Milne-Eddington ( M-E ) inversion codes for the radiative transfer equation are the most widely used tools to infer the magnetic field from observations of the polarization signals in photospheric and chromospheric spectral lines .
Unfortunately , a comprehensive comparison between the different M-E codes available to the solar physics community is still missing , and so is a physical interpretation of their inferences .
In this contribution we offer a comparison between three of those codes ( VFISV , ASP/HAO , and HeLIx ^ { + } ) .
These codes are used to invert synthetic Stokes profiles that were previously obtained from realistic non-grey three-dimensional magnetohydrodynamical ( 3D MHD ) simulations .
The results of the inversion are compared with each other and with those from the MHD simulations .
In the first case , the M-E codes retrieve values for the magnetic field strength , inclination and line-of-sight velocity that agree with each other within \sigma _ { B } \leq 35 ( Gauss ) , \sigma _ { \gamma } \leq 1.2 ^ { \circ } , and \sigma _ { v } \leq 10 m s ^ { -1 } , respectively .
Additionally , M-E inversion codes agree with the numerical simulations , when compared at a fixed optical depth , within \sigma _ { B } \leq 130 ( Gauss ) , \sigma _ { \gamma } \leq 5 ^ { \circ } , and \sigma _ { v } \leq 320 m s ^ { -1 } .
Finally , we show that employing generalized response functions to determine the height at which M-E codes measure physical parameters is more meaningful than comparing at a fixed geometrical height or optical depth .
In this case the differences between M-E inferences and the 3D MHD simulations decrease to \sigma _ { B } \leq 90 ( Gauss ) , \sigma _ { \gamma } \leq 3 ^ { \circ } , and \sigma _ { v } \leq 90 m s ^ { -1 } .