# Dark-Field Hyperspectral Microscopy for Carbon Nanotubes Bioimaging
## 2 Dark-Field Microscopy  
Dark-field microscopy is a scattering-based imaging technique where elastically scattered light from a specimen entering the objective forms the image, while incident light is blocked (Figure 1A). The fact that the light scattered from particles passes the objective leads to generating a clear and dark background with bright appearing objects, i.e., giving a higher signal-to-noise ratio (SNR) than in a conventional optical system [40]. In the case of nanosized objects, the scattering intensity may be approximated by the Rayleigh scattering theory, where the ratio of the refractive index of particles to the media is crucial to distinguish objects from the background [41]. Additionally, in noble metal nanoparticles, the prominent influence on the intensity provides a localised surface plasmon resonance (LSPR) effect, occurring when the electric field of incident light causes collective oscillations of electron density on the surface of particles [42]. Notably, the larger particles also scatter more intense light than the smaller ones [41; 43]. Although carbon nanotubes could be directly observed through dark-field microscopy due to high aspect ratio [44] and Rayleigh scattering [45], deposition of nanoparticles with larger diameters or LSPis applied to visualise individual nanotubes (Figure 2A) [46; 47] and produce enhanced scattering agents for cell imaging [48]. Besides endogenous factors of materials, the exogenous parameters, such as the medium of the sample, method of illumination, angle of incidence, and numerical aperture of the objective, also influence the resulting image. Thus, the CytoVivaTM enhanced dark-field illumination system (CytoViva, Auburn, Al, USA), widely used in biology and medicine, increases the SNR up to ten times by efficiently utilising these features [49; 50]. In the enhanced dark-field microscopy (EDFM), the fibre optic illumination source is directly connected to the cardioid annular oil immersion dark-field condenser to reflect the aberration-free light at an oblique angle [51]. That type of condenser, in combination with high numerical aperture (NA) oil objectives, makes it possible to collect the scattered light of particles at wider angles, resolving nanoscale particles in biological samples [52; 53]. Since the scattered spectrum of particles is highly affected by their physical, optical and electrical properties, dark-field microscopes may be equipped with hyperspectral sensors, thus obtaining spectral information with narrow bands at each pixel of an image (Figure 1B) [54]. Typically, the hyperspectral sensors used in biological studies acquired data of elastic scattering in the visible near-infrared range (VNIR; 400-1000 nm wavelength range), although there are setups with sensing in the short-wave infrared range (SWIR; 900-1700) or Raman scattering [55]. The hypercubes are captured from samples as three-dimensional data with two spatial dimensions (\(x\), \(y\)) and one spectral (\(z\)). During the scan, the light from the specimen is almost entirely blocked, except the part that enters the narrow slit. Then, the collimated light is dispersed by a diffraction grating, and the detector captures its constitutive wavelengths. In the general scanning technique, called  
Figure 1: (**A**) Representative optical diagram of dark-field microscopy and (**B**) a scheme of spectral data cube acquisition on the example of 200 nm polystyrene nanoparticles. \"push broom\", one spatial and spectral dimension is captured at a time. Thus, the process is performed line by line for the whole image. The resolving power (\(R_{s}\)) of the sensor is mainly determined by the diffraction grating and, similarly to the spatial resolution, could be described by [PERSON]'s criterion:  
\[R_{s}=\frac{\lambda}{\Delta\lambda}, \tag{2}\]  
where \(\Delta\lambda\) is the wavelength interval between two spectral lines resolved by the grating.