Modelling of the "Pi of the Sky" detector

TL;DR

This paper models the point spread function of the "Pi of the Sky" detector to improve astrometric accuracy and develop a simulation tool, aiding the detection of optical transients like Gamma Ray Bursts.

Contribution

It introduces a Zernike polynomial-based PSF model that enhances astrometry and provides a Monte Carlo image simulator for the "Pi of the Sky" project.

Findings

Over 2x improvement in astrometry accuracy for bright stars

Recalculated optical precursor limits for GRB080319B, higher by 0.75 mag

Validated the simulator's effectiveness with real and synthetic data

Abstract

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.