1. Introduction

Interferometric scattering (iSCAT) microscopy is a label-free optical method for detecting, localizing, and tracking nanoparticles [1–5], measuring the orientation of nanorods [6], and imaging cellular components [7–9] with high spatial and temporal resolutions. The broad spectrum of iSCAT applications is possible due to its distinctive features like stable homodyne detection, high sensitivity, and unlimited observation time [10–13]. In this paper, we explore an application of iSCAT microscopy to nanoparticle (NP) size characterization.

The iSCAT signal from an NP small enough to ignore the pure scattering term is known to be proportional to the volume of the particle [1,2]. It was reported that the volume of a nanometric object such as NPs [14] and proteins [1,2] could be measured just from the iSCAT contrast. To truly quantify the size of an NP from scattering, however, we need to consider several factors contributing to the iSCAT signal, such as material properties of the scatterer, illumination wavelength, optical system properties (for example, numerical aperture (NA), size of beam waist, and polarization), refractive index mismatch, and optical aberration [15–17]. Another obstacle comes when the size of the NP exceeds the limit of Rayleigh scattering and the scattering becomes asymmetric.

Here, we consider small scatterers far below the Abbe diffraction limit but not necessarily smaller than the Rayleigh scattering limit. Although we cannot obtain images of the actual shape of an NP, we can determine the vertical position of its scattering dipole with the aid of rigorous theoretical calculation. Placing the source of this dipole, i.e., NP, on the cover glass surface, we demonstrate an accurate measurement of the height of this dipole from the cover glass, which, as we confirmed, quantitatively correlates with the size of the NP. In this way, we can measure the size of NPs.

Our method exploits the variation of the iSCAT signal over an extended range of vertical (z) focus scanning and utilizes a theoretical model to fit the experimental data. Successful reconstruction of experimental data by the theoretical model with suitable parameters enables us to extract quantitative information about individual NPs with nanometric accuracy, making it stand out amongst NP characterization techniques such as AFM or TEM for its all-optical approach and compatibility with the aqueous environment. As an optical method, it is also capable of simultaneous 3D tracking and bioimaging. Amongst optical techniques, through-focus scanning optical microscopy was introduced to determine the size of NPs via a calibration-based method [18]. Our approach is different from other optical methods because it accomplishes both optical imaging and model-based size measurement of individual NPs. Theoretical models similar to the one used in the present work have been used in various studies: to localize metallic NPs in a medium by scattering microscopy [15], to study metallic NPs by photothermal imaging [16,17], and to compare scattering properties of metallic and dielectric NPs [19]. However, those studies did not address the quantitative measurement of NP size. With our approach, we successfully measured the size of spherical NPs with nanometric accuracy and precision without direct contact.

Besides introducing a new approach to measure the size of NPs with the iSCAT signal, we also gain a better insight into scattering signals from high-refractive-index NPs such as fluorescent nanodiamonds (fNDs) and their fluorescence properties. Our study reveals a correlation between the iSCAT contrast and fluorescence intensity of fNDs. The axial profiling of interferometric scattering proposed here would be a versatile technique in nanoscience for NP size determination, together with the distinct advantages of iSCAT.

2. Materials and methods

2.1 Fluorescence combined iSCAT microscope (F-iSCAT)

The iSCAT setup and its fluorescence extension were already described in detail in the previous reports [6,10]. Fig. S1(a) shows the simplified schematics of F-iSCAT. The light (532 nm) from the laser (OBIS-FP-532LX, Coherent, USA) is steered in both X and Y directions using the acousto-optic deflector (AOD, DTS-XY400-532, AA Optoelectronics Ltd, France). It is sent through the 4f telecentric lens system (L1 and L2, AC254-500-A, Thorlabs, USA), the polarizing beam splitter (PBS, CCM1-PBS25-532, Thorlabs, USA), and the quarter-wave plate (QWP, WAQ10M-532, Thorlabs, USA) onto the back-focal plane of the objective lens (O, PLAPON60XO, oil-immersion, NA = 1.42, Olympus, Japan). The sample is placed on the high precision XYZ-piezo stage (P-545.3C8S, Physik Instrumente, Germany). The back-scattered light is then reflected by the dichroic mirror (DM, Di03-R532-t1-25x36, Semrock, USA) and projected through a lens (TL1, same as L1) on the sCMOS (pco-edge 4.2, PCO, Germany). The emitted fluorescence light is projected through a lens (TL2, same as L1) on the EMCCD (iXon897, Andor, UK). The stray light and leakage of the excitation beam are blocked by a notch filter (F1, NF03-532E-25, Semrock, USA) and an emission filter (F2, FF01-709/167-25, Semrock, USA).

