In this work, we derive closed-form expressions for determination of the linear birefringence and linear dichroism of uniaxial crystals utilizing transmission ellipsometry measurements at small angles of incidence in $ c $c-cut crystal substrates. The model-free method we use is an algebraic generalization of the method reported in Appl. Opt.44, 3153 (2005).APOPAI0003-693510.1364/AO.44.003153 The optical anisotropy of substrates of sapphire, 4H-SiC, and 6H-SiC single crystals is measured for illustration.