## 3 Optical Sensing with NDs
### Magnetic Sensing  
Magnetic field sensing with commercial NV-NDs has been demonstrated to detect feeble magnetic fields with a limit of sensitivity down to \(\approx\) nT/\(\sqrt{\text{Hz}}\)[13; 18]. The spatial scale involved within this detection scheme is potentially a nanometric one, and this astonishing spatial resolution is inherently  
Figure 9: (**a**) Carbon phase diagram. Stability regions of diamond (D), graphite (G), vapor (V), and liquid carbon (L) are indicated, respectively, in white, grey, blue, and green. The purple arrow shows the graphite–liquid–diamond transition used to explain ND formation under pulsed laser irradiation of graphite in LN\({}_{2}\). The tilted red lines show the region known as “diamond-like liquid” [33], where undercooled liquid carbon and metastable diamond coexist. Typical PL wide-field images of NDs synthesized by Pulsed Laser Deposition (PLD) in nitrogen atmosphere (**b**) and by PLA in liquid nitrogen (**c**). (**d**) PL strength comparison between the two samples, obtained by integrating the intensity of the whole PL image after background subtraction: LN\({}_{2}\)-NDs show a more than 10\(\times\) higher emission compared to Diamond-like Carbon (DLC)-embedded NDs. The error bars of (**d**) are given by the standard deviation of the different integrated images. Reproduced with permission from [65], Elsevier, 2019.  
due to the point-like nature of the NV color center and to its nm-proximity to the ND surface. The interest in measuring nanometrically-resolved tiny magnetic fields is strong, and a few examples include their use for measurement of in-vivo neuronal activity [11], blood hemoglobin oxygenation [80], or more generally non-invasive biological measurements of intra-cellular moving charge states. The basic idea and the experiments behind such detection schemes are reported in Figure 10.  
NV-NDs are good candidates for biological magnetic field sensing due to the B-sensitivity they offer. A continuous wave electron paramagnetic resonance (CW-EPR)optically-detected magnetic resonance (ODMR) B-detection scheme capable of sensing magnetic fields down to few mT was recently demonstrated (Figure 11) [82]. Another interesting magneto-optical application of commercial NDs is related to the magnetic modulation of the red NV-fluorescent signal, allowing for background-free imaging of the fluorescence of complex biological systems containing NDs, where the sensing characteristics of NDs are exploited to filter out the target fluorescence signals. As evidenced by [83], the magnetic modulation achieved  
Figure 11: ODMR spectra under external magnetic field: zero-field (red curve), 1 mT (blue curve), and 3 mT (green curve). The circles are the experimental data while the lines are multi-gaussian fits. Adapted with permission from [82], Royal Society of Chemistry, 2016. Figure 10: (**a**) Photoluminescence spectrum of an ensemble of NV centers under 532 nm laser pumping. The NV\({}^{0}\) (575 nm) and NV\({}^{-}\) (638 nm) zero phonon lines are indicated. The red phonon sideband (PSB) is evident. (**b**) Continuous wave optically-detected magnetic resonance (CW-ODMR) spectrum of NV centers at zero magnetic field (**b**) recorded using the optically detected magnetic resonance technique. (**c**) CW-ODMR with an external magnetic field B \(\
eq\) 0, where the degeneracy of the m\({}_{\text{s}}\) = \(\pm\)1 states is removed, thus leading to two different optical transitions split by the Zeeman factor 2\(\gamma\)B, with \(\gamma\) being the electron gyromagnetic ratio. Panels (**b**,**c**) adapted from [81]. by [84] allowed for the creation of high-contrast imaging of NV-PL in high background environments (see Figure 12 for more details). The cutting edge of research in the field of opto-magnetic imaging of NDs is represented in the work by the authors of [86], who successfully monitored the position of fluorescent NDs by using them as beacons for the early diagnosis/imaging of tumors via their positioning inside biological tissues.