Metallic nanoparticles supporting a localized surface plasmon resonance have emerged as promising platforms for nanoscopic labels, sensors, and (photo-) catalysts. To use nanoparticles in these capacities, and to gain mechanistic insight into the reactivity of inherently heterogeneous nanoparticles, single-particle characterization approaches are needed. Single-particle scattering spectroscopy has become an important, highly sensitive tool for localizing single plasmonic nanoparticles and studying their optical properties, local environment, and reactivity. In this review, we discuss approaches taken for collecting the scattered light from single particles, their advantages and disadvantages, and present some recent applications. We introduce techniques for the excitation and detection of single-particle scattering such as high-angle dark-field excitation, total internal reflection dark-field excitation, scanning near-field microscopy, and interferometric scattering. We also describe methods to achieve polarization-resolved excitation and detection. We then discuss different approaches for scanning, ratiometric, snapshot, and interferometric hyperspectral imaging techniques used to extract spectral information. Finally, we provide a brief overview of specialized setups for in situ measurements of nanoparticles in liquid systems and setups coupled to scanning tip microscopes.
The localized surface plasmon resonance (LSPR) is the collective oscillation of free electrons excited by incident light (see Figure 1A) , [ 2]. The LSPR depends on the shape , , , , size , , , , composition , , , and local environment of the nanoparticle , [ 15]. As a result, the LSPR is a sensitive probe of chemical reactions on the nanoparticle’s surface , , , , changes in the surrounding refractive index , , , and charge  and energy transfer  to nearby species. Further, the LSPR functions as a nanoantenna , [ 25], focusing the energy of the incident light to a nanoscopic volume, enhancing the catalytic activity , , , local heating capacity , Raman scattering of molecules attached to the surface , , , and fluorescence of nearby fluorophores , , . Finally, as a result of their large scattering cross-sections, metal nanoparticles can be readily characterized in a standard dark-field microscope and localized with nanometer precision , [ 36], allowing them to serve as nonbleaching labels for biological samples . The combination of the ability of the LSPR to efficiently drive reactions, spectrally monitor these reactions, and localize them, has resulted in 30+ years of intensive research into the optical properties of metal nanoparticles, especially those made of gold , [ 39].
Tracking the LSPR on the single-particle level has emerged as the standard for characterizing the structure-function relationships of plasmonic nanomaterials , , . Both lithographically fabricated and especially chemically synthesized nanoparticles have heterogeneous size and shape distributions , [ 65]. Such nanoparticle heterogeneity makes quantitative monitoring with ensemble spectroscopy difficult or impossible, since contributions from a nanoparticle subpopulation having potentially the most interesting properties can be easily averaged out and hence missed. While trends can be established, single-particle spectroscopy, often correlated with electron microscopy, is required to gain a complete understanding of nanoparticle properties . To optically monitor single particles, several imaging and spectroscopic techniques have been developed including dark-field scattering , [ 46], extinction , photothermal imaging , , , scanning photoionization microscopy , [ 52], photoluminescence , [ 54], and transient absorption spectroscopy , [ 56]. Of the single-particle techniques, dark-field scattering spectroscopy is arguably the most ubiquitous  due to its ease of implementation, high-throughput capabilities, and high spectroscopic resolution.
Dark-field microscopy has become a popular research tool in the nanoscience community , , , . Dark-field microscopy is based on the principle that the incident light is reflected, refracted, physically blocked, or confined in the near-field in a way that the only light collected by the detection optics is that scattered by the nanomaterial , , . Dark-field excitation can be achieved via commercial dark-field condensers, evanescent wave excitation, subwavelength apertures, or normal incidence light with spatial filtering. Single-particle scattering spectroscopy can be implemented in a dark-field microscope by attaching a spectrograph, filters, or an interferometer to characterize the intensity of the scattered light as a function of wavelength. Dark-field microscopy is nearly background-free and the large scattering cross-sections of plasmonic nanoparticles allow facile single-particle imaging, localization, and spectral acquisition. The unique capabilities of single-particle scattering spectroscopy have enabled recent advancements such as monitoring catalysis in real-time , measuring biomolecule adsorption , and quantifying single DNA modifications within cell nuclei . Furthermore, in the absence of heterogeneity, dark-field scattering spectroscopy makes it possible to gain key insights into nanoparticle-driven reaction mechanisms  and polarized-light matter interactions , [ 64].
This review focuses on several recently developed single-particle scattering spectroscopy methods and is organized as follows: Section 2 covers the physical principles of light scattering by plasmonic nanoparticles. Section 3 describes several dark-field excitation and collection geometries, with both near-field and far-field light excitation, scanning near-field optical microscopy (SNOM), interferometric scattering techniques, and polarization-resolved analysis. Section 4 describes spectroscopic and imaging methods for single-particle scattering, including those based on scanning, ratiometric, snapshot, and interferometric detection. Section 5 covers specialized techniques for acquiring spectra in situ in electrochemical cells or biological media, and dark-field spectroscopy coupled with tip-based microscopy techniques.
2 Physical principles of light scattering by plasmonic nanoparticles
When light is incident on a metallic nanoparticle, the free electrons of the metal are driven to oscillate 180° out of phase with respect to the light’s instantaneous electric field (Figure 1A) . Meanwhile, the nuclei of the particle lattice attract the electrons to return to their equilibrium positions. Just as in a harmonic oscillator, the electrons overshoot equilibrium, however, and continue to oscillate back and forth. When the frequency of the incoming light matches the frequency of this oscillation, a resonance condition is met and the particle efficiently absorbs and scatters light . The LSPR allows a particle to absorb and scatter light from a much larger cross-section than the physical size of the nanoparticle, and gives rise to a strong field enhancement around the particle’s surface . The light that is absorbed by the particle can excite electronic transitions leading to hot carrier generation , , , followed by photoluminescence  and charge transfer , [ 69] to the surroundings , , , . Most of this absorbed energy decays nonradiatively through coupling to nanoparticle phonons and vibrational modes of the surroundings, generating heat. Radiative decay of the plasmon occurs through Rayleigh scattering at the incident frequency . These processes ultimately dampen the plasmon oscillation, leading to line broadening, and result in a spectrum of wavelengths over which the particle strongly interacts with light.
In 1908, Gustav Mie provided an analytical solution to Maxwell’s equations for the extinction, scattering, and light absorption cross-sections ( ) of small, spherical particles . Although simulation methods that discretize the particle’s shape and therefore can be applied to any nanoparticle have emerged since , , , Mie theory still remains in use today for modeling and illustrates best the underlying physics . The cross-sections are expressed as a series expansion of a class of spherical harmonics , [ 13]. The expansion is over the plasmon modes from , the dipolar plasmon mode, to truncation at a maximum value (multipolar modes). In the dipolar mode, the free electrons are all polarized from one side of the particle to the other, while in multipolar modes, the free electrons maintain collective oscillations, but in multiple antinodes around the surface of the particle. The determination of is dependent on the size of the sphere and the cross-sections are given by Equations (1–3) , :
In order to gain mechanistic insight on the influence of the particle’s surroundings and volume, it is useful to consider the Mie theory solution for just the dipolar mode . While this assumption is only strictly correct for particles smaller than ∼10 nm in diameter , the general conclusions are valid for a variety of particle sizes . The extinction cross-section for the dipolar plasmon mode is given by , [ 13]:
Similar in form, the scattering cross-section can be approximated by:
According to Equations (7) and (8), the scattering cross-section increases as a function of V2, whereas the absorption cross-section increases linearly with particle volume. Therefore, the extinction spectra are dominated by absorption for small particles and by scattering for large particles. Moreover, for small imaginary components of the dielectric function of the metal, the extinction cross-section is maximized when , which reflects the dependence of the LSPR peak on the dielectric function of the medium. Finally, the Lorentzian forms of the cross-sections reveal that the peak locations are primarily governed by , the real part of the dielectric function of the metal, while governs the line-width. Dark-field spectroscopy characterizes the light scattered by the nanoparticle, which, according to Equation (7) contains information easily related to the refractive index of the surroundings, the material, and the size of the nanoparticle.
3 Single-particle scattering excitation and collection geometries
Due to the much smaller signal from individual nanoparticles compared to an ensemble, a vanishing background is necessary to measure the scattering spectra of single nanoparticles. The principle of dark-field microscopy relies on blocking the collection of the incident light, while collecting the scattered light from individual nanoparticles. Numerous instrument geometries have been developed to excite nanoparticles in the far-field and near-field while following this principle , , . Far-field and near-field excitation techniques are introduced here, and are thoroughly discussed in Sections 3.1 and 3.2, respectively.
Far-field excitation geometries avoid collection of the excitation light by using high incidence angles that miss the collecting objective or by using direct beam blocks. Figure 1B shows three different examples of far-field excitation based dark-field geometries. Condenser and objective-based high-angle dark-field (HADF) excitation geometries work by using a larger excitation cone, or numerical aperture (NA), than the acceptance cone of the collecting objective lens (Figure 1B, left and center). The NA can be calculated from the refractive index , of the medium and the half-angle of the incident light cone, :
Condenser-based HADF excitation places a central beam stop in the excitation path, producing a hollow cone at an oblique angle, such as 43° (NA = 0.9) in the example given here. The forward-scattered light is collected at an angle of 27° (NA = 0.7), limiting the collection of the high-angled excitation light transmitted through the sample.
