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We present a detailed spectroscopic investigation of a thermal $^{87}$Rbatomic vapour in magnetic fields up to 0.4T in the Voigt geometry. We fitexperimental spectra with our theoretical model \textit{ElecSus} and findexcellent quantitative agreement, with RMS errors of $\sim 0.3$%. We extractthe magnetic field strength and the angle between the polarisation of the lightand the magnetic field from the atomic signal and find excellent agreement towithin $\sim 1$% with a commercial Hall probe. Finally, we present aninvestigation of the relative sensitivity of this technique to variations inthe field strength and angle with a view to enabling atom-based high-fieldvector magnetometry.

Quantitative optical spectroscopy of $^{87}$Rb vapour in the Voigt geometry in DC magnetic fields up to 0.4T