  We analyse the capability of distinguishing between different intensities in
a monochromatic, pixellated image acquisition system at low light intensities.
In practice, the latter means that each pixel detects a countable number of
photons per acquired image frame. Primarily we compare systems based on pixels
of the click-detection type and photon-number resolving (PNR) type of
detectors, but our model can seamlessly interpolate between the two. We also
discuss the probability of errors in assigning the correct intensity (or "gray
level"), and finally we discuss how the estimated levels, that need to be based
on threshold levels due to the stochastic nature of the detected photon number,
should be assigned. Overall, we find that PNR detector-based system offer
advantages over click-detector-based systems even under rather non-ideal
conditions.
