A Tikhonov regularization method is used to estimate the orientational distribution function from deuteron NMR line shapes. Two sets of data, obtained for different orientations of a sample with respect to the magnetic field, are used in the regularization procedure to overcome the ambiguity arising from the superposition of the two NMR transitions of the spin I=1 system. A refined model of the NMR signal that takes into account line shape distortions resulting from finite pulse duration is developed. Tests on simulated data show that the results of the regularization procedure obtained with this model and a simple one that does not consider the finite pulse width differ significantly for broad spectra. The regularization method is applied to lyotropic liquid crystals of surfactant/water mixtures. The director distributions estimated for both hexagonal and lamellar lyomesophases give evidence of director undulations in the hexagonal phase.

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