Objective-based HADF excitation uses the same objective to excite the sample and collect the backscattered light. Excitation light is first shaped into an annulus using a central beam block and then directed through an annular dark-field mirror. The light reflected by the mirror is sent into a dark-field objective designed with a hollow collar around the lenses. A curved mirror within the collar illuminates the samples with a hollow cone at a 75° angle (NA = 0.97). Scattered light is collected in the lens of the objective at 53° (NA = 0.8), while avoiding the collection of reflected light from the surface.
Normal incidence dark-field excitation (Figure 1B, right) illuminates nanoparticles at normal incidence and blocks the transmitted beam while collecting light scattered at higher angles. One way to block the transmitted light is to use a reflecting objective, which has a beam block right before the primary mirror of the objective. When placed correctly, the normal incidence excitation light is blocked while a large collection angle of 41° (NA = 0.65) collects the forward-scattered light from the nanoparticle. Another approach to normal incidence dark-field excitation is to use a lens-based objective with a central beam block located after the back aperture of the objective lens . This approach is limited to well-collimated and tightly-focused excitation, typically from a laser, so that the spot size does not exceed that of the block.
Near-field excitation techniques limit the amount of unwanted excitation light detected by exciting particles with near-field confined light. Figure 1C shows geometries that generate an evanescent wave by total internal reflection (TIR). TIR occurs when light passes from an optically dense medium with refractive index into a less dense medium with refractive index above the critical angle , for that interface, given by Equation (10) :
For the geometries shown in Figure 1B, the critical angle is 41° for the air-glass interface. An evanescent wave is generated in the less dense medium, exciting the nanoparticles. Due to its nonpropagating nature into the far-field and short penetration depth, the evanescent wave does not enter the objective.
For example, 650 nm light at an air/glass interface has a penetration depth of 71 nm when exciting at 55°. The evanescent field intensity away from the interface can be calculated using Equation (12) :
Dark-field scattering based on prism-coupled TIR excitation (Figure 1C, left) places a prism on the back of a coverslip, leading to TIR at the interface where the particles are deposited. Forward-scattered light from the nanoparticles is collected by the objective. Waveguide dark-field excitation (Figure 1C, center) couples light into a coverslip , [ 82] or optical fiber , , , , , , , ,  above the critical angle to confine light to the substrate. When the beam meets the interface, the beam cannot escape and instead totally internally reflects, creating an evanescent wave. Waveguide dark-field excitation benefits from the flexibility in sample location above or below the waveguide without the need for a prism or condenser on the side opposing the objective.
Near-field excitation can also be achieved using SNOM, demonstrated in Figure 1D. SNOM generates an evanescent wave using an aperture that is smaller than the wavelength of light, or by scattering light off a tip . The evanescent wave excites the plasmon of nanoparticles near the tip and the forward-scattered light is collected by conventional far-field optics.
3.1 Far-field excitation geometries
Far-field excitation geometries are particularly convenient for imaging through media such as aqueous samples in a spectroscopic cell, as the incident light can penetrate through the whole cell, as opposed to near-field light, which cannot , [ 61]. Further, the polarization properties of the exciting light change as a function of incident angle , [ 94], potentially resulting in different scattering spectra for steeper excitation angles or near-field excitation , , . When preserved polarization properties are required, normal incidence dark-field excitation or HADF excitation techniques employing a shallow angle can therefore be an attractive option. In this section, we will discuss specific examples and provide more details on far-field excitation techniques enabling collection of both backscattered and forward-scattered light.
3.1.1 Far-field techniques for collecting backscattered light
Collecting the light backscattered from particles can be a convenient approach for reducing background noise from other components in the sample and isolating the scattering from nanoparticles. For example, spherical nanoparticles that are 100 nm in size forward- and backscatter with approximately equal intensities, but larger media, such as cells, primarily forward-scatter . Therefore, backscattering approaches can limit noise from extraneous media in biological samples. Two key methods for collecting the light backscattered from nanoparticles are objective-based HADF excitation, in which the collection objective also gives an annulus of illumination, or HADF excitation from a single direction using separate illumination and collection optics.
22.214.171.124 Objective-based HADF excitation
As described in Section 3 above, objective-based HADF excitation uses the objective as both the excitation and collection lens. Objective-based HADF excitation can be conveniently implemented, as only a single optical element needs to be aligned to the sample, increasing measurement stability . While objective-based HADF excitation has been successfully implemented in a number of studies , , , this technique has drawbacks limiting the signal-to-noise ratio. The excitation angle and direction are not adjustable and much of the incident light is spatially filtered from reaching the sample. Further, the NA of the collection lens is limited to lower values.
The Baumberg group created an annular HADF technique for monitoring nanoparticle growth in solution using a white-light laser and a high-NA objective . The authors used a supercontinuum laser, expanded the beam size, and blocked the center of the beam, creating a ring of light, which emerged from the objective as an annulus. The backscattered light was collected and analyzed by a spectrograph. The use of a supercontinuum laser enabled short exposure times and a high signal-to-noise ratio.
126.96.36.199 Unidirectional HADF excitation
Unidirectional HADF excitation overcomes some of the limitations facing objective-based HADF excitation. Namely, there is greater control and flexibility in the incident angle and direction, and the light can be easily polarized, allowing optical characterization of anisotropic particles , , . While objective-based HADF excitation gives an annular-symmetric cone of incident light, exciting the sample evenly from all in-plane directions, unidirectional HADF excitation has a single propagation direction. Unidirectional HADF excitation can be implemented through two methods: reflection of the incident light off the same side of the coverslip that has the nanoparticles, with the objective directly above the particles (Figure 2A) , or refraction at a high angle through the opposite side of the coverslip . The reflection method can be achieved by simply directing light from a fiber-coupled source or laser onto the sample at an angle . Alternatively, Tcherniak et al. used a dark-field objective described above and passed laser light through the hollow collar around the lenses from a single direction . In both cases, the light reflected at high angles is then missed by the acceptance angle of the objective, while light backscattered from the sample is collected. The reflected light approach is convenient for characterizing the scattering of nanostructures on opaque substrates . In the refraction method, the incident light is directed to the back of the coverslip at an angle below the critical angle. The light then refracts at a high angle as it crosses the glass-air or glass-water interface, excites the sample, misses the objective lens, and forward-scattered light is collected. A few studies have utilized this method , , , but it is a less common approach than reflected-light unidirectional HADF excitation because the incident angle of the light is limited by the refractive index of the substrate and the incident polarization can be distorted by the refraction.
The Capasso, Halas, and Nordlander groups have utilized the reflected light unidirectional HADF excitation approach to explore the effect of the incident angle on the single-particle scattering spectra of nanoparticle oligomers that support Fano resonances . Fano resonances occur when bright scattering modes and dark absorbing plasmon modes spectrally overlap and interfere, resulting in a sharp dip in the scattering spectra . They compared the scattering spectra of single heptamers with HADF excitation with a 70° incident angle and an alternative approach of exciting through the objective lens at a smaller 20° angle (Figure 2A and B) . In the former, the unidirectional excitation reflected off the sample interface and only the light backscattered by the particle was collected by the objective. In the latter, the excitation light was spatially filtered and aligned to the left edge of the back aperture of the objective lens. The left side of the objective then focused the light onto the sample giving the excitation a single propagation direction. The light backscattered by the oligomer was collected with the same objective and the excitation light also collected was then spatially filtered. The authors found that with the traditional 70° incident angle, there were increased retardation effects, caused by the phase change of light as it propagated through the sample laterally . These retardation effects caused excitation of additional dark modes in the heptamer, which ultimately broadened the scattering spectra and blue-shifted the Fano resonance (Figure 2C). In contrast, with a 20° incident angle, retardation effects were minimal as the light mostly propagated through the shallow depth of the oligomer and the spectra featured sharper peaks. A simple adjustment of incident angle through unidirectional excitation geometries can significantly alter the scattering spectra of large nanoparticles and assemblies that support dark modes .
3.1.2 Far-field techniques for collecting forward-scattered light
For transparent samples containing nanoparticles free from strongly scattering media, far-field excitation geometries collecting forward-scattered light can yield high signal-to-noise ratios. Two commonly employed excitation geometries for the collection of forward-scattered light are normal incidence excitation and condenser-based HADF excitation. Both provide symmetric excitation either normal to the sample, or in an annulus, and require less spatial filtering of the excitation light compared to the objective-based HADF excitation described above.
188.8.131.52 Normal incidence excitation
Normal incidence far-field excitation does not require spatial filtering of the incident light. Instead, the excitation must be spatially filtered from the collected scattered light after the sample. The Kukura group implemented normal incidence excitation and placed a circular beam block after the back-aperture of the objective lens to block the excitation light . The gold nanoparticles were excited with a white-light laser, and the forward-scattered light was collected with a high-NA objective (Figure 2D). While many dark-field excitation geometries still have some stray light from the excitation, this approach of directly blocking normal incidence light extinguished the excitation by a factor of >107 . The authors successfully employed this technique to collect the single-particle scattering spectrum of a 10 nm gold particle (Figure 2E), while typical dark-field setups can only collect single-particle spectra down to 20 nm gold particles . In addition, filter-free single-molecule fluorescence signals can be acquired by this technique. A similar approach was taken by Kirchner and Smith et al. who focused a white-light laser through the sample and onto the beam stop of a reflecting objective. The primary mirror only collected light scattered at high angles from the nanoparticles, while the back of the secondary mirror blocked the incident light .
Normal incidence excitation can also be achieved by illuminating light through the objective using a dot mirror , which is essentially the opposite of an annular dark-field mirror (Figure 2B center). A dot mirror sits in the center of a filter cube to reflect light in the center of a collimated beam and to allow light transmission at the sides. Light is reflected by the dot mirror to emerge at a normal incidence through the sample. Light backscattered at high angles by the particle is collected by the objective, while reflected incident light from the substrate is blocked by the dot mirror. The Berry group has achieved a similar setup using a small rod mirror .