The iSCAT and fluorescence signals are detected simultaneously. The iSCAT signal containing the back-scattered signal from an NP was recorded over a range (3 ∼ 6 µm) of focal depth centered at the vertical position of the NP by moving the sample stage along the z-axis (Fig. S1(b)). Laser power was adjusted according to the size of the NP to avoid the saturation of both scattering and fluorescence intensities. All other parameters were set to be the same for all NP samples.

2.2 Nanoparticles and their characteristics

We used two polystyrene (PS) bead samples (FluoSpheres Carboxylate-Modified Microspheres, fluorescent (540/560), F8792 (dia.: 0.047 ± 0.0055 µm) and F8809 (dia.: 0.2 ± 0.0160 µm) ThermoFisher Scientific, USA) and two latex bead samples (Amidine latex bead, 4%, ‘0.1 µm’, A37313 (dia.: 0.10 ± 0.009 µm), Life Technologies, USA; Aldehyde/Sulfate latex bead, 4%, ‘0.1 µm’, A37287 (dia.: 0.12 ± 0.009 µm), Life Technologies, USA). Hereafter, we mention their nominal radius, R_nom = 20, 50, 60, and 100 nm for the PS and latex beads.

We also used a commercial fND sample (900172, Sigma-Aldrich, USA), which has one to four nitrogen vacancy (NV^-) centers per particle. We measured the size of the fND particle with nanoparticle tracking analysis (NTA) (NanoSight LM10, Malvern Panalytical, UK) or transmission electron microscopy (TECNAI G2, FEI, USA).

2.3 Sample preparation for iSCAT measurement

All NP samples were sufficiently diluted from a stock solution and then sonicated for homogeneous mixing so that individual particles were sparsely and uniformly distributed for precise localization at the single-particle level when spread out on the glass surface. For PS and latex beads, the diluted samples were pipetted into the sample chamber (µ-Slide I Luer, 80167, ibidi, Germany), where the negatively charged beads were bound to the glass surface. Similarly, we pipetted the diluted fND sample into the sample chamber and washed out suspending particles to prevent overloading and forming clusters.

2.4 Measurement of the iSCAT contrast and fluorescence from nanoparticles

The iSCAT signal results from the interference between the scattered field from the sample and the reference field reflected from the cover glass surface. The total iSCAT intensity at the detector is given by

The fluorescent signal from an fND particle was measured in the fluorescence detection channel of F-iSCAT. An fND particle appeared as a round spot in the channel, and the PSF of the spot was also described by the same Eq. (2). Thus, we calculated the fluorescence contrast (I_fl) by taking the ratio of the amplitude (A) and background offset (B), that is, I_fl= A/B

3. Theoretical model

3.1 Point spread function model for iSCAT imaging

To understand the scattering from NPs and extract the information about them, we need to use an appropriate model to describe our system. A successful theoretical model should reproduce the PSF of an NP. Such a PSF model could be derived using either a vectorial or scalar approach. Scalar models derived from the diffraction theory of light use the approximation of the Fresnel-Kirchhoff integral to describe the propagation of a spherical wave through an aperture [20]. The scalar diffraction model by Gibson and Lanni (G-L) is computationally simpler and practically convenient as it directly introduces the experimental conditions as input parameters [21,22]. It calculates the imaging aberration from the optic path difference (OPD) between the design and experimental conditions of the layers between the objective and the sample [23].

On the contrary, the vectorial model by Richards and Wolf (R-W) is rather complicated, but it provides an accurate ray tracing method for a radiating dipole in a focused beam [24,25]. Their vectorial approach is based on Maxwell’s equations and calculates the electromagnetic field vectors [20,26,27], the x, y, and z components of which need to satisfy the corresponding wave equation [27]. The R-W model was later reformulated by Török and Varga [28] (T-V) for more general use when the electromagnetic waves are focused through a stratified medium with mismatched refractive indices. Haeberlé [21,29] then demonstrated that such vectorial models could be used together with the G-L OPD, which provides an accurate and convenient way to model the PSF for optical microscopy. Therefore, we chose to simulate a fitting function for our experimental data with the T-V model using the G-L expression for OPD as a phase term.

