We report an extensive series of transitions (including collisional transfer lines) from pure and mixed levels of the NaK A 1 Σ + and b 3 Π states to the X 1 Σ + state, observed in Lyon using Fourier transform spectroscopy. We then combine these data with previously reported data on these states from emission from the B 1 Π and C 1 Σ + states and from mutually perturbed levels of the D 1 Π and d 3 Π states. We obtain 2758 distinct term values: the full data set includes 11624 term values, with many multiple determinations from transitions over a range of vibrational and rotational levels. The data are analyzed by fitting to potentials of the "Hannover" form (Samuelis et al., Phys. Rev. A 63, 012710 (2000)) plus spin-orbit (SO) functions in a simple Morse form, yielding an rms residual of approximately 0.029 cm −1. The empirical SO functions agree well with their ab initio counterparts obtained from electronic structure calculations based on non-empirical effective core potentials. From level energies of the A − b complex calculated from the fitted potentials and SO functions, we identify reasonable candidates for transitions between Feshbach resonance states and mixed singlettriplet gateway levels of the A 1 Σ + − b 3 Π manifold leading either to v=0 levels of the X state, or to mixed singlet-triplet levels at higher energies that can be used for perturbation-facilitated double resonance experiments.