184.108.40.206 Condenser-based HADF excitation
Condenser-based high-angle excitation is perhaps the most convenient dark-field excitation geometry, as commercial dark-field condensers are readily available and typically do not require customization , [ 42]. Moreover, many commercial dark-field condensers have annular symmetric excitation resulting in better signal-to-noise ratios than those found with typical unidirectional excitation geometries discussed above. The Irudayaraj lab has implemented condenser-based HADF excitation (Figure 2F) for identifying two different cytosine modifications to DNA in cell nuclei . In this work, silver nanoparticles labeled 5-carboxyl-cytosine (5caC) modifications and gold nanoparticles labeled 5-methyl-cytosine (5mC) DNA modifications. By spectrally monitoring single particles in the cell nuclei and simulating spectra, the authors identified wavelength ranges corresponding to scattering from single silver and gold particles, and dimers of gold and silver particles (Figure 2G and H) . The three spectral windows were used to form three images corresponding to the distributions of 5caC, 5mC, and co-localized 5caC–5mC modifications within the nucleus (Figure 2I). The overlaid image (Figure 2J) displays the relative amounts of all cytosine modifications in the cell nucleus .
3.2 Near-field techniques
Near-field excitation geometries rely on using confined light that does not propagate in free space, and therefore does not reach the objective. The interaction of nanoparticles with near-field light leads to far-field scattered light, which is collected by an objective. TIR excitation techniques typically offer higher signal-to-noise ratios compared to far-field excitation techniques , and allow new polarization geometries . In this section we also discuss SNOM, the only technique discussed in this review that can spatially super-resolve plasmon spectra .
3.2.1 TIR excitation
In a typical TIR excitation microscopy setup, nanoparticles are immobilized on a coverslip and light is coupled into the back of the coverslip above the critical angle, leading to TIR at the interface where the nanoparticles sit. Furthermore, the NA of the objective is not limited by the excitation angle like in HADF illumination and high-NA objectives can therefore be used. However, the refractive index requirements for TIR can limit its application. For example, some studies chose to cover nanoparticles in immersion oil to create a uniform refractive index , which is not possible with TIR microscopy since TIR requires an interface with a changing refractive index.
220.127.116.11 Prism-coupled TIR excitation
Prism-coupled TIR excitation is one of the most common ways to create an evanescent field for dark-field microscopy and allows flexibility in choosing illumination source, direction, polarization, wavelength, and incident angle, which changes the penetration depth, but not the direction of the wave vector , , , , , , . While it is possible to achieve TIR by shining light at a coverslip directly , prisms are often used to control the incident angle and avoid refractions . This illumination technique gives unidirectional excitation similar to unidirectional HADF excitation outlined above. In fact, prism-coupled TIR excitation may be thought of as a special case of unidirectional HADF excitation where the illumination angle is high enough that it leads to TIR, instead of refraction. For white-light illumination, halogen lamps are often used due to their relatively flat spectra . When high power densities are required, a white-light laser can be used with power densities on the order of tens of kW per cm−2, creating high enough scattering signals to capture spectra with 1 ms exposure , [ 117]. Wavelength-dependent and polarized excitation are possible by placing spectral filters and polarizers in the excitation path , [ 118]. By modifying the incident angle, the penetration depth of the field can be modulated , , , . Typical incidence angles range from just above the critical angle (42° for an air-glass interface) all the way to 90° (parallel to the coverslip) . Prism-coupled TIR excitation can also be achieved at glass-water interfaces for measuring nanoparticles in spectroscopic cells, as long as the incident angle is adjusted to ensure TIR at the glass-water interface (see Section 5.1) , , , .
Control of the incident direction and polarization allows visualization and distinction of bonding and antibonding plasmon modes . When plasmonic nanoparticles are close to each other with an edge-to-edge separation smaller than ∼2.5 times their diameter , their individual plasmons can hybridize to form lower energy bonding modes and higher energy antibonding modes, analogous to molecular orbital theory . The Gwo group excited gold octahedra at different interparticle separations with polarized light (Figure 3A and B) . When the light was polarized along the longitudinal axis of the dimer, the authors observed a bonding mode, which red-shifted as the distance between the particles was decreased. When the authors polarized light in the transverse direction, they observed only the antibonding mode (Figure 3C). As the interparticle distance decreased, the spectrum blue-shifted, confirming stronger antibonding character.
The Garini group used the exponentially decaying nature of the evanescent field in prism-coupled TIR excitation to determine the conformation of DNA by tethering gold nanospheres to a coverslip using DNA in a liquid cell . Movements of the DNA in the x- and y-directions could be monitored directly by a charge-coupled device (CCD) camera while movements in the z-direction were calculated from the scattering intensity, which scales with the excitation field intensity and hence the distance from the surface. The probability of finding the sphere close to the surface of the coverslip was disproportionally low, which was explained by the entropic penalty resulting from the reduced possible conformational states as the DNA moved closer to the substrate.
Using a parabolic prism instead of a triangular prism allows decoupling the incident angle from the spot position . One of the disadvantages of prism-based TIR excitation is that a change in incident angle also leads to a change in the position of the beam spot. Diez and coworkers eliminated this limitation by using a prism with parabolic sides . The parabolic shape always focused the light to the same spot in the center of the prism. By walking the beam along the flat side of the prism, the authors controlled the incident angle of the beam and penetration depth of the evanescent field. The beam spot did not move when the angle of incidence was adjusted . Similar parabolic mirrors have also been used for TIR fluorescence microscopy .
18.104.22.168 Condenser-based TIR excitation
Condenser-based TIR excitation enables symmetric excitation, similar to condenser-based HADF excitation (see Section 22.214.171.124), but with near-field confined light. To achieve TIR, a central beam block is placed in the condenser, and an annulus of light is focused on the back of the coverslip above the critical angle. This annular configuration allows excitation from all directions, giving a high signal-to-noise ratio method to study the properties of nanoparticles , , . By placing a polarizer in the excitation path, excitation with polarized light can be achieved, which unlike prism-coupled TIR excitation, comes from all directions , [ 130]. An oil-immersion condenser is required to achieve TIR at the sample.
126.96.36.199 Objective-based TIR excitation
In objective-based TIR excitation, light is focused through the objective at an angle sufficient to cause TIR. Although this excitation technique is more commonly used in fluorescence microscopy where the excitation beam can be spectrally filtered from the Stokes shifted emission , objective-based TIR microscopy and spectroscopy of nanoparticles have been reported by multiple groups , [ 112127], . A particular advantage is that excitation and collection are carried out on the same side of the sample, allowing free access to the nanoparticles by other tools, such as an atomic force microscopy (AFM) tip (see Section 5.2) , [ 139].
Excitation and signal collection are performed with the same high-NA objective. In a typical setup, a beam splitter or dark-field mirror is placed in the filter wheel of the microscope to bring light through the objective to the sample, similar to objective-based HADF excitation illustrated in Figure 1B. Light is focused on the side of the back focal plane of a high-NA oil-immersion objective. The light emerges on the side of the objective through the immersion oil at a maximum angle, :
When , the light undergoes TIR at the interface between the coverslip and the surrounding medium. The reflected beam is recollected by the same objective, with the scattered light collected by the center of the objective lens. The reflected beam is then spatially filtered from the scattered light. When a dark-field mirror is used, the reflected beam is reflected off the mirror . When a beam splitter is used, a beam block or iris in the detection path may be used to remove the reflected beam . Comparing Equation (13) to Equation (10), it becomes clear that TIR can only be achieved when the NA of the objective exceeds the refractive index of the less dense medium , [ 140].
The Martin group used objective-based TIR excitation to monitor optical trapping of gold nanoparticles in the gaps of dimers . The authors lithographically deposited gold nanorods with a 25 nm gap on a coverslip and mounted the sample on an inverted microscope, with water covering the nanoparticles (Figure 3D). A 1.45 NA oil-immersion objective was used to achieve TIR excitation with white light from a halogen lamp. Trapping was achieved with a laser operating at 800 nm. The reflected light was blocked spatially using a dark-field mirror. Additionally, scattered laser light was eliminated with a notch filter. The light scattered from the nanoparticles was directed to a spectrograph and spectra were acquired. When a colloidal solution of 20 nm gold spheres was added, the plasmon red-shifted from 690 to 740 nm as nanoparticles were trapped by the 800 nm laser (Figure 3E and F, indicated by times T1 and T2). When the laser was turned off, the authors observed a gradual shift back to 690 nm as the 20 nm particles were no longer trapped and diffused away (Figure 3G and H, indicated by time T3).
Objective-based TIR excitation has been reported to show a higher signal-to-noise ratio and a lower background than through-the-objective normal incidence dark-field excitation. Noji and coworkers built a hybrid setup that can achieve objective-based TIR excitation and through-the-objective normal incidence dark-field excitation with minimal modifications . Objective-based TIR excitation was achieved with a 1.45 NA objective and a 532 nm laser using a dark-field mirror to direct light through the side of the objective and to spatially filter the scattered light from the reflected beam. Normal incidence excitation was achieved by replacing the dark-field mirror with a dot mirror and steering the beam to the center of the dot mirror, which allowed the beam to emerge normal through the objective, while only collecting backscattered light at high angles. The authors note a higher signal-to-noise ratio and a lower, more uniform background for objective-based TIR excitation compared to normal incidence dark-field excitation.
