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We model lidar-relevant optical properties of mineral dust aerosols and compare the modelling results with optical properties derived from lidar measurements during the SAMUM field campaigns. The Discrete Dipole Approximation is used for optical modelling of single particles. For modelling of ensemble properties, the desert aerosol type of the OPAC aerosol dataset is extended by mixtures of absorbing and non-absorbing irregularly shaped mineral dust particles. Absorbing and non-absorbing particles are mixed to mimic the natural mineralogical inhomogeneity of dust particles. A sensitivity study reveals that the mineralogical inhomogeneity is critical for the lidar ratio at short wavelengths; it has to be considered for agreement with the observed wavelength dependence of the lidar ratio. The amount of particles with low aspect ratios (about 1.4 and lower) affects the lidar ratio at any lidar wavelength; their amount has to be low for agreement with SAMUM observations. Irregularly shaped dust particles with typical refractive indices, in general, have higher linear depolarization ratios than corresponding spheroids, and improve the agreement with the observations.