The isotropic and linear dichroic triplet-singlet difference spectra of the Fenna-Matthews-Olson (FMO) complex of the green sulfur bacterium Prosthecochloris aestuarii measured with absorbance detected magnetic resonance (ADMR) are presented. The absorption, linear dichroic (LD), circular dichroic (CD), triplet-minus-singlet (T-S), and LD(T-S) spectra are simultaneously analyzed by means of an exciton model. In this analysis the dependence of the T-S(alpha) spectrum on the angle alpha between the optical and microwave transition moments was taken into account. The present simulation procedure yields fits of the absorption and LD spectra of FMO that are about equally good as those in the literature, while the fits of the CD, T-S, and LD(T-S) spectra show significant improvements. We find that the interaction energies are roughly 25% higher than in previous analyses. The simultaneous fit of all available optical (difference) spectra with correct procedures offers a precise and detailed description of pigment-pigment interactions in the FMO complex.