Application of kernel principal component analysis for optical vector atomic magnetometry

Vector atomic magnetometers that incorporate electromagnetically induced transparency (EIT) allow for precision measurements of magnetic fields that are sensitive to the directionality of the observed field by virtue of fundamental physics. However, a practical methodology of accurately recovering the longitudinal angle of the local field through observations of EIT spectra has not been established. In this work, we address this problem of angle determination with an unsupervised machine learning algorithm utilizing nonlinear dimensionality reduction. The proposed algorithm was developed to interface with spectroscopic measurements from an EIT-based atomic rubidium magnetometer and uses kernel principal component analysis (KPCA) as an unsupervised feature extraction tool. The resulting KPCA features allow each EIT spectrum measurement to be represented by a single coordinate in a new reduced dimensional feature space, thereby streamlining the process of angle determination. A supervised support vector regression (SVR) machine was implemented to model the resulting relationship between the KPCA projections and field direction. If the magnetometer is configured so that the azimuthal angle of the field is defined with a polarization lock, the KPCA-SVR algorithm is capable of predicting the longitudinal angle of the local magnetic field within 1 degree of accuracy and the magnitude of the absolute field with a resolution of 70 nT. The combined scalar and angular sensitivity of this method make the KPCA-enabled EIT magnetometer competitive with conventional vector magnetometry methods.