We have performed off axis heterodyne holography with very weak illumination
by recording holograms of the object with and without object illumination in
the same acquisition run. We have experimentally studied, how the reconstructed
image signal (with illumination) and noise background (without) scale with the
holographic acquisition and reconstruction parameters that are the number of
frames, and the number of pixels of the reconstruction spatial filter. The
first parameter is related to the frequency bandwidth of detection in time, the
second one to the bandwidth in space. The signal to background ratio varies
roughly like the inverse of the bandwidth in time and space. We have also
compared the noise background with the theoretical shot noise background
calculated by Monte Carlo simulation. The experimental and Monte Carlo noise
background agree very well together
