Kerr effect measurements with non-uniform electric field distributions whose direction changes along the light path

Electric field distributions measured using the Kerr effect cause a phase shift between light components polarized parallel and perpendicular to the applied electric field, proportional to the magnitude squared of the applied electric field components in the plane perpendicular to light propagation integrated over the light path length. One wishes to recover the applied electric field distribution from measurements of light phase shifts. If the applied electric field direction changes along the light path, it becomes necessary to account for the change in direction of the light components parallel and perpendicular to the applied electric field and the light polarization equations are generalized