Numerical method for inverse scattering in two-layered background in near-field optics

Figures & data

Figure 1. The geometry of the model problem. The scatterer $q(\mathit{x})$ is in a compact support in $D$, the measurements are taken on $\mathrm{\Gamma }$ and $\mathrm{\Omega }$ is a compact set containing $D$ and $\mathrm{\Gamma }$.

Figure 2. Direct discretization method and Tikhonov regularization of problem (4.14.1 $$\begin{array}{c}\hfill g(t)={\int }_0^1{e}^{-ts}f(s)ds,t\in [0,1],\end{array}$$4.1 ).

Figure 3. Moment method and moment method with truncated SVD for problem (4.14.1 $$\begin{array}{c}\hfill g(t)={\int }_0^1{e}^{-ts}f(s)ds,t\in [0,1],\end{array}$$4.1 ).

Figure 4. Computing model.

Figure 5. $2c=\mathit{\lambda }/2$, $b=\mathit{\lambda }/2$, $\mathit{\sigma }=0$, $\mathrm{\Lambda }={10}^{-8}$.

Figure 6. $2c=\mathit{\lambda }/2$, $b=\mathit{\lambda }/2$, $\mathit{\sigma }=0$, $\mathrm{\Lambda }={10}^{-6}$.

Figure 7. $2c=\mathit{\lambda }/2$, $b=\mathit{\lambda }/2$, $\mathit{\sigma }={10}^{-6}$, $\mathrm{\Lambda }={10}^{-6}$.

Figure 8. $2c=\mathit{\lambda }/2$, $b=\mathit{\lambda }/2$, $\mathit{\sigma }={10}^{-6}$, $\mathrm{\Lambda }={10}^{-3}$.

Figure 9. $2c=\mathit{\lambda }/2$, $b=\mathit{\lambda }/2$, $\mathit{\sigma }={10}^{-3}$, $\mathrm{\Lambda }={10}^{-6}$.

Figure 10. $2c=\mathit{\lambda }/2$, $b=\mathit{\lambda }/2$, $\mathit{\sigma }={10}^{-3}$, $\mathrm{\Lambda }={10}^{-3}$.

Figure 11. $2c=\mathit{\lambda }/2$, $b=\mathit{\lambda }$, $\mathit{\sigma }=0$, $\mathrm{\Lambda }={10}^{-6}$.

Figure 12. $2c=\mathit{\lambda }/2$, $b=\mathit{\lambda }$, $\mathit{\sigma }={10}^{-6}$, $\mathrm{\Lambda }={10}^{-6}$.

Figure 13. $2c=\mathit{\lambda }/2$, $b=\mathit{\lambda }$, $\mathit{\sigma }={10}^{-3}$, $\mathrm{\Lambda }={10}^{-3}$.

Figure 14. $2c=\mathit{\lambda }/4$, $b=\mathit{\lambda }/2$, $\mathit{\sigma }=0$, $\mathrm{\Lambda }={10}^{-6}$.

Figure 15. $2c=\mathit{\lambda }/4$, $b=\mathit{\lambda }/2$, $\mathit{\sigma }={10}^{-3}$, $\mathrm{\Lambda }={10}^{-3}$.

Figure 16. $2c=\mathit{\lambda }/4$, $b=\mathit{\lambda }$, $\mathit{\sigma }=0$, $\mathrm{\Lambda }={10}^{-6}$.

Figure 17. $2c=\mathit{\lambda }/4$, $b=\mathit{\lambda }$, $\mathit{\sigma }={10}^{-3}$, $\mathrm{\Lambda }={10}^{-3}$.

Figure 18. $2c=\mathit{\lambda }/8$, $b=\mathit{\lambda }/2$, $\mathit{\sigma }=0$, $\mathrm{\Lambda }={10}^{-6}$.

Figure 19. $2c=\mathit{\lambda }/8$, $b=\mathit{\lambda }$, $\mathit{\sigma }=0$, $\mathrm{\Lambda }={10}^{-6}$.

Figure 20. $n_0=1.5,$$2c=\mathit{\lambda }/8$, $b=\mathit{\lambda }/2$, $\mathit{\sigma }=0$, $\mathrm{\Lambda }={10}^{-6}$.

Figure 21. $n_0=1.5,$$2c=\mathit{\lambda }/8$, $b=\mathit{\lambda }$, $\mathit{\sigma }=0$, $\mathrm{\Lambda }={10}^{-6}$.

Figure 22. $\mathit{\theta }\in [-\mathit{\pi }/2,-{\mathit{\theta }}_{cr}]\cup [{\mathit{\theta }}_{cr},\mathit{\pi }/2],$$2c=\mathit{\lambda }/8$, $\mathit{\sigma }=0$, $\mathrm{\Lambda }={10}^{-6}$.

Figure 23. $\mathit{\theta }\in [-{\mathit{\theta }}_{cr},{\mathit{\theta }}_{cr}]$, $2c=\mathit{\lambda }/8$, $\mathit{\sigma }=0$, $\mathrm{\Lambda }={10}^{-6}$.