Reliability in reconstruction of the axisymmetric refractive index profiles from transverse interferograms. Accurate versus approximate methods: A comparative study

A mathematical formalism related to the approximate as well as the accurate interferometric data reduction schemes is briefly outlined and subsequently applied in the reconstruction of the assumed (Luneburg) axisymmetric refractive index distribution. The presented comparative analysis confirms the generally held opinion that the approximate methods (“straight-line” and Kokubun-Iga approaches) may provide quite reasonable results in the examination of refractively inhomogeneous disturbances characterized by weak gradient and moderate index variation. On the other hand, the accurate scheme for transverse interferometric data interpretation and reduction, based on the close-form correlation between the fringe shift and the deflection function, [1] remains the only method for reliable reconstruction of strongly refracting index profiles, independently of magnitude of refraction and ambiguity of the fringes. This fact is of considerable importance for transverse interferometry of fibers (preform rods) and/or GRIN-rod lenses characterized by high numerical apertures.