188.8.131.52 Waveguide TIR excitation
When the substrate is used as a waveguide, it can be illuminated from the side, allowing access to the other side of the sample, similar to objective-based TIR excitation but without the high-NA requirements or the need to spatially filter the reflected excitation beam from the scattering signal of the nanoparticles. Waveguides are especially useful in sample configurations where direct access from both sides is blocked by other instrumentation such as an AFM tip over the sample and an objective below the sample .
As illustrated in Figure 1C, a coverslip can be used as a waveguide for dark-field imaging when a beam of light is coupled into the side of the coverslip with a prism above the critical angle. Light is confined to the coverslip and continues to travel through the coverslip by successive TIR events until it can escape through a second prism, creating evanescent fields at the coverslip interface. The spacing between the TIR sites depends on the incident angle and the coverslip thickness: a shallow incident angle or a thick coverslip will lead to a larger distance traveled between the top and the bottom of the coverslip, resulting in a larger spacing between the TIR sites. Calculations for coverslip thickness and incident angle can be found in an article by Burghardt . To improve light confinement, materials of high refractive indices such as tantalum pentoxide  and silicon nitride , both with a refractive index of approximately 2.2, have been used. Instead of using a prism, Matsuda used the high viscosity and high refractive index of glycerin to couple white light into a coverslip from an optical fiber .
Waveguide illumination can also be achieved by coupling light from a focused halogen lamp into the side at an angle that leads to total internal reflection (Figure 3I) , [ 82]. A comparison between objective-based annular reflected HADF excitation and waveguide TIR excitation of gold nanorods is shown in Figure 3J and K. The Cahoon group clearly demonstrated an improved signal-to-noise ratio for TIR excitation compared to HADF excitation in the images (Figure 3J and K) and the spectra (Figure 3L and M), consistent with other TIR illumination techniques. The authors also confirmed that polarized excitation is possible using their setup.
The non-collimated nature of LED light can be used to achieve very simple, yet effective waveguide illumination , , , , . When the LED is placed next to a coverslip without any focusing lenses, some of the light from the LED naturally meets the coverslip at angles between 90° and the critical angle, resulting in some light being coupled into the coverslip. Cladding, such as cardboard or rubber, between the LED and the microscope objective may be used to block stray light that is not coupled into the coverslip from reaching the objective. While this method only uses part of the LED light, the high contrast of TIR excitation techniques still enables a good signal-to-noise ratio. Furthermore, this method is easy to incorporate into existing microscopy setups.
Optical fibers have also been used as waveguides for dark-field illumination , , , , , , , , . Optical fibers are essentially cylindrical waveguides: light is coupled into the fiber from the end and prevented from escaping by TIR. The outside of the fiber is surrounded by an evanescent field, exciting nanoparticles deposited on the optical fiber. The fiber is mounted to the sample holder of the microscope to allow the objective to focus on the fiber , , , , , , , , . A slight disadvantage is the cylindrical shape of the fiber, as the curvature can lead to loss of focus for particles along the radial direction, making the effective measurable field of view long but narrow .
3.2.2 SNOM-based excitation and detection
SNOM breaks the diffraction limit of light by scanning across a sample with near-field confined light using a sub-wavelength sized aperture or scattering tip , , , , , . The diffraction limit of light is a fundamental limitation in how well an imaging system can distinguish two nearby emitters and is defined as , where is the excitation wavelength. In 1928, E. H. Synge proposed that the diffraction limit could be overcome by illuminating the sample through a subwavelength hole . In 1984, D.W. Pohl realized this technique by puncturing a hole in an AFM tip and collecting the near-field signal scattered from a transparent sample , [ 159]. This work inspired future studies featuring a variety of excitation and collection geometries, and SNOM is now a powerful technique for near-field imaging , , .
Near-field instruments are usually separated into two categories depending on the type of tip used: with or without aperture , [ 164]. Aperture-SNOM encompasses configurations where a nanoaperture is used either as a nanocollector  or as a local source of illumination . The resolution of these configurations is defined by the size of the aperture and the tip-sample separation . When the aperture is used as an illumination source, light from a laser is guided through an optical fiber and emerges from the subwavelength aperture at the fiber tip to locally illuminate the sample, such as organic molecules , [ 166] and nanostructures , [ 167]. Light scattered, reflected, or transmitted by the sample is detected in the far-field with an objective  or guided back through the aperture . In other geometries incident light is illuminated from the side or at normal incidence through an objective and the near-field signal is collected via the SNOM aperture , [ 167]. Aperture-SNOM setups have been employed to image nanoparticles , [ 170] and spectroscopically monitor reshaping of silver nanoparticles . Fritzsche and coworkers used an aperture with a 80 nm diameter in transmission mode of a microscope to detect DNA binding to individual nanoparticles .
Homogeneous line-widths of single and coupled nanoparticles were determined using an aperture-SNOM setup by Feldmann and coworkers . Individual 40 nm nanospheres embedded in a titania film were imaged by scanning a wavelength tunable laser coupled to an optical fiber with an opening of 80 nm (Figure 4A). The transmitted light was directed to a photodiode and single-particle spectra were collected by recording transmitted light intensities at different excitation wavelengths (Figure 4B). The resulting spectra had homogenous line-widths and were visibly narrower than the broadened ensemble spectrum of the film composite. The relative transmission was larger than unity, indicating a transmission enhancement, as expected from plasmonic nanoparticles with large scattering cross-sections. The collected spectrum of particle one also compared well to Mie theory of a 40 nm gold nanosphere (Figure 4B). However, as evident in the spectra of particles two and three, heterogeneity in line-width and spectral shape were observed (Figure 4C). The authors attributed the differences in line-width to variations in local refractive index due to imperfections in the titania and to variations in particle size. The spectrum shown in Figure 4D was determined to be that of a coupled dimer and agreed well with the simulated spectrum of two 20 nm gold spheres with a 6 nm inter-particle separation.
In apertureless SNOM, also called scattering-type SNOM (s-SNOM), scattering is collected in the near-field at the surface of a specimen that is illuminated by far-field optics . The sample is illuminated with a laser and subwavelength resolution is obtained by scanning a metallic tip while recording the field scattered by the tip . The desired signal originating from the local interaction between the tip and the object of interest is filtered from the background through vertical modulation of the tip position in tapping mode and demodulation of the optical signal at the tip oscillation frequency Ω, or one of its higher harmonics , [ 175]. s-SNOM has been used more frequently for imaging , , ,  and spectroscopy , [ 180] than aperture-SNOM. Hillenbrand, Aizpurua, and coworkers, used the fact that the substrate-tip distance can be controlled to study weak and strong coupling between gold nanodisks and scattering tips .
The Suchowski group employed s-SNOM coupled with interferometric detection to collect super-resolved spectra from gold nanorods . Half of the light from a supercontinuum laser was focused onto an AFM tip, while the other half was diverted to a Michelson interferometer (Figure 4E). The laser pulse at the AFM tip excited the nanoantennas, and the tip then interacted with the sample’s electric near-field. Spectral information was obtained from the interference between the extracted near-field signal and a reflected reference beam (Figure 4F and G). The spectral information was collected at each location as the tip was scanned across the sample, forming a spectral image (Figure 4F). The setup allowed a spatial resolution of 30 nm and spectral resolution of 50 cm−1 . Recent reviews covering the application of SNOM for sensing and spectroscopy of nanoparticles have been published by Zhang and coworkers , and Fanchini and coworkers .
3.3 Interferometric scattering techniques
The detection of very small particles can be achieved by interferometric scattering (iSCAT) techniques , [ 185]. Interferometric scattering signals are obtained from the interference between scattered light from nanoparticles and light reflected from a glass coverslip, as reported by Sandoghdar and coworkers . A beam splitter was used to excite nanoparticles deposited on a glass coverslip at normal incidence through an air-spaced objective (Figure 5A). Approximately 5% of the light was reflected by the air-glass interface  while the rest of the light excited the particle. The scattered light from the particle and the reflected light from the coverslip were collected by the same objective and directed towards a spectrograph. The reflected field, was used as the reference and can be described by:
The detected signal is thus the sum of the reflected beam (first term), the scattered light (second term), and the interference between the scattered and reflected electric fields (third term). While the pure scattering signal scales with the volume squared, interference can now be seen to scale linearly with volume, shown by the third term of Equation (16). For larger nanoparticles (diameter > 30 nm), the scattering signal dominates over the interference term. However, as the particle size decreases, the interference term only shrinks linearly, rather than with the square of the volume, allowing characterization of particles that are otherwise below the detection limit for noninterferometric scattering techniques.
In 2004, the Sandoghdar group acquired spectra of 5 nm plasmonic nanoparticles using the interference mechanism described above with a supercontinuum laser beam in confocal scanning mode (Figure 5A–C) . For 60 nm particles, the signal was dominated by scattering and the authors observed a bright signal on a dark background, and spectra with a positive spectral intensity after background subtraction (Figure 5C). For 20, 10, and 5 nm particles, however, the signal was dominated by the interference signal and the particles appeared as dark spots with negative spectra (Figure 5B and C). A 31 nm particle exhibited intermediate behavior.
Related interferometric techniques have been developed where the reference beam is created by different mechanisms to allow independent attenuation and improvements in signal-to-noise ratio. From Equation (16), the interference signal can be increased by increasing the intensity of the incident field. However, the background (e.g., the reflected light) will then also be increased. Therefore, the signal-to-noise ratio is increased when the incident light intensity is increased while attenuating the reference beam , [ 188].
