# Electromagnetic Induction Imaging with Atomic Magnetometers: Progress and Perspectives
## 5 Discussion and Conclusions  
Electromagnetic induction imaging has a long history, and many key use cases have been identified thoughout the years. However, EMI failed to fulfill its potential, as many factors limited its performances. An important factor was the loss of sensitivity of inductive sensors at low frequency. The demonstration of electromagnetic induction imaging with atomic magnetometers in 2014 showed how it was possible to overcome this, and opened up the path to a tremendous development, culminated with the demonstration in 2020 of imaging of a few ml of saline solutions with conductivity below 1 S/m, thus bringing EMI-AM in the domain of biomedical imaging. High sensitivity at low frequency also led to the demonstration of through-barrier imaging, of relevance to security applications. This development saw the involvement of many groups worldwide. Since the first demonstration at UCL [26], EMI-AM research was also conducted at the University of Mainz [30], the National Physical Laboratory [38; 41; 42; 43; 44; 45] and the University of Copenhagen [36]. However, despite the tremendous progress in the sensitivity of the sensor, other limiting factors remain, and work is ongoing in different directions. An important area where development is needed is image reconstruction. The standard approach relies on the solution of the inverse problem of electromagnetism, with a tomographic image constructed from measurmeents of the secondary field at a finite set of points. However, the problem is ill posed, the inversion is computationally challenging and a set of assumptions about the object at hand are required to make the procedure viable. Research on the inverse solution of the problem of electromagnetism is ongoing, and continuous progress is reported. An alternative approach is based on machine learning alghoritms. Widely used for ray-optics, the procedure was recently validated for the diffusive imaging of MIT, and investigations are in progress to evaluate its potential for complex and cluttered scenes. Another important limitation of EMI is the low spatial resolution. Although EMI will never be able to compete with imaging systems based on ray-like propagation such as X rays, developments can be envisaged to improve the resolution of EMI-AM systems. For objects relatively far (cm or more) from the sensor, an important limiting factor is the spreading of the primary field, which induces eddy currents in the entire object. Selective excitation of eddy currents in different portions of the object would allow for better resolution. Improvements in this direction can be achieved by primary field shaping, moving away from the standard single coil design and adopting more complex schemes based on the solution of optimisation problems. Of interest to nanotechnolgy is also the case where the sample is in close proximity of the sensor, with the aim to produce high-resolution conductivity maps. In this case, an important limiting factor is the size of the sensor. Instead of using relatively (few mm) large ensembles of atoms in a vapour cell, progress can be made by adopting ultra-cold atom systems, with atomic clouds of few tens of micron size in close proximity to the object surface. A first step in this direction was recently achieved with the demonstration of a cold atom RF-AM [46], which can be used for EMI. It is worth mentioning that for this specific application, where the minute size of the sensor plays a central role, a valid alternative may also be constituted by NV diamond based EMI systems, as recently demonstrated by the Mainz group [47]. The entire development to date of EMI-AM systems, and resulting increase in sensitivity, has been based on AMs operating at best at the standard quantum limit. This limitation can be overcome, with a further increase in sensitivity, by using squeezed light or squeezed atomic spins [48]. Radio-frequency field detection below the standard quantum limit [49] may thus be the key to increase even further the ability of imaging low-conductivity samples.