The electric field at the observation space (focal region over the detector) can be expressed in the form of the R-W integral with the additional OPD term as follows [30,31]

To derive ${\vec{E}_\infty }({{\theta_d},\phi } )$ for reference and scattered fields, we start with a plane wave with linear polarization (${\vec{E}_i}$) and trace the vectorial components of the reference and scattered electric fields by the generalized Jones matrix formalism, as illustrated in Fig. S2. The strength vector of the ‘far-field’ reference field can be expressed as follows:

The strength vector of the scattered field by an NP is usually described by the Rayleigh scattering theory, which is only valid for particles smaller than the Rayleigh scattering limit. Thus, we consider the Mie theory [32] instead, for accurate modeling of the scattered field from NPs whose size is beyond the Rayleigh regime. The strength vector of the ‘far-field’ scattered field can be expressed as follows:

The iSCAT contrast depends on the phase difference between E_R and E_S, which is determined by the size and geometry of a scattering object, illumination wavelength, refractive index mismatch in the optical path, and NA [15,16,19]. The phase term, according to the G-L model, accounts for the aberration caused by index mismatch and finite thickness of multiple layers along the optical path [22]. The aberration can be described by considering the OPD (Λ) between the real (experimental) and ideal (design) beam paths (Λ = [ABCD] – [PQRS], where [ABCD] and [PQRS] are the pathlengths of real and ideal paths, respectively), as illustrated in Fig. 1 [22,23].

 

Fig. 1. Sample configuration and optical paths of ray ABCD under experimental conditions and PQRS under design conditions. n’s (n_i, n_i*, n_g, n_g*, and n_s) and t’s (t_i, t_i*, t_g, and t_g*) are the refractive indexes and thicknesses of various layers, respectively. The subscripts i, g, and s designate the immersion oil, cover glass, and sample, respectively. z_p is the height of the induced dipole. n_p is the refractive index of NP. Asterisk (*) is used to mark the design parameters.

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In the axial scan, the sample stage moves while the objective lens stays stationary, which results in changing the distance between the stage and the objective and therefore altering the thickness of the immersion oil layer. In that case, t_i should be expressed in terms of other parameters as [20,23]

 

Fig. 2. (a) Propagation of the scattered field (E_S) from a nanoparticle and the reference field (E_R) from the sample-surface interface. (b-i) Images of axially (as a function of z_f) stacked horizontal profiles of various field quantities: (b-c) Real part of the electric field of (b) the reflected light E_R and (c) the scattered light E_S. (d-e) Phase of the electric field of (d) the reflected light E_R and (e) the scattered light E_S. (f-g) Amplitude of (f) the reflected light, |E_R| and (g) the scattered light, |E_S|. (h-i) SHIP image of iSCAT PSF (h) by simulation and (i) by experimental measurement. (j) Axial intensity profiles at the center of a nanobead, i.e. x = 0 (experimental: blue dots; simulation: red dots). The range of z_f used to compare the two profiles is shown in green.

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To express the OPD in terms of the parameters of the relevant layers (immersion oil, cover glass, sample), we resort to Snell’s law of refraction and find that [20]

The OPD of the reference field (Λ_OPD,_Ref) is given by those of the normally incident and reflected rays with respect to ideal rays along the same path:

The scattered field depends on the height of the dipole (center position of the spherical scatterer) and thus the OPD of the field (Λ_OPD,_Scat) can be calculated using the ray geometry considered by the G-L formalism. The OPD of the scattered light is given as:

The reference (Eq. (5)) and scattered (Eq. (6)) fields are inserted in the R-W integral (Eq. (4)) with the aforementioned OPD terms and the integral is evaluated over Φ, which leads to the simplified form (Eq. (S11-S13)). Then, the iSCAT contrast is computed by subtracting the background from the signal and normalizing the difference with the background as:

To reproduce experimental results by computation, we calculated the reference field by reflection and the scattered field from a dielectric particle as a function of the relative position of the focal plane (z_f) and visualized the axially stacked horizontal profiles of the reference and scattered fields (real part, phase, and amplitude) and of iSCAT (I_sim) in Figs. 2(b-h).

