We measure the polarization state of each guided transversal mode propagating in step-index large-mode-area fibers (V≈4) using a correlation-filter based measurement technique in combination with a Stokes parameter measurement. The entire emerging beam, expressed in terms of a phase-dependent superposition of linearly polarized modes, demonstrates spatially varying polarization properties. By knowing the information about modal amplitudes and phase differences, full information about the optical field is available.