  One of the possible approaches to detecting optical counterparts of GRBs
requires monitoring large parts of the sky. This idea has gained some
instrumental support in recent years, such as with the "Pi of the Sky" project.
The broad sky coverage of the "Pi of the Sky" apparatus results from using
cameras with wide-angle lenses (20x20 deg field of view). Optics of this kind
introduce significant deformations of the point spread function (PSF),
increasing with the distance from the frame centre. A deformed PSF results in
additional uncertainties in data analysis. Our aim was to create a model
describing highly deformed PSF in optical astronomy, allowing uncertainties
caused by image deformations to be reduced. Detailed laboratory measurements of
PSF, pixel sensitivity, and pixel response functions were performed. These data
were used to create an effective high quality polynomial model of the PSF.
Finally, tuning the model and tests in applications to the real sky data were
performed.
  We have developed a PSF model that accurately describes even very deformed
stars in our wide-field experiment. The model is suitable for use in any other
experiment with similar image deformation, with a simple tuning of its
parameters. Applying this model to astrometric procedures results in a
significant improvement over standard methods, while basic photometry precision
performed with the model is comparable to the results of an optimised aperture
algorithm. Additionally, the model was used to search for a weak signal --
namely a possible gamma ray burst optical precursor -- showing very promising
results. Precise modelling of the PSF function significantly improves the
astrometric precision and enhances the discovery potential of a wide-field
system with lens optics.
