  The magnetic topology of the solar photosphere in its quietest regions is
hidden by the difficulties to disentangle magnetic flux through the resolution
element from the field strength of unresolved structures. The observation of
spectral lines with strong coupling with hyperfine structure, like the observed
MnI line at 553.7 nm, allows such differentiation.
  The main aim is to analyse the distribution of field strengths in the network
and intranetwork of the solar photosphere through inversion of the MnI line at
553.7 nm.
  An inversion code for the magnetic field using the Principal Component
Analysis (PCA) has been developed. Statistical tests are run on the code to
validate it. The code has to draw information from the small-amplitude spectral
feature oppearing in the core of the Stokes V profile of the observed line for
field strengths below a certain threshold, coinciding with lower limit of the
Paschen-Back effect in the fine structure of the involved atomic levels.
  The inversion of the observed profiles, using the circular polarization (V)
and the intensity (I), shows the presence of magnetic fields strengths in a
range from 0 to 2 kG, with predominant weak strength values. Mixed regions with
mean strength field values of 1130 and 435 Gauss are found associated with the
network and intranetwork respectively.
  The MnI line at 553 nm probes the field strength distribution in the quiet
sun and shows the predominance of weak, hectoGauss fields in the intranetwork,
and strong, kiloGauss fields in the network. It also shows that both network
and intranetwork are to be understood at our present spatial resolutions as
field distributions of which we hint the mean properties.
