M. Zahn, TRANSFORM RELATIONSHIP BETWEEN KERR-EFFECT OPTICAL-PHASE SHIFT AND NONUNIFORM ELECTRIC-FIELD DISTRIBUTIONS, IEEE transactions on dielectrics and electrical insulation, 1(2), 1994, pp. 235-246
Electric field distributions measured using the Kerr effect cause a ph
ase shift between light components polarized parallel and perpendicula
r to the electric field, proportional to the magnitude squared of the
electric field components in the plane perpendicular to light propagat
ion integrated over the light path length. One wishes to recover the e
lectric field distribution from measurements of light phase shifts. Fo
r axisymmetric geometries where the electric field depends only on the
radial co-ordinate and whose direction is constant along the light pa
th, as is the case along a planar electrode, the total phase shift for
light propagating at a constant distance from the center of symmetry
and the electric field distribution are related by an Abel transform p
air, a special case of Radon transforms typically used in image recons
tructions with medical tomography and holography. The more general Rad
on transform relates the optical phase shift to non-axisymmetric elect
ric field distributions but is restricted to cases where the applied e
lectric field is perpendicular to the plane of light propagation. If t
he applied electric field direction changes along the light path, it b
ecomes necessary to account for the change in direction of the light c
omponents parallel and perpendicular to the applied electric field and
the light polarization equations are generalized.