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.
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