  In order to determine the orbital characters on the various Fermi surface
pockets of the Fe-based superconductors Ba$_{0.6}$K$_{0.4}$Fe$_{2}$As$_{2}$ and
FeSe$_{0.45}$Te$_{0.55}$, we introduce a method to calculate photoemission
matrix elements. We compare our simulations to experimental data obtained with
various experimental configurations of beam orientation and light polarization.
We show that the photoemission intensity patterns revealed from angle-resolved
photoemission spectroscopy measurements of Fermi surface mappings and
energy-momentum plots along high-symmetry lines exhibit asymmetries carrying
precious information on the nature of the states probed, information that is
destroyed after the data symmetrization process often performed in the analysis
of angle-resolved photoemission spectroscopy data. Our simulations are
consistent with Fermi surfaces originating mainly from the $d_{xy}$, $d_{xz}$
and $d_{yz}$ orbitals in these materials.
