  Developing avoidance or mitigation strategies of runaway electrons (RE) in
magnetic confinement fusion (MCF) plasmas is of crucial importance for the safe
operation of ITER. In order to develop these strategies, an accurate diagnostic
capability that allows good estimates of the RE distribution function in these
plasmas is needed. Synchrotron radiation (SR) of RE in MCF, besides of being
one of the main damping mechanisms for RE in the high energy relativistic
regime, is routinely used in current MCF experiments to infer the parameters of
RE energy and pitch angle distribution functions. In the present paper we
address the long standing question about what are the relationships between
different RE distribution functions and their corresponding synchrotron
emission simultaneously including: full-orbit effects, information of the
spectral and angular distribution of SR of each electron, and basic geometric
optics of a camera. We study the spatial distribution of the SR on the poloidal
plane, and the statistical properties of the expected value of the synchrotron
spectra of runaway electrons. We observe a strong dependence of the synchrotron
emission measured by the camera on the pitch angle distribution of RE, namely
we find that crescent shapes of the spatial distribution of the SR as measured
by the camera relate to RE distributions with small pitch angles, while ellipse
shapes relate to distributions of runaways with larger the pitch angles. A weak
dependence of the synchrotron emission measured by the camera with the RE
energy, value of the q-profile at the edge, and the chosen range of wavelengths
is observed. Furthermore, we find that oversimplifying the angular dependence
of the SR changes the shape of the synchrotron spectra, and overestimates its
amplitude by approximately 20 times for avalanching RE and by approximately 60
times for mono-energetic distributions of runaways.
