Context :

Aims : The thermodynamic and magnetic field structure of the solar photosphere is analyzed by means of a novel 3-dimensional spectropolarimetric inversion and reconstruction technique .

Methods : On the basis of high-resolution , mixed-polarity magnetoconvection simulations , we used an artificial neural network ( ANN ) model to approximate the nonlinear inverse mapping between synthesized Stokes spectra and the underlying stratification of atmospheric parameters like temperature , line-of-sight ( LOS ) velocity and LOS magnetic field .
This approach not only allows us to incorporate more reliable physics into the inversion process , it also enables the inversion on an absolute geometrical height scale , which allows the subsequent combination of individual line-of-sight stratifications to obtain a complete 3-dimensional reconstruction ( tomography ) of the observed area .

Results : The magnetoconvection simulation data , as well as the ANN inversion , have been properly processed to be applicable to spectropolarimetric observations from the Hinode satellite .
For the first time , we show 3-dimensional tomographic reconstructions ( temperature , LOS velocity , and LOS magnetic field ) of a quiet sun region observed by Hinode .
The reconstructed area covers a field of approximately 12 000 \times 12 000 km and a height range of 510 km in the photosphere .
An enormous variety of small and large scale structures can be identified in the 3-D reconstructions .
The low-flux region ( B _ { mag } = 20 G ) we analyzed exhibits a number of tube-like magnetic structures with field strengths of several hundred Gauss .
Most of these structures rapidly loose their strength with height and only a few larger structures can retain a higher field strength to the upper layers of the photosphere .

Conclusions :