The derivation of vector magnetic fields from stokes profiles: Integral versus least squares fitting techniques

We compare the results of two distinct methods for deriving photospheric vector magnetic fields from the Zeeman effect as observed in the Fe I line at 6302.5 A at high spectral resolution (45 mA.). One method ignores magneto-optical effects but allows for an absolute determination of B from the integral properties of the Stokes profiles, under the assumption of weak field strength. The other method is an iterative least-squares fitting technique developed by Lites and Skumanich which fits the observed Stokes profiles to the profiles predicted by the Unno-Rachkovsky solution to the radiative transfer equation. We find empirically that for sunspot fields above 1500 gauss the two methods agree in derived azimuthal and inclination angles to within ± 20 degs., Furthermore, for such fields, the estimate of the line of sight field and the transverse field derived using the two methods agree to within ± 500 gauss. In weak field strength regions the integral method can be used with little error and computational load in the estimation of the line of sight field, the transverse field and the inclination angle but the disagreement in derived azimuthal angle is considerable ( ± 90 degs.).