to 
. The scale factor function
proved to be particularly useful. This function is not simply an empirical fit, but can be justified as an actual model of the scattering of the disordered solvent.
If we assume that every piece of density is either part of the molecule or part of the solvent, we can state that
or, because the Fourier transform is a linear operator,
In the case where the contrast between 
and 
is low, and assuming that there is little detail in either function, as
at low resolution, Babinet's principle can be used to state:
To restrict this relationship to low resolution,
in Equation 6 is multiplied by 
. Also, because there really is a difference in contrast between the solvent
and the molecule,
should be multiplied by 
, which will be renamed 
. With these modifications Equation 6
becomes:
and Equation 5 becomes:
or
