Inverse Abel transform algorithms to determine the radial profile of the photoelastic coefficient of glass optical fibers

We compare two algorithms to determine the radial profile of the photoelastic coefficient C in glass optical fibers. We first measure the retardance profile of a transversally illuminated fiber as a function of tensile load. The radial profile C(r) is obtained from the inverse Abel transform of this retardance profile. Our first algorithm expands the measured retardance in its Fourier coefficients before computing the inverse Abel transform. With the second algorithm the expected result of the inverse Abel transform is expanded and the forward Abel transform of that expansion is compared to the measured retardance. We apply both approaches on the retardance measurement of commercially available single mode and multi-mode fibers.