Nonuniformly polarized light can be used for Mueller polarimetry of homogeneous linear samples. In this work, a set up based on using azimuthally polarized input light and a modified commercial light polarimeter is proposed and developed. With this set up, a Mueller submatrix of a sample can be obtained by measuring the Stokes parameters at only three different positions across the output beam section. Symmetry constraints for linear deterministic samples allow the complete Mueller matrix to be deduced for this kind of specimens. The experimental results obtained for phase plates and for a linear polarizer confirm the validity of the proposed method.