Particles as small as 2 nm , [ 188] have been detected and interferometric contrast techniques have found application for scattering labels in biological imaging , , , . The technique has been used to determine the size , dielectric function , and with polarized excitation, the orientation  of nanoparticles. Extensive reviews were published by Sandoghdar  and Kukura .
3.4 Polarized excitation dark-field microscopy
Polarized dark-field scattering spectroscopy is a powerful tool to optically characterize the orientation and geometric properties of anisotropic and chiral nanostructures. The scattering of anisotropic plasmonic nanostructures can be modulated by adjusting the incident light’s linear polarization, revealing single-particle orientation. Chiral nanoparticles are those that are not superimposable with their mirror images. The handedness of the chirality can be assigned using circular differential scattering (CDS), which measures the differential intensity of light scattered under left- and right-handed circularly polarized light (LCP and RCP, respectively) , , . The polarization state of the incident light can be easily tuned by placing a series of polarizers and waveplates in the excitation path. Linearly polarized light is achieved by adding a linear polarizer and circularly polarized light is generated by placing a linear polarizer and a quarter-wave plate in the excitation path.
3.4.1 Linearly polarized excitation
The Willets group observed an unexpected anisotropy in nanoprisms under a polarized excitation field generated by TIR . The excitation light, with wavelengths selected by a liquid-crystal tunable filter (LCTF), was sent through a linear polarizer before reaching the sample. Figure 6A shows the representation of the coordinate system for the polarization-resolved setup with objective-based TIR excitation. The blue arrows indicate two incident polarization components: p and s. p-polarized excitation has an electric field vector parallel to the plane of incidence, while that of s-polarized light is perpendicular to the plane of incidence. The single-particle scattering spectrum of a nanoprism acquired by scanning the incident wavelengths in 1 nm steps and recording the scattered intensity at each wavelength is shown in Figure 6B. To characterize the anisotropy of the nanoprisms, Willets and coworkers adjusted the polarization of the incident light in 10° steps from 0 to 360° while holding the excitation wavelength constant. The recorded scattering intensities were analyzed in a polar plot and overlaid on scanning electron microscopy (SEM) images of the nanoprisms (Figure 6C and D). The nanoprisms showed an unexpected wavelength-dependent anisotropy. For example, the plasmon modes of the nanoprism at 660 and 650 nm were orthogonally polarized (Figure 6C and D). However, under condenser-based HADF excitation, the authors observed that the scattering from the nanoprisms was isotropic. Therefore, the origin of the anisotropy was assigned to the unique polarization properties of the evanescent wave. Due to the exponential decay of the evanescent field, light that was initially p-polarized becomes elliptically polarized in the (x, z) plane (Figure 6A) . Meanwhile s-polarized light maintained its polarization with only a y-component. Depending on the nanoprism’s orientation, the polarization properties of the evanescent wave lifted the degeneracy of the orthogonal modes, clearly resolving them in the wavelength-dependent polar plots.
3.4.2 Circularly polarized excitation
The Landes and Link groups utilized CDS measurements of single particles to uncover the origin of chirality from bovine serum albumin (BSA)-aggregated gold nanorods . Chiral assemblies were prepared by aggregating gold nanorods with low concentrations of BSA and spin-coating the complexes onto transparent conductive substrates. In the CDS measurements, unpolarized white light from a tungsten-halogen lamp was sent through a linear polarizer and a quarter-wave plate before entering a dark-field condenser (Figure 6E). Then, scattering spectra from single aggregates were acquired under LCP and RCP excitation. Calculating the differences between the two spectra, with appropriate corrections for linear artifacts , gave CDS spectra (Figure 6G and H). By repeating CDS measurements of ∼100 single aggregates, the authors obtained distributions of chiral and achiral subpopulations of gold nanorod-BSA complexes (Figure 6F). The results revealed that single gold nanorods coated with BSA do not have measurable CDS, while aggregates do, suggesting that aggregated BSA-gold nanorods were the origin of the chirality in an ensemble sample. Single-particle CDS measurements were then correlated with transmission electron microscopy to understand the origin of the chirality from each individual aggregate (Figure 6G and H). By combining CDS measurements with correlated tomographic reconstruction and electromagnetic simulations, structural chirality was determined to predominately give rise to CDS in aggregates (Figure 6G). However, CDS was also observed from aggregates found to be structurally achiral (Figure 6H). The origin of this signal was attributed to chiral dipole-dipole coupling  between the gold nanorods and the BSA, suggesting the possibility of single-molecule chirality sensing reported through the CDS of plasmonic particles.
Karst et al. used CDS to compare the optical activity of chiral helicoids and found that minute morphological differences can manifest themselves in pronounced chiroptical differences . The left panel in Figure 6I shows the schematic of chemically synthesized chiral gold nanostructures. The diagram includes left-handed (L), achiral, and right-handed (D) gold nanostructures. The authors measured the scattering, S, of the helicoids under LCP and RCP excitation, which they used to calculate the asymmetry, or g-factor:
The right panel in Figure 6I shows the averaged g-factor of 26 L-handed (red), 26 achiral (black), and 26 D-handed nanoparticles. The averaged single nanoparticle g-factor agreed with that of the ensemble measurement. However, due to the heterogeneity of the nanoparticles prepared by colloidal synthesis, a large variance in g-factors was observed in the single-particle spectra. One of the advantages of single-particle CDS is the ability to distinguish minute differences in nanoparticle morphologies that are otherwise inaccessible using other characterization methods .
3.5 Polarization resolved detection of single-particle scattering
While polarized excitation can significantly modulate the scattering of single particles, analysis of the polarization state of light scattered by the nanoparticle can similarly provide valuable information about the orientation and geometric properties of anisotropic particles , , , , . For example, by placing a polarizing beam splitter in the detection path, the orientations of nanorods in biological media have been tracked . The scattering intensity of a single dipole scatterer like a gold nanorod varies with a dependence where is the angle between the long axis of the nanorod and the angle of the linear polarization . In a typical experiment, nanoparticles are immobilized on a substrate and a linear polarizer is rotated in the detection path. A single-particle scattering spectrum or image is collected at each angle. By fitting the resulting intensity of the LSPR to a dependence, it is possible to determine the nanorod’s orientation using only optical techniques. Polarization-resolved detection of single-particle scattering can often be easier to implement without the polarization distortions induced by the high-NA optics used in dark-field excitation , [ 205]. However, the polarization information captured in the image plane is a two-dimensional projection of that contained in the scattered light, limiting the ability to track out-of-plane polarization phenomena, such as tilt angle .
3.5.1 Linear polarization detection
Käll and coworkers have implemented an interesting variant of orientation sensing by placing a linear polarizer with a fixed angle in the detection path but utilizing a circularly polarized optical trap to rotate a single nanorod (Figure 7A and B) . The transfer of angular momentum from the circularly polarized light caused the nanorod to rotate. By characterizing the intensity of the scattered light that passed through the fixed linear polarizer with an avalanche photodiode (APD) and autocorrelator, the authors could characterize incredibly fast rotation rates of the nanorod of up to 42 kHz (∼2.5 million revolutions per minute) depending on the laser power of the trapping beam (Figure 7C). A significant portion of the optical torque on the nanorod was attributed to resonant scattering of the circularly polarized light from the optical trap (Figure 7D).
3.5.2 Stokes polarimetry
The Stokes parameters form a vector, S, that contains the complete polarization state of light:
S0 describes the full intensity of the polarized light, S1 describes if the linear polarization components are more aligned at 0 or 90°, S2 is similar to S1, but for 45 and 135°, and S3 describes any right- or left-handed circular polarization . Stokes polarimetry can easily be implemented with common microscopy techniques with the addition of a quarter-wave plate and linear polarizer in the detection path. Stokes polarimetry is often combined with Fourier-plane imaging, also called k-space imaging, which captures the back-focal plane of the objective lens. Fourier-plane imaging characterizes the momentum-space of the emission or scattering of an analyte . Commonly implemented in photoluminescence studies, k-space polarimetry simultaneously captures the polarization state and direction of the emission of dyes , , . The Koenderink group has utilized k-space polarimetry to characterize the polarization state of light scattered by a lithographically-patterned plasmonic antenna shaped like a bullseye as a function of the incident light polarization . Using this technique, the researchers observed that plasmonic bullseyes can convert linearly polarized light to circularly polarized light, and convert from right-to left-handed polarizations .
3.5.3 Mueller matrix spectroscopy
The Ghosh group has implemented an advanced polarization analysis approach by performing Mueller matrix spectroscopy in a dark-field microscope (Figure 7E) . The Mueller matrix is the 4 × 4 matrix that transforms the initial light polarization state (starting Stokes parameters) to the final polarization state . Mueller matrix spectroscopy of a single nanoparticle then quantitatively describes how a particle interacts with polarized light and alters its polarization state. The authors carefully calibrated the polarization state generation and analysis values required to correct for the high-NA imaging system using polarizers as standards. The resulting Mueller matrix captured only the polarization information of the scatterer. With this technique, the authors recorded the Mueller matrix of a single gold nanorod with significant intensity in the transverse mode (Figure 7F). The Mueller matrix demonstrated linear diattenuation (Figure 7E – blue elements) resulting from the differential excitation of both the transverse and longitudinal modes. Linear retardance (Figure 7E – red elements) described the phase retardation between the orthogonal plasmon modes. Finally, the black elements of the Mueller matrix were evidence of depolarization due to excitation of the nanorod with a focused beam, averaging over the planes of azimuthal scattering as well as over the collection angle of the objective lens . The Ghosh group has since applied this successful proof-of-principle demonstration to oligomers with Fano resonances .
