Direct refractive index retrieval from interferometry measurements.

We present an alternative numerical method to the Abel inversion technique, which can be applied to complex non-symmetrical systems. A comparison with the Abel inversion algorithm was conducted. For benchmarking, the method was applied to a synthetic trace representing a plasma waveguide characterized by a constant parabolic density profile. Furthermore, the temperature and refractive index of a plume of hot air surrounding a non-cylindrical soldering iron were retrieved. Temperatures between 50 °C and 200 °C were successfully retrieved within the instrument precision. The proposed method allows robust and fast data retrieval while maintaining the accuracy and resolution of well-known methods, as Abel inversion.