The solar magnetic field is measured routinely onlyin the solar photosphere. While reliable measurementsof the photospheric magnetic field vector are only availablein active regions, in the quiet Sun at present only the vertical component of the magnetic field can be obtained accurately. To derive magnetic field structures throughout the solar atmosphere, from the chromosphere to the corona, we extrapolate these photospheric measurementsinto the upper photosphere, chromosphere and corona with a magneto-hydro-staticmodel. We optimize free model parameters by comparing the modelled magneticfield lines with structures observed in solar images. The comparison isdone automatically with a number of quantitative measurements andthe optimal model parameters are found with the help ofa downhill simplex minimization. This newly developed modelling approach canprovide an accurate and deep understanding of the magnetic field structuresthat extend to any height in the solar atmosphere.