The Higgs mechanism is the best candidate theory for explaining how elementary particles obtain masses, but the Higgs boson predicted by this theory is as of today not observed. The Higgs to gamma gamma channel is one of the most promising decay channels for finding a light Higgs boson with the ATLAS detector at CERN. ATLAS is one of four detectors at the Large Hadron Collider. In this thesis, a study of this channel with emphasis on a background study has been made using full simulation. A search for a signal-free area has been made, in order to study the background without being disturbed or biased by the signal. A test was carried through of whether the invariant mass distribution of the signal and/or background was distorted by the choice of region in the parameter plane of missing transverse momentum versus non-planarity of the gamma gamma pair. The ideal case, what is desired, is that the signal and background distributions remain unaffected by the choice of parameter regions. Testing this, fits of the signal alone using a Gaussian description and a fit of the background alone using an exponential description have been made. In addition, a combined fit of the signal and the irreducible background together has been made using three combinations of a polynomial or exponential description of the background together with a Gaussian or Crystal Ball description of the signal.