As shown in Figs. 2(b-g), the reference and scattered fields propagate with the planar and quasi-spherical wavefronts, respectively. Moreover, the SHIP images and their axial cuts (axial variation of iSCAT signal at the center of an NP) from the actual measurement and numerical computation look almost identical, as illustrated in Figs. 2(h) and (i). Our analysis showed that we could produce simulation results highly similar to experimental observations with only a specific set of parameters, indicating that our approach is robust and reliable (Fig. 2(j)).

3.2 Strong dependence of dipole's iSCAT signal on its height as the basis for accurate measure of the size of a dielectric sphere

The interferometric signal between reference and scattered fields critically depends on the OPD variation, which originates from the axial location of the NP relative to the reference interface. Thus, the location of the scattering source would affect the shape of the wavefront and thus the spatial variation of the phase. It is well known that the incident field induces and drives the dipole moment in a dielectric nanoparticle. Therefore, we simulated the propagation of fields using the PSF model discussed above in order to understand how the height of the dipole, equivalently, the radius of the spherical NP affects the phase variation or the whole signal profiles. The numerical results as a function of the height of the dipole (z_p) are displayed in Figs. 3(a-c), together with the axial profiles for three representative values of z_p (0, 50, and 100 nm) shown in Figs. 3(d-f). As shown in Figs. 3(a) and (d), E_R has no dependence on the size of an NP as expected. On the contrary, the modulation of the scattered field slightly shifts along the axial direction (z_f) as z_p changes as shown in Fig. 3(e) (see inset). This phase shift is responsible for the axial variation of the iSCAT signal shown in Fig. 3(f) as well as in Figs. S3 and S4, which show that a small change in n_i influences the phase variation of E_S significantly, indicating that n_i needs to be precisely determined for accurate measurement of z_p.

 

Fig. 3. Stacked axial contrast profile as a function of z_p. (a) |E_R|, (b) |E_S| and (c) |E_RE_S^*+ E_R*E_S| calculated in the range of z_p= 0 ∼ 100 nm with n_i= 1.52. All calculated values are normalized and scaled to fit to [0,1] and displayed in gray scale (hence, labelled as |E_R|_norm, |E_S|_norm, and |E_RE_S^*+ E_R*E_S|_norm in (d-f), respectively). The blue, green and red colored lines indicate z_p= 0, 50, and 100 nm. (d-f) Cross-sections of the reference field (d), the scattered field (e), and the interference term (f). Insets in (d) and (e) show the phase variation of the fields and highlight the sensitivity of the fields to different values of z_p. The axial intensity profile by the interference term exhibits more pronounced variation with z_p, accounting for sensitive detection of the size of nano-objects by iSCAT. In this figure, z_f is the computational input parameter before the offset (δz) is adjusted.

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Thus, a small change in z_p results in a notable change in the axial profile, which warrants a reliable and unambiguous analysis of experimental data. The scattering signal itself varies in amplitude, but due to its interference with the reference field, the change in the shape and amplitude of the interferometric signal becomes more pronounced. Therefore, the axial profile of the iSCAT signal significantly enhances the sensitivity to particle size. It becomes clear that our approach based on the quantitative fitting analysis of the axial pattern of the iSCAT signal can be an incisive tool for distinguishing NPs with different sizes.

4. Results and discussion

4.1 Reconstruction of axial PSF variation

The realistic model and accurate fitting of experimental data can be achieved only with fitting parameters close to reality. In the computation of PSF, the wavelength of illumination and the NA used were 532 nm and 1.35, respectively. The refractive indexes and thicknesses used were: n_s = 1.33 (for water), n_p = 1.59 (for polystyrene and latex nanoparticles) or 2.4 (for nano-diamond particles), n_g = n_g* = 1.52 (for cover glass), n_i* = 1.52 (for immersion oil), t_g = t_g* = 170 µm (for cover glass), and t_i* = 100 µm (for immersion oil). Symbols with and without asterisk represent parameters in real (experimental) and ideal (design) conditions as used in the G-L model (Eq. (7), (8)) [23]. The t_i, ‘real’ parameter of oil thickness, is a parameter to be adjusted in the G-L model.

