Figure 2 | Scientific Reports

Figure 2

From: Easy-hard phase transition in parameter estimation for optical waveguides

Figure 2

Examples for the behaviour of the energy landscape given by R(d) at \(d_{\text {real}} = 100\, \upmu \hbox {m}\) under variation of the absorption coefficient \(\kappa \). Left: pure measurement signal, right: noisy measurement signal. As can be seen, the transparent phase, i.e. \(\kappa = 0\), is characterised by periodically spaced local minima, while the weak-transparent phase with \(\kappa = 3.5\times 10^{-3}\) only exposes one single, global minimum. The local minima disappear one after another in the intermediate regime around \(\kappa = 2.2\times 10^{-3}\). The case with noise leads to a shift of the optima up, and for \(\kappa =3.5\times 10^{-3}\) the global optimum shifts also left away from the true radius value.

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