeV - PeV range. It is equipped with 400 plastic scintillators covering an area of 25000 m$^2$ and a muon detector spread in an area of 560 m$^2$. The precise measurement of particle densities from each detector is very important for any air shower experiment. Photo-multiplier tubes (PMT) are widely used as a transducer to collect the light produced in detector medium to electric signals. These signals are then processed to measure the particle densities. However, these PMTs tend to show non-linearity and saturation at higher signals due to the large shower core landing near the detector. The GRAPES-3 detectors record $\sim$ (50 -70) particles in the linear range. This results in improper shower size estimation near the knee energy. In order to overcome this situation and to estimate the correct shower size, a systematic approach has been devised and demonstrated to correct the particle density beyond the linear range. It is seen from the method allows us to estimate particle densities $\sim$ (500 - 800) which can improve the measurements beyond knee.
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