We varied n_i and z_p to describe the spherical aberration in the axial profile. Numerical values of these fitting parameters were determined by the root mean square error (RMSE) evaluation. First, we define the parameter space for n_i and z_p to be examined. For each set of n_i and z_p values, we generate the PSF (equivalently, I_exp) at the focal space of the imaging lens (equivalently, on the detector surface) with various depths of the focal plane of the objective (i.e., z_f in Eq. (7) or z in the definition of z_f) from the R-W integral in Eq. (S7,8,11-13). Typically, we vary z within a few µm from z = 0. Since we are only interested in its center value, I_exp(x₀,y₀), we can get the axial profile of the center of the PSF by setting r = 0 in the R-W integral. This simulated PSF (I_sim) is likely to be off with respect to I_exp due to the non-ideal experimental parameters (causing spherical aberration) and the finite size of scatterers, thus we shift I_sim by δz to find the optimal I_sim with the lowest RMSE for the given n_i and z_p by compensating for a potential offset (the compensating offset giving the least RMSE is denoted as δz*). By sequentially varying δz (distance translated for I_sim with respect to I_exp as illustrated in Fig. S5(a)) with a fine increment within a reasonable range, one would find the least RMSE with the best δz* (Fig. S5(b)) and obtain I_sim that best matches I_exp under the given set of n_i and z_p. This least RMSE is called the representative RMSE value for the given n_i and z_p.

4.2 Axial profiling of the PSF center enables accurate determination of nanoparticle size

We carried out the RMSE estimation for axial intensity profiles generated with various values of n_i and z_p as shown in Fig. S6(a). From the minimization of RMSE, we could determine the values of n_i and z_p as shown in Fig. S6(b). To validate our approach, we tested polystyrene (PS) and latex beads because they are highly uniform in size and shape (spherical), not to mention that they are homogeneous. The size uniformity of beads was confirmed by our NTA and TEM measurements shown in Fig. 4(a-c).

 

Fig. 4. (First column) Representative TEM images that were analyzed to obtain the size of PS (a), latex ((b) and (c)) and fND (d) particles. (Second column) Outlines of detected particles used for calculation of the Feret diameter. (Third column) Histograms of size of particles measured by different techniques (TEM, PSF (iSCAT), and NTA analysis – see graph legend in (a)). Nominal radius (R_nom): (a) 20 nm PS beads, (b) 50 nm latex beads, (c) 60 nm latex beads, and (d) 40 nm for commercial fNDs. Radius deduced from TEM images was obtained by measuring the Feret diameter. Scale bar: (a) 100 nm, (b) 200 nm, (c) 500 nm, (d) 100 nm.

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Using the PSF model and adjusting the parameters carefully, we were able to make the computational results nearly identical to the corresponding experimental data: the experimental and theoretical SHIP images are remarkably similar for different-sized beads as shown in Fig. S7. Interestingly, the results from those NPs showed that z_p determined by our method is in excellent agreement with the expected radius of those NPs. From our model fitting, we obtained the sizes of PS and latex beads, which closely match their R_nom's in Fig. 5(a): (i) for 20-nm PS beads, z_p ∼ 17 (± 7) nm; for this PS bead, the NTA method failed to give reasonable results because it is substantially smaller than the size limit for reliable measurements by NTA (dia. ∼ 60 nm with 642 nm excitation [33]) but TEM provided R ∼ 23(± 2.8) nm, consistent with the result from our PSF modeling; (ii) for 50-nm latex beads, we got z_p ∼ 40 (± 1.2) nm while NTA and TEM gave R ∼ 50 (± 18) nm and ∼ 50 (± 3.2) nm, respectively, both supporting the result from PSF modeling; (iii) for 60-nm latex beads, we got z_p ∼ 56 (± 10) nm while NTA and TEM gave R ∼ 55 (± 21) nm and ∼ 61 (± 2.5) nm, respectively, supporting the result from PSF modeling again; (iv) for 100-nm PS beads, we got z_p ∼ 93 (± 10) nm while NTA gave R ∼ 102 (± 20) nm, supporting the result from PSF modeling. As shown here, TEM is a reliable and accurate tool to measure the size of NP by direct visualization, but the limited accessibility of TEM and the low throughput and technical difficulty of the technique hampers easy and wide applications to samples in the condensed phases. This dipole-modeling-based result is consistent with our view that the dipole of those scatterers is located near the center of the particles and the particles are in good contact with the interface.

