  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.