4 Spectral characterization of single particles
In Section 3, we discussed different approaches of detecting scattering from single nanoparticles. While many applications simply seek to localize nanoparticles as labels, more information can be gained from the plasmon spectrum. LSPR position for example can give valuable information on the shape, size, and local environment of the nanoparticle, while the homogeneous line-width of a single nanoparticle can be used to directly study the dephasing of the plasmon and thus different damping mechanisms including charge and energy transfer . In this section, we will describe several techniques that have been developed to spectrally resolve the scattering of single particles, including push-broom scanning hyperspectral imaging, wavelength scanning spectral imaging, multiple-channel spectral imaging, snapshot hyperspectral imaging, and interferometric detection. Broadly, single-particle scattering spectra can be acquired by dispersing the wavelengths of scattered light with a diffraction grating, or by filtering the incident light, and recording the intensity of the scattered light as a function of the wavelength. Table 1 provides an overview of the key techniques for spectral characterization along with their typical time and spectral resolutions.
|Technique||Method of wavelength separation||Widefield acquisition possible?||Typical time resolution for complete image acquisition||Typical spectral resolution|
|Push-broom scanning hyperspectral||Diffraction grating in detection path||No||∼8 min ||≤1 nm |
|Wavelength scanning||Tunable filter in excitation path||Yes||<1 min , [ 219]||≤10 nm , [ 219]|
|Multiple channel single-particle spectral imaging||Fixed filters in detection or excitation path||Yes||0.1 –0.5 s ||Select wavelengths only|
|Snapshot hyperspectral imaging||Diffraction grating in detection path||Yes||1 ms ||≤1 nm |
|Interferometric detection||Interferometer in detection path||Yes||5 s ||2 nm , [ 223]|
Note that the time resolution for push-broom hyperspectral imaging is partially limited by the size of the scanning area, as an image must be acquired at each step of the scan. The time resolution given here is for the acquisition of a 140 × 200 μm image with 100× magnification . For widefield acquisition techniques, the entire field of view is captured, allowing larger image sizes such as 659 × 496 μm with 50× magnification for interferometric detection .
4.1 Scanning single-particle spectral imaging methods
A dark-field microscope combined with a spectrometer or a wavelength-tunable excitation source is a powerful tool for characterizing the scattering spectra of single nanoparticles. Particle-by-particle acquisition approaches have been successfully implemented . In these techniques, an intensity integrated image is typically first acquired to locate individual particles, followed by centering a single particle in the microscope field of view. A slit or pinhole is placed in the detection path to spatially filter the scattering of the particle of interest from that of neighboring particles. The scattered light is then directed to a spectrograph, which disperses the collected light with spectral resolution defined by the chosen grating. The dispersed light is then imaged onto a CCD camera or other array detector to measure the intensity of the scattering as a function of wavelength. Once the spectrum of one particle is collected, the next particle is centered in the field of view and its spectrum is acquired in the same fashion. This process is repeated until the spectra of all particles of interest are sequentially acquired. Particle-by-particle accumulation techniques provide high spectral resolution but, unless fully automated , can be prohibitively time consuming when acquiring the spectra of a high number of particles. As a result, several spectral acquisition techniques based on automated position or wavelength scanning have been implemented to efficiently achieve high spectral resolution of many individual particles in parallel instead of consecutively.
4.1.1 Push-broom scanning hyperspectral imaging
One popular implementation of push-broom single-particle spectral acquisition is hyperspectral imaging, which collects a three-dimensional (3D) data cube containing the x- and y-positions of the nanoparticle, as well as the scattering spectra at each (x, y) location , , , . In scanning hyperspectral dark-field imaging, either the sample stage  or spectrometer  is scanned across the field of view in the y-direction. The scattered light from the nanoparticles is spatially filtered by a slit aperture placed before the spectrograph, and the dispersed light from the slit is imaged onto a two-dimensional (2D) CCD camera (Figure 8A). The images acquired at each step are 2D matrices containing the x-location of the particle along the slit and the intensity as a function of wavelength recorded along the z-axis. Scanning the stage or spectrometer over many steps in the y-direction allows for the collection of a three-dimensional (3D) data cube from which spectra can be extracted by summing the spectral data from a square region of pixels containing the particle of interest. The Landes and Link groups achieved hyperspectral detection by scanning a spectrograph and CCD camera across the field of view to acquire 3D data cubes (Figure 8B) , , , , . This technique has the benefit of being less expensive to implement than stage-scanning, as the scanning step can be larger by the amount of objective magnification, and thus can be accomplished by a simple linear actuator. Alternatively, scanning the stage often requires the finer step sizes of a piezoelectric actuator. While a piezoelectric stage has reduced hysteresis relative to a linear actuator, the precision of a linear actuator is often more than sufficient to perform hyperspectral imaging. Byers et al. were able to utilize this hyperspectral technique to quantify changes in LSPR maxima across tens of particles as a potential was applied in an electrochemical cell (Figure 8C) .
A push-broom method implemented by Ringe and coworkers scanned a piezoelectric stage in 0.8 µm steps to acquire a new 2D matrix with each step (Figure 8D–F) forming the 3D data cube (Figure 8G) . The hyperspectral image size was determined by the magnification, the height of the slit, and the scanning range of the stage. The diffraction-limited spatial resolution was determined by the number of pixels in the CCD camera and the scanning step size of the stage, while the spectral resolution was determined by the grooves/mm of the chosen diffraction grating. The acquired data cube was integrated along the wavelength axis to produce a spectral image (Figure 8H) from which single-particle spectra were extracted (Figure 8K). The technique by Ringe and coworkers also had the flexibility to characterize transmission and reflectance by altering the excitation geometry (Figure 8I and J) .
4.1.2 Wavelength scanning spectral acquisition
Another scanning method for single-particle spectral imaging is scanning the wavelength of the excitation with a tunable filter, such as an acousto-optical tunable filter (AOTF) or LCTF while holding the stage and camera location constant . Typically, wavelength-scanning approaches are implemented in a widefield fashion, in which a 2D array detector captures images of the field of view at each wavelength step, building up a 3D data cube similar to the push-broom hyperspectral techniques discussed above , , , . While push-broom methods often have higher spectral resolution, wavelength scanning approaches can have faster acquisition times . The Mulvaney group successfully implemented a wavelength-scanning approach to achieve a higher signal-to-noise ratio than lamp-based push-broom hyperspectral techniques . The particles were excited by a spectral slice selected from a white-light laser with an AOTF. The excitation wavelength was scanned in 1 nm steps at a rate of 0.5 nm/s (Figure 8L). The scattered intensity was spatially filtered by a 50 µm pinhole and recorded by a photomultiplier tube (PMT) in single-photon counting mode with the resulting spectrum shown in Figure 8M. The combination of high-intensity laser excitation and PMT detection offered high signal-to-noise ratios. Moreover, in this approach, the particles are only briefly excited on resonance with intense illumination, which is useful for reducing particle deformation due to melting. Finally, holding the excitation wavelength constant allowed for direct monitoring of changes in particle intensity with a 1 ms bin time .
4.2 Multiple channel single-particle spectral imaging
Multiple channel spectral imaging techniques enable characterization of all particles within the field of view simultaneously , , , , . Push-broom hyperspectral imaging methods offer high spectral resolution , [ 217], but spectral acquisition of ∼20 particles can often take 1–2 min. Multiple channel spectral imaging techniques utilize filters or digital color analysis to acquire spectral information in a single exposure without a slit or pinhole with high time-resolution .
4.2.1 Ratiometric imaging
Ratiometric imaging records the ratio of the scattering intensity at two well-separated wavelengths for the entire field of view . Therefore, this technique is ideally suited for quickly characterizing significant spectral shifts, such as those that occur upon coupling to nearby nanoparticles, especially in a biological context for studying dual-labeled DNA  and protein interactions . Ratiometric imaging (Figure 9A) has been successfully implemented by the Reinhard group to perform plasmon coupling microscopy . Plasmon coupling microscopy relies on the principle that the LSPR red-shifts as one or more neighboring particles increase in proximity resulting in plasmon coupling (Figure 9C) . In ratiometric imaging, the particles are excited with a white-light source, often from a dark-field condenser, and the scattering from the particles is spectrally separated into long and short wavelengths by a beam splitter. The resulting light is then filtered and imaged onto two separate halves of a CCD camera. One imaging channel is centered around the LSPR of a single particle, and one is centered around the LSPR of a closely spaced dimer. Reinhard and coworkers successfully employed this technique to track the formation of gold nanoparticle dimers in HeLa cells below the diffraction limit (Figure 9B) . The ratio of the intensities of the two channels allowed for assigning the time at which two particles coalesced, even within a diffraction-limited point spread function (Figure 9D). For example, upon dimer formation, the intensity of the red channel (I580) increased at the same time as the intensity of the green channel (I530) decreased, signifying the particles were within the plasmon coupling regime.
