Modelling of the "Pi of the Sky" detector
  The ultimate goal of the "Pi of the Sky" apparatus is observation of optical
flashes of astronomical origin and other light sources variable on short
timescales. We search mainly for optical emission of Gamma Ray Bursts, but also
for variable stars, novae, etc. This task requires an accurate measurement of
the brightness, which is difficult as "Pi of the Sky" single camera has a field
of view of about 20*20 deg. This causes a significant deformation of a point
spread function (PSF), reducing quality of measurements with standard
algorithms. Improvement requires a careful study and modelling of PSF, which is
the main topic of the presented thesis. A dedicated laboratory setup has been
created for obtaining isolated, high quality profiles, which in turn were used
as the input for mathematical models. Two different models are shown:
diffractive, simulating light propagation through lenses and effective,
modelling the PSF shape in the image plane.
  The effective model, based on PSF parametrization with selected Zernike
polynomials describes the data well and was used in photometry and astrometry
analysis. No improvement compared to standard algorithms was observed in
photometry, however more than factor of 2 improvement in astrometry accuracy
was reached for bright stars. Additionally, the model was used to recalculate
limits on the optical precursor to GRB080319B - a limit higher by 0.75 mag
compared to previous calculations has been obtained.
  The PSF model was also used to develop a dedicated tool to generate Monte
Carlo samples of images corresponding to the "Pi of the Sky" observations. The
simulator allows for a detailed reproduction of the frame as seen by our
cameras. A comparison of photometry performed on real and simulated data
resulted in very similar results, proving the simulator a worthy tool for
future "Pi of the Sky" hardware and software development.
