  The photon density on the ground is a fundamental quantity in all experiments
based on Cherenkov light measurements, e.g. in the Imaging Air Cherenkov
Telescopes (IACT). IACT's are commonly and successfully used in order to search
and study Very High Energy (VHE) gamma-ray sources. Difficulties with
separating primary photons from primary hadrons (mostly protons) in Cherenkov
experiments become larger at lower energies. I have calculated longitudinal and
lateral density distributions and their fluctuations at low energies basing on
Monte Carlo simulations (for vertical gamma cascades and protonic showers) to
check the influence of the detector parameters on the possible measurement.
Relative density fluctuations are significantly higher in proton than in photon
induced showers. Taking into account the limited detector field of view (FOV)
implies the changes of these calculated distributions for both types of primary
particles and causes an enlargement in relative fluctuations. Absorption due to
Rayleigh and Mie scattering has an impact on mean values but does not change
relative fluctuations. The total number of Cherenkov photons is more sensitive
to the observation height in gamma cascades than in proton showers at low
primary energies. The relative fluctuations of the density do not depend on the
reflector size in the investigated size range (from 240 m^2 up to 960 m^2).
This implies that a single telescope with a mirror area larger than that of the
MAGIC telescope cannot achieve better energy resolution than estimated and
presented in this paper. The correlations between longitudinal and lateral
distributions are much more pronounced for primary gamma-ray than for primary
proton showers.
