Extracting elemental ratios from X-ray photoelectron spectroscopy (XPS)
I found some information in Skoog, Principles of Instrumental Analysis, 6th ed.  On page 597:


  Quantitative Applications.  Once, XPS was not considered to be a very useful quantitative technique. However, there has been increasing
  use of XPS for determining the chemical composition of the surface
  region of solids.  If the solid is homogenous to a depth of several
  electron mean free paths, we can express the number of photoelectrons
  detected each second $I$ as $$I = n \phi \sigma \epsilon \eta A T \ell$$ where $n$ is the number density of atoms ($\text{atoms cm}^{-3}$) of the sample, $\phi$ is the flux of the incident X-ray
  beam ($\text{photons cm}^{-2} \text{ s}^{-1}$), $\sigma$ is the
  photoelectric cross section for the transition
  ($\text{cm}^{2}/\text{atom}$), $\epsilon$ is the angular efficiency
  factor for the instrument, $\eta$ is the efficiency of producing photo
  electrons ($\text{photoelectrons/photon}$), $A$ is the area of the
  sample from which photoelectrons are detected ($\text{cm}^{2}$), $T$
  is the efficiency of detection of the photoelectrons, and $\ell$ is
  the mean free path of the photoelectrons in the sample ($\text{cm}$).
  
  For a given transition, the last six terms are constant, and we can
  write the atomic sensitivity factor $S$ as $$S = \sigma \epsilon \eta A T \ell$$  For a given spectrometer, a set of relative values of $S$
  can be developed for the elements of interest.  Note that the $I/S$ is
  directly porportional to the concentration $n$ on the surface.  The
  quantity $I$ is usually taken as the peak area, although peak heights
  are also used.  Often, for quantitative work, internal standards are
  used.  Relative precisions of about 5% are typical.  For the analysis
  of solids and liquids, it is necessary to assume that the surface
  composition of the sample is the same as its bulk composition.  For
  many applications this assumption can lead to significant errors. 
  Detection of an element by XPS requires that it be present at a level
  of at least 0.1%.  Quantitative analysis can usually be performed if
  5% of the element is present.