Local birefringence is determined from a scatter signature of a birefringent waveguide. Four copies of a Rayleigh scatter time delay domain signature of the fiber are collected from two orthogonal polarization received states and from two orthogonal polarization launched states to form a Jones transfer matrix. Obtaining the Jones transfer matrix for the waveguide eliminates the need to align the instrument polarization launch state to the birefringence axes. Birefringence is determined from an autocorrelation of a polarization state averaged function calculated from the transfer matrix terms. Alternatively, the transfer matrix is rotated until fast and slow eigenvectors are separated, fast and slow amplitude functions are generated, and a cross-correlation is performed on the fast and slow amplitude functions in order to determine the birefringence. Because the shift is determined at a high signal-to-noise level with improved sensitivity to the spectral shift, the local birefringence is determined more accurately.