  We present the quantum theory of the measurement of bosonic particles by
multipixel detectors. For the sake of clarity, we specialize on beams of
photons. We study the measurement of different spatial beam characteristics, as
position and width. The limits of these measurements are set by the quantum
nature of the light field. We investigate how both, detector imperfections and
finite pixel size affect the photon counting distribution. An analytic theory
for the discretized measurement scheme is derived. We discuss the results and
compare them to the theory presented by Chille et al. in "Quantum uncertainty
in the beam width of spatial optical modes," Opt. Express 23, 32777 (2015),
which investigates the beam width noise independently of the measurement
system. Finally, we present numerical simulations which furnish realistic and
promising predictions for possible experimental studies.
