Isolated and non-isolated photon rates at LEP

We present the results of the calculation of the photon' +~1 jet rate at ${\cal O}(\alpha \alpha_{s})$ for LEP energies. By comparing these results with the data from the ALEPH Collaboration we make a next-to-leading order determination of the quark-to-photon fragmentation function $D_{q\to \gamma}(z,\mu_{F})$ at ${\cal O}(\alpha \alpha_{s})$. The predictions obtained using this fragmentation function for the isolated rate, defined as the photon’ +~1 jet rate for $z>0.95$, are found in good agreement with the ALEPH data. The next-to-leading order corrections are moderate demonstrating the perturbative stability of this particular isolated photon definition. We have also computed the inclusive photon energy distribution and found good agreement with the OPAL data.