The following approximations were used to derive an analytical function from the complicated intensity expression (eq. 4):
(i) All two dimensional transversal distributions are assumed to be Gaussian and approximated
by azimuthal symmetrical Gaussian.
(ii) A mean *MS* variance is used, averaged over the crystal.
(iii) A combined total electron divergence (*ED*) distribution
from a folding of
the *MS* and *BD* distributions is used instead.
(iv) The variation of *g*_{t}, being in second order of
and therefore much smaller than
the variation in *g*_{l}, is neglected in the intensity.
With that the uncollimated coherent intensity (eq. 4) in terms of the variation *l*of *g*_{l} due to *ED* is expressed as follows:

Owing to the delta function the integration is trivial and the expression separates into the coherent intensity in terms of the functions and a collimation function . The treatment of collimation in the incoherent case works analogous, but the different angular dependence leads to a remaining integral (note:

Therefore, a single collimation function accounts for experimental deficiencies in both cases of coherent and incoherent bremsstrahlung production. After these derivations,