4.2.2 Multi-channel spectral imaging with digital single-lens reflex (SLR) cameras
Based on principles similar to ratiometric imaging, a digital SLR camera can function as a three-channel spectrometer by measuring the ratio between the red (R), green (G), and blue (B) intensities of the image , , , . Odom and coworkers have implemented such a design with a digital SLR camera in a standard dark-field microscope equipped with a spectrometer for calibration (Figure 9E) . Optional filters and polarizers can be added for even more sensitive spectral separation of different particles. This approach was applied to gold nanopyramids on a substrate orientated either up or down, thereby impacting their spectral characteristics. Specifically, the tip-down orientation was found to scatter with greater intensity than the tip-up orientation in the near-infrared (NIR) wavelength range (Figure 9F). To rapidly differentiate nanoparticles in these two orientations, the authors inserted an 850 nm bandpass filter before a digital camera optimized for NIR. Then, the ratio of R/G intensity values from the digital camera image was plotted (Figure 9H) demonstrating a clear threshold between tip-up and tip-down orientations with R/G = 3.2. Note that intensity was recorded in the G channel at NIR wavelengths, potentially due to NIR transmission of the Bayer filter used in digital color cameras . This threshold was applied to a widefield image and the orientations were unambiguously assigned (Figure 9G). Confirmation via SEM verified the assignment with 100% accuracy and the authors applied the same principles to distinguish between particles with different compositions, and with the insertion of a polarizer, were able to identify the orientation of the long axis of a nanostar. Moreover, the use of a digital SLR camera as a three-channel spectrometer decreases the cost of the detection path by more than an order of magnitude, increasing the ease of implementation of dark-field scattering spectral characterization.
4.3 Snapshot hyperspectral imaging
Snapshot hyperspectral imaging techniques combine the high spectral resolution of push-broom hyperspectral techniques with the high temporal resolution of ratiometric techniques by taking entire large-area spectra in just one snapshot . The goal of snapshot hyperspectral imaging is to capture entire spectra of multiple nanoparticles in one shot, to achieve the temporal resolution necessary to monitor dynamic chemical or electrochemical changes of nanoparticles , [ 242], and to quickly monitor changes in multiple nanoparticles’ surroundings for biosensing . Figure 10A shows an instrument diagram of the snapshot hyperspectral imaging approach taken by Kirchner and Smith et al. . Scattered light from the tube lens of the microscope was directed through a 30:70 beam splitter. 30% of the light was refocused onto a complementary metal-oxide-semiconductor (CMOS) detector (labeled CMOS1) to find the zeroth-order scattering (i.e., the position) of the particle (Figure 10B). The remaining 70% was directed to a 300 groves/mm transmission grating. The first order diffracted light was refocused onto a second CMOS detector (labeled CMOS2) to give spectral information (Figure 10C). A slit was placed in the first image plane at the focal point of the tube lens (Figure 10A) and standard lamps were used to calibrate the distance between the position given by CMOS1 and each pixel of the first order diffraction recorded on CMOS2. The calibration was then used to convert the difference in pixel position between the zeroth order and each pixel in the first order diffraction into a wavelength, with a spectral resolution of 0.21 nm per pixel. The slit was removed for measuring nanoparticles. By using a white-light laser, enough photons were scattered off the particles to give a temporal resolution of 1 ms, limited by the frame rate of the camera. Figure 10D shows a representative spectrum of a single gold nanorod. When particles were close together, their spectra overlapped, and appeared as two merged Lorentzian curves (Figure 10F). To avoid overlapping spectra, a relatively low particle density had to be used. The major disadvantage of snapshot hyperspectral imaging compared to push-broom hyperspectral imaging, other than the lower particle density, is a higher background as the absence of a slit allows light from the entire field of view to enter the detection path.
Snapshot hyperspectral imaging with a single detector can be achieved by using a diffraction grating with fewer grooves per millimeter, dispersing light less and capturing the zeroth and first orders on the same detector chip, as implemented by the Yeung and Gai groups , [ 245]. The setup reported by Kirchner and Smith et al. was also used in a one camera setup by Al-Zubeidi and Hoener et al. by replacing the 300 groves/mm grating with a 75 grooves/mm grating and capturing both the zeroth and first order diffracted light with CMOS2 . This setup allowed a higher number of particles to be measured simultaneously by dispersing the light less and hence allowing a higher particle density. Furthermore, a higher signal-to-noise ratio was achieved since the lower dispersion resulted in more photons per pixel, while sacrificing some spectral resolution (1 nm per pixel).
Su et al. developed a snapshot hyperspectral imaging setup by placing a diffraction grating between the sample and the objective and directing the light to a camera . As the light passed through the diffraction grating, it was split into its components and the objective then captured both the zeroth and first order scattering of the particles. The captured image consisted of the particle with its spectrum next to it. Figure 10G shows the intensity distribution for a few rows of pixels. The big spike on the right corresponds to the zeroth order scattering of the particle. The wider, less intense peak on the left gives the spectrum. The authors used this setup to monitor refractive index changes surrounding 50 nm gold nanoparticles with 1 s time resolution. When the nanoparticles were functionalized with biotin, binding of streptavidin was sensed in solution by tracking LSPR shifts.
A dynamic hyperspectral imaging technique that combines the time resolved nature of snapshot techniques with the high signal-to-noise ratio of slit or pinhole-based techniques is fast single-particle spectroscopy, developed by the Sönnichsen group . The setup is based on a commercial spectrograph but replaces the slit at the image plane with a liquid-crystal device (LCD) shutter to allow light transmission from only a selected subset of particles, essentially forming an array of switchable pinholes. In a typical measurement, all LCD pixels were first made transparent, the spectrograph grating was moved to the zeroth order, and an image of all particles was taken. Particles were then selected and grouped into horizontally nonoverlapping groups of up to 20 particles. All particles in one group were imaged at the same time, while groups were imaged consecutively. The response time of the LCD shutter was 40 ms, allowing fast scanning across the groups. Areas close to the particles and white-light scatterers (dust or large silica beads) were used for correction of the background and the incident light spectrum, respectively. This setup was employed to monitor the growth of gold nanoparticles in real time. Gold nanorods were placed in a liquid cell containing a growth solution that consisted of cetrimonium bromide, silver ions, gold ions, and ascorbic acid. Figure 10H shows the evolution of the LSPR of a gold nanorod, illustrating that growth occurred preferentially on the sides, leading to a blue-shift in the LSPR peak as particles became more spherical. The peak LSPR for 20 nanoparticles measured simultaneously in 30 s intervals demonstrates that nearly all particles became more spherical as the reaction proceeded (Figure 10I).
4.4 Interferometric detection
Another way to achieve hyperspectral imaging is by using an interferometer , , . Similar to snapshot hyperspectral imaging techniques, interferometric detection aims to achieve spectral imaging of the entire field of view at a higher temporal resolution compared to scanning techniques . Typically, the collected light from the objective lens is separated by a beam splitter with portions sent to both a permanent mirror and a movable mirror . The light is then recombined at the beam splitter and collected by a detector. Since both beams originate from the same source, they can constructively or destructively interfere, depending on the path difference. By changing the position of the movable mirror, an interferogram of the field of view is formed by measuring the interferometric signal at each pixel. A Fourier transform generates a spectrum at each pixel position .
Sung and coworkers used a home-built Michelson interferometer to measure single-particle spectra (Figure 11A) . Light from a dark-field microscope was sent through a beam splitter. The reflected beam was sent to a stationary mirror M2, while the transmitted beam was sent to a mirror M1 mounted on a piezoelectric stage. Reflected beams from M2 and M1 were recombined by the beam splitter and sent to a CCD detector. By carefully controlling the position of M1 and hence the beam path of the transmitted light, interferograms were collected, allowing the spectrum at any point of the field of view to be reconstructed (Figure 11B, green). A hyperspectral data cube of a 659 × 496 μm field of view was collected in 5 s, a significant improvement over push-broom hyperspectral imaging. The authors compared their interferometer with a commercial spectrograph (Figure11B, red line) for 40 nm gold spheres and found a significant improvement in signal-to-noise ratio for their system compared to the commercial spectrograph. Stranik and coworkers used a similar setup to measure single-particle spectra of gold nanospheres in water and glycerol, demonstrating the use of interferometer-based detection for refractive index sensing (Figure 11C).
5 Specialized sample configurations
Much of the research and applications involving nanoparticles focuses on the use of nanoparticles as sensors, scattering labels, and catalysts , , , . These measurements typically require the particles to be submerged in solutions or dispersed on electrodes. Additionally, combining single-particle dark-field or SNOM spectroscopy with tip-based scanning techniques provides complementary information on the reactivity and sensing-relevant adsorption properties of nanoparticles , , , . To measure particles in solutions, liquid filled spectroscopic cells are commonly used , [ 120], which can be used on most microscopy setups with small modifications of the excitation angle. Recently, some groups have opted to use water-immersion objectives for measuring in liquid to increase the sensitivity of their setups , , . Liquid cells and water-immersion setups designed for electrochemical measurements are particularly relevant for catalyst research, due to the growing interest in using plasmonic nanoparticles as antennas for photo-electrochemical reactions , , , , . Correlated scattering spectroscopy and AFM or scanning electrochemical cell microscopy (SECCM) is possible by combining an inverted microscope with a scanning tip , , .
5.1 Measurements in liquid
To study reactions on plasmonic nanoparticles or use plasmonic nanoparticles as scattering labels, spectroscopic cells are often used , , , , , . Spectroscopic cells sandwich the nanoparticles between two coverslips with a spacer between them and can be filled with liquids. Figure 12A shows an example of a flow cell on an upright microscope used by the Sönnichsen group . Nanoparticles were immobilized on a coverslip with six holes in it, three on each side forming three flow channels. Parafilm with three laser-cut flow channels was placed over the coverslip, with the flow channels matching the holes. A second coverslip was added on top and the parafilm was placed on a hot plate to melt the parafilm and create airtight channels with the coverslip. Tubing was added to the holes to flow liquid through the cell . Figure 12B shows an example of a spectrum recorded using this cell. This setup has been used to investigate the mechanism of chemical interface damping in gold nanorods  and to monitor conformational dynamics of single proteins . In the latter work, heat shock protein 90 was studied, which is known to exist in open and closed configurations. Gold nanospheres were attached to the ends of the protein. As the protein changed between the open and closed configurations, the coupling between the gold nanospheres increased and decreased, allowing the authors to monitor the conformation by tracking the scattering intensity over time.
The orientation of the substrate determines which excitation and collection geometries can be used. If the substrate forms the side of the spectroscopic cell that is positioned further away from the collecting objective, as illustrated in Figure 12A, both HADF excitation and prism-coupled TIR excitation are possible. The option to use prism-coupled TIR excitation opens up the opportunity to use a white-light laser for excitation, giving high enough intensities to collect spectra with millisecond time resolution , [ 117]. The disadvantage of this configuration is that the scattered light needs to penetrate the entire water layer and the opposing coverslip, undergoing multiple refractive index changes and possible scattering events, and requiring an objective with a long working distance to image through the bottom coverslip of the spectroscopic cell. If the particles are placed on the other coverslip close to the objective (i.e., the top coverslip in the upright configuration in Figure 12A), light only needs to travel through the substrate coverslip, reducing the number of interfaces and the working distance of the objective, making it even possible to employ an oil-immersion objective. However, the excitation light now has to travel through the medium before reaching the sample, making TIR excitation impossible. Typically, HADF excitation is used in these cells .
Spectroscopic cells can be used to optically monitor electrochemical reactions by using conductive substrates , , , . The nanoparticles need to be deposited on a conductive transparent substrate such as indium tin oxide (ITO), which is used as the working electrode. A platinum wire may be placed in the cell slightly away from the field of view to function as a counter electrode. Alternatively, the other coverslip can be coated with ITO and used as the counter electrode. In both cases, a platinum pseudo-reference electrode may be added in the cell. The Landes and Link groups used a spectroelectrochemical cell to probe the dependence of electrochemiluminescense enhancement through plasmonic nanoparticles , to characterize electrodissolution inhibition of gold nanorods through oxoanions , and to track the reversible formation of charge transfer plasmons by electrochemical oxidation and reduction of silver in a chloride solution . A flow cell designed for TIR excitation with a white-light laser enabled electrochemical reactions to be studied with millisecond time resolution using snapshot hyperspectral imaging (see Section 4.3) , [ 117].
To avoid the added noise and background associated with multiple refractive index changes, some groups use water-immersion objectives and place the objective directly into the analyte solution , , . Figure 12C shows a spectroelectrochemical setup used by the Maier and Cortés groups, with a spectrum recorded using this setup given in Figure 12D , [ 255]. They used a dark-field condenser to excite nanoparticles and collect light through a water-immersion objective . Since the electrochemical cell does not need to be sealed, the authors had enough space next to the objective to use a saturated calomel electrode as a reference electrode, which provides a more stable reference potential than a pseudo-reference electrode.
The He group employed light-sheet illumination for dark-field imaging, to sense hydrogen sulfide at a sensitivity of 0.1 nM . Light-sheet microscopy may be viewed as a specialized case of unidirectional HADF excitation as described in 184.108.40.206 where a cylindrical lens in the excitation path is used to focus a laser beam into a sheet of light . The light sheet is maneuvered to dissect the sample by illuminating the entire field of view in the x-y direction but only a thin limited cross-section in the axial dimension. Light-sheet illumination has become a popular choice for fluorescence microscopy , [ 265]. In the work done by He, a supercontinuum laser was sent through a wavelength selector to create discrete bands of light and then shaped into a light sheet using a cylindrical lens (Figure 12E). The inset of Figure 12E illustrates the spectrum of the supercontinuum and the wavelength filtered beam. The light scattered from silver-coated gold nanorods was collected and sent to a color camera. Spectral changes were monitored as changes in color. Upon exposure to hydrogen sulfide, the silver layer oxidized to silver sulfide, leading to a change in refractive index and a visible color change from red to green, enabling the optical detection of 0.1 nM sodium hydrosulfide, as shown in Figure 12F.
5.2 Integrated multi-modality setups
Dark-field spectroscopy can be combined with tip-based scanning probe techniques such as AFM. The Zijlstra group implemented an objective-based TIR setup coupled to an AFM (Figure 12G) . A white-light source was focused on the side of the back aperture of a high-NA oil-immersion objective to achieve TIR excitation. The reflected excitation beam was spatially filtered from the scattered light, which was directed to an electron multiplying CCD camera. Bandpass filters were inserted in the detection path before the camera to collect spectra of the nanoparticles. The top of the coverslip allowed access to an AFM tip. Figure 12H shows AFM topography maps and spectra of the same single gold nanorods. The authors observed LSPR red-shifts upon binding of single proteins, which were also detected by AFM. The Booksh group measured plasmon coupling between a nanoparticle and a nanohole array by attaching a gold nanoparticle to an AFM tip and scanning the tip across a gold film containing nanoholes . The authors found 10 nm shifts in the LSPR when the tip approached the surface close enough for the plasmon of the nanoparticle to couple to the plasmon modes of the nanohole array.
Dark-field spectroscopy coupled with single-particle electrochemical sensing was reported by the Hill group, who combined SECCM with a dark-field microscope to investigate the correlation between electrochemical reactivity and particle shape , [ 267]. The authors first took a hyperspectral image of a region of interest and then used the hyperspectral image to guide the SECCM tip to scan all particles of interest. In this way, the electrochemical reactivity was correlated to the spectrum and hence the particle shape. Notably, they found no correlation between particle size and electrochemical reactivity, further confirmed by correlated SEM, indicating that the often reported interparticle heterogeneity in reactivity is not purely due to variations in size. Hill and coworkers attribute the variations in surface reactivity to surface restructuring and variations in ligand density.
6 Conclusions and outlook
Overall, we provided an overview of single-particle scattering techniques and discussed different ways to excite, detect, and measure plasmon scattering spectra of single nanoparticles. Far-field HADF techniques rely on excitation at high angles to avoid collecting the excitation beam with the objective and only collect the forward- or backscattered light. Normal incidence excitation allows excitation perpendicular to the sample by blocking the incident beam and collecting scattering at high angles. These techniques excite particles in the far-field and allow excitation of nanoparticles in a wide variety of angles and refractive indices, including in refractive index-matched immersion oil. Near-field techniques rely on creating evanescent fields through prisms, objectives, condensers, waveguides, fibers, tips, or apertures and typically show very high signal-to-noise ratios but have some constraints when it comes to refractive indices and excitation geometries. Detection of nanoparticles down to 2 nm can be achieved by interferometric scattering techniques, which measure the interference of the scattered light with a reference beam, rather than the pure scattering signal. Far-field and near-field techniques can be used to detect the interaction of nanoparticles with polarized light, with some setups polarizing in the excitation path, while others place polarizers the detection path, or both.
Numerous detection methods were introduced, from high-resolution scanning techniques to millisecond resolved snapshot and interferometric approaches. Sub-nanometer spectrally resolved and high signal-to-noise ratio measurements of single nanoparticles can be achieved by scanning a spectrograph with a slit or pinhole across the field of view. However, this method usually takes on the order of minutes. Ratiometric and snapshot techniques can achieve millisecond time resolution, while sacrificing some spectral resolution. Interferometers are less commonly used but have shown great potential for acquiring entire hyperspectral data cubes in seconds. Finally, we described how the different excitation and detection schemes have been combined with liquid cells, electrochemical cells, and AFM and SECCM probes to use plasmonic nanoparticles as sensors and to study their role as catalysts.
We expect single-particle scattering spectroscopy to continue to grow as an important tool in nanoscience. Single-particle spectroscopy is a relatively new field that has grown rapidly over the last 20 years, made possible by advancements and falling costs of microscopy and spectroscopy components, especially detector chips. In particular, CMOS chips are becoming cheaper, with higher frame rates and higher contrast. At the same time, interest in plasmonic nanoparticles as highly sensitive optical sensors and as catalysts or light-harvesting antennas is growing. To continue pushing the detection limit for biological sensors, single-particle scattering techniques will continue to be an important tool. The strong push towards renewable fuels has put plasmonic nanoparticles into the spotlight due to their high photon absorption cross-section and hence applications as catalytic substrates driving reactions through both hot carriers and heat. While ensemble studies have revealed great potential, researchers are increasingly making use of single-particle studies to gain a mechanistic understanding of these heterogeneous processes. The examples given here clearly demonstrate the need for single-particle approaches to avoid ensemble averaging and thereby missing important information.
Funding source: Basic Energy Sciences
Award Identifier / Grant number: DE-SC0016534
Funding source: Division of Chemistry
Award Identifier / Grant number: 1903980
Funding source: Division of Graduate Education
Award Identifier / Grant number: 1842494
Funding source: Army Research Office
Award Identifier / Grant number: W911NF1910363
Funding source: Welch Foundation
Award Identifier / Grant number: C-1664
Author contributions: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: The authors acknowledge funding from the Army Research Office (Grant No. W911NF1910363), supporting A.A.-Z., the Department of Energy (Grant No. DE-SC0016534), supporting T.S.H., and the National Science Foundation (Grant No. CHE-1903980), supporting A.R.-M. S.L thanks the Robert A. Welch Foundation (Grant No. C-1664) for support. L.A.M. acknowledges support from the National Science Foundation Graduate Research Fellowship Program (1842494) and from the Lodieska Stockbridge Vaughn Fellowship, Rice University.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
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