# Battery Characterization via Eddy-Current Imaging with Nitrogen-Vacancy Centers in Diamond
## 6 Conclusions and Outlook  
We demonstrated microwave-free eddy-current imaging with NV centers in diamond exploiting the cross-relaxation feature between the NV centers and P1 centers occurring at 51.2 mT. The magnetic sensitivity is 40 nT/\(\sqrt{\text{Hz}}\) with 100 kHz bandwidth, but as previously  
Figure 6: Magnetic field and phase shifts generated by the battery at frequency of 5 kHz. (**a**) Calibrated magnetic field generated by the battery. (**b**) Phase shifts generated by the battery.  
Figure 7: Determination of spatial resolution. The blues dots signify the average cross section of the 0.3 mm-width electrode imaged by the sensor, the green trace denotes the width of electrode of battery as a square function, and the red curve represents a Gaussian function, as a convolution kernel of the green trace to fit the experimental data, noted as a blue trace.  
demonstrated [11], it can be extended to a few MHz. The diamond-based sensor is used to noninvasively image a mm-sized solid battery. The spatially resolved amplitude and phase lock-in signals were used to determine the dimension and shape of the battery features, including a 1 mm-wide artificial defect and 0.3 mm-wide electrodes, from which the spatial resolution was calibrated as 360(2) um, which was limited by the distance between the sensor and the battery. Furthermore, the diamond-based probe also identified an anomaly and a crevice inside the battery, demonstrating its ability to detect internal anomalies that are not visible to the naked eye. The maximum magnetic field and phase shift generated by the battery at a modulation frequency of 5 kHz were estimated as 0.04 mT and 0.03 rad, respectively.  
This paper mainly focuses on testing solid batteries. For future studies, the spatial resolution could be further improved by either using a thinner diamond sample or a diamond with a shallow implanted NV layer to shorten the sensor-sample distance. By tuning the bandwidth, it would be possible to identify structures at different depths inside the battery including electrodes, electrolytes [20] and even material components, which could be useful for battery assessment and development.  
[PERSON], [PERSON] and [PERSON] conceived the initial idea for the experiment in consultation with [PERSON], [PERSON], [PERSON] and [PERSON] designed the experiment with input from all authors. [PERSON] and [PERSON] wrote and implemented control and automation software. [PERSON], [PERSON] and [PERSON] constructed the apparatus, performed the experiments, and analyzed the data, with assistance from [PERSON] and [PERSON] in data acquisition. All authors discussed results and contributed to the writing of the manuscript. All authors have read and agreed to the published version of the manuscript.  
This work was funded in part by a grant from the U.S. National Science Foundation under award CBET 1804723 and the the German Federal Ministry of Education and Research (BMBF) within the Quantumtechnologien program (FKZ13N14439 and FKZ 13N15064), and by EU FET-OPEN Flagship Project ASTERIQS (action 820394).  
The authors declare no conflict of interest.