How accurately can one reconstruct an index profile from transverse measurement data?

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Abstract
The question posed by the title is addressed by analyzing the size dependence of the reconstruction error\deltan (\bar{r}) = n (\bar{r})_{reconst} - n (\bar{r})_{true}on the numerical aperture of the glass structure being profiled. This error is generated by means of computer simulation for two commonly used reconstruction methods. One method is accurate in the sense that it is based on rigorous ray theory and its use is shown to lead to only insignificant numerical errors. The second method is based on an approximate treatment of the ray equation and its application results in a systematic reconstruction error of magnituden(R)\Delta^{2}/2. Hence, the latter method provides increasingly less accurate results as Δ increases. If one considers a reconstruction error of 1 part in 104acceptable, then application of either method leads to satisfactory results in fiber-preform profiling work. However, care should be exercised in assessing the adequacy of a particular profile reconstruction method if it is to be used in profiling work on objects characterized by a larger numerical aperture than that typical of fiber preforms.