 

Fig. 5. Representative results of particle size determination by PSF analysis. (a) Accuracy of the axial profile method to determine the size of spherical nanoparticles (PS and latex bead). z_p, radius of bead acquired by the axial profile method, is not only linearly correlated with but also nearly identical to ‘Nominal radius (R_nom)’ provided by manufacturers. Linear fit y = 1.0114·x – 6.657. (b) Correlation of the fluorescence intensity (I_fl) and volume (V_ND) of ‘40 nm’ fND together with a linear fit of the data. For a better idea about the fND size, the upper x-axis shows the value of z_p determined by iSCAT. Several values of z_p are indicated by vertical dashed lines. Correlation coefficient: $\mathbf{\mathscr{R}}$(V_fl,V_ND)₄₀= 0.57.

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Next, we estimated the size of fND using the PSF model. fNDs have drawn much attention for their remarkable properties and wide applications in biological imaging and sensing [34,35]. We generated theoretical SHIPs of fNDs with carefully adjusted parameters, which are in good agreement with the experimental SHIPs as shown in Fig. S8. The measured sizes (z_p) of fNDs were broadly distributed, as shown in Fig. 5(b), consistent with the TEM result shown in Fig. 4(d). It, however, turned out that the size of an fND estimated by our approach was correlated with the fluorescence intensity of the fND. We shall discuss this issue in the next section.

Although NTA is a well-known and popular tool for size determination of NPs, it has several technical pitfalls [36], which our method could overcome. First, the size distribution measured by NTA was considerably broader than that acquired by our axial profile-fitting method. It is likely because our single-particle method enables us to choose individual NPs and avoid clusters, significantly larger NPs, and impurities in the sample, which is intrinsically impossible with the NTA method. Second, the NTA is less straightforward in measuring the size of small NPs because instrumental settings and user inputs are critical for such NPs. While NTA could be of some use for measuring NPs of size below 60 nm, the uncertainty would be large, as exhibited in Fig. 4. In contrast, the sensitivity of our method is high, so our approach enables accurate measurements of the size of PS beads as small as R = 20 nm and that of fNDs down to 15 nm in radius (Fig. 5). Although several potentially useful methods have been recently developed such as iNTA that combines the advantages of NTA and iSCAT [37] and holoNTA that uses holographic imaging for larger sample volume and higher sensitivity [38], they have not been commonly used yet.

4.3 Correlation of fND volume and fluorescence intensity

fNDs are fluorescent owing to the negatively charged NV^- centres in their diamond lattice. The fluorescence intensity I_fl is proportional to the number of NV^- centres in a given fND. From N_NV = c_NV · V_ND (c_NV: concentration of NV^- centres, V_ND: volume of fND), the fluorescence intensity should also increase linearly with the volume of fND. Regarding the correlation between them, we shall consider the following degrading factors: (i) inhomogeneous incorporation of NV^- centres throughout nanodiamond lattice, (ii) the inaccurate assumption that the fNDs have a spherical shape, in fact, our fNDs appear significantly jagged as confirmed by TEM (Fig. 4(d)), (iii) weaker fluorescence emission by NV^- centres placed near the particle surface than in the centre of the particle [39], and (iv) batch-to-batch variation of the number of NV^- centres in the fabrication process.

Figure 5(b) shows the relationship between the volume of fND, V_ND, calculated from its radius, z_p, determined by iSCAT, and the fluorescence intensity I_fl of fND. To describe the correlation between the fluorescence intensity and fND volume, we used the Pearson correlation coefficient and obtained the correlation $\mathbf{\mathscr{R}}$(V_fl,V_ND)₄₀ = 0.57, which signifies only a moderate correlation. There are several particles that deviate considerably from this correlation. The main reasons for scattered points would be, as assumed above, non-uniform incorporation of NV^- centres in the diamond lattice and the non-spherical shape of the nanoparticles. This implies that the size of fNDs cannot be deduced accurately from their fluorescence intensity alone. On the other hand, we found that the distributions of fND size obtained by different methods (PSF, TEM, NTA) were well overlapped, supporting that the value of z_p (or the size of NP) acquired by the PSF model analysis is valid. From this, we suggest that the PSF analysis proposed here can even determine the size of NPs of non-spherical shape such as fNDs with reasonable accuracy.

5. Conclusions

The iSCAT microscopy has evolved into a useful label-free optical technique that enables both imaging and tracking nanoscopic objects with high precision. Here, we demonstrated that it could be used to characterize the size of NPs all-