Kinetic energy of electrons emitted in Photoelectron Spectroscopy

In multiple sources ([example](http://www.phy.cuhk.edu.hk/course/surfacesci/mod3/m3_s4.pdf)), I found the information that the kinetic energy $E\_k$ measured using (Ultraviolet / X-ray) Photoelectron Spectroscopy is given by: 


$E\_k = h\nu - B.E.\_F - \phi\_{spec}$


where $h\nu$ is the energy carried by the incident photon, $B.E.\_F$ the energy difference between the energy level of the electron and the Fermi energy and $\phi\_{spec}$ the work function **of the spectrometer**.


As far as I understood the measurement process, the actually measured quantity in Photoelectron Spectroscopy is the kinetic energy $E\_k$ of the electron. This energy is measured by the radius of the electron in a homogeneous electric field. Thus, the kinetic energy of the electron after the emission would $E\_k = h\nu - B.E.\_F - \phi\_{sample}$, this independent of the work function of the spectrometer. So where does this difference come from?




From [Wikipedia](http://en.wikipedia.org/wiki/X-ray_photoelectron_spectroscopy) (emphasis mine):



> 
> Because the energy of an X-ray with particular wavelength is known
>  (for aluminum Kα X-rays, Ephoton = 1486.7 eV), and because the emitted
>  electrons' kinetic energies are measured, the electron binding energy
>  of each of the emitted electrons can be determined by using an
>  equation that is based on the work of Ernest Rutherford (1914):
> 
> 
> \begin{equation}
>  E\_\text{binding} = E\_\text{photon} - \left(E\_\text{kinetic} + \phi\right) \end{equation}
> 
> 
> where $E\_\text{binding}$ is the binding energy (BE) of the electron, $E\_\text{photon}$ is
>  the energy of the X-ray photons being used, $E\_\text{kinetic}$ is the kinetic
>  energy of the electron as measured by the instrument and $\phi$ is the
>  work function dependent on both the spectrometer & the material. This
>  equation is essentially a conservation of energy equation. **The work
>  function term $\phi$ is an adjustable instrumental correction factor
>  that accounts for the few eV of kinetic energy given up by the
>  photoelectron as it becomes absorbed by the instrument's detector.** It
>  is a constant that rarely needs to be adjusted in practice.
> 
> 
> 


So, it is the absorbtion of the photoelectron by the detector of the spectrometer that causes the work function term. The work function of the measured sample should be part of $E\_\text{binding}$ as this is the ionisation energy of the electron. However, I think the equation you quote might have it slightly wrong because if $B.E.\_F$ is the energy difference between the energy level of the electron and the Fermi energy then there is indeed some portion of the work function of the sample missing since $B.E.\_F$ is not equal to the ionisation energy.


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