Machine Learning Based Localization and Classification with Atomic Magnetometers

We demonstrate identification of position, material, orientation, and shape of objects imaged by a ${}^{85}\mathrm{Rb}$ atomic magnetometer performing electromagnetic induction imaging supported by machine learning. Machine learning maximizes the information extracted from the images created by the magnetometer, demonstrating the use of hidden data. Localization 2.6 times better than the spatial resolution of the imaging system and successful classification up to 97% are obtained. This circumvents the need of solving the inverse problem and demonstrates the extension of machine learning to diffusive systems, such as low-frequency electrodynamics in media. Automated collection of task-relevant information from quantum-based electromagnetic imaging will have a relevant impact from biomedicine to security.

Figure 1

(a) Sketch of the experimental apparatus; PBS indicates a polarizing beam splitter. (b) Details of the imaging technique. Samples are moved by an $XY$ stage in the plane marked by dotted arrows. $B_{\text{rf}}$ is the rf field driving the AM and inducing eddy currents (in white). The EMI secondary field is drawn in red. (c)–(f) Frequency response of the rf AM, in operational conditions, at ${\nu }_0=200\mathrm{kHz}$: in-phase ($X$, filled circles) and quadrature ($Y$, empty squares) components. Traces were acquired in the same conditions every 24 h. (g)–(j) Examples of low-resolution EMI images used for this work: Al rectangle ($50\times 25\times 3{\mathrm{mm}}^3$, $\sigma =3.77\times {10}^7\mathrm{S}/\mathrm{m}$), obtained with 8 mm scan step size at 200 kHz. (g) Amplitude ($R$) image at 0° orientation. (h) Corresponding phase ($\mathrm{\Phi }$) image. (i) $R$ image at $+45°$ orientation. (j) Corresponding $\mathrm{\Phi }$ image. Raw data displayed, with the same color scale for $R$ and $\mathrm{\Phi }$. A thin dashed line marks the orientation of the rectangle main axis.

Figure 2

Orientation $ϵ$ versus $N$: (green squares) sample $A$, 8 mm step; (blue upward triangles) sample $B$, 8 mm step; (orange disks) sample $B$, 4 mm step. Isolated markers are the blind data set results. The shaded area marks the 95% CI of the mean cross-validated performance. The error bars for the blinded results indicate the 95% CIs of system performance given the limited amount of blinded data. The dashed line marks the baseline performance (${ϵ}_l=75\%$). The thick horizontal line marks the ceiling performance (${ϵ}_h=0\%$).

Figure 3

Localization RMSE versus $N$: (green squares) sample $A$, 8 mm step; (blue upward triangles) sample $B$, 8 mm step; (orange disks) sample $B$, 4 mm step. Isolated markers are the blind data set results. The shaded area marks the 95% CI of the mean cross-validated performance. The error bars for the blinded results indicate the 95% CIs of system performance given the limited amount of blinded data. The dashed line marks the baseline performance (${\mathrm{RSME}}_l=12.38\mathrm{mm}$). The thick horizontal lines mark the ceiling performance ${\mathrm{RMSE}}_h=4$ and 2 mm, respectively.

Figure 4

Shape classification $ϵ$ versus $N$. The isolated mark is the blind data set result. The shaded area marks the 95% confidence interval of the mean cross-validated performance. The error bars for the blinded results indicate the 95% CIs of system performance given the limited amount of blinded data. The dashed line marks the baseline performance (${ϵ}_l=75\%$). The thick horizontal line marks the ceiling performance (${ϵ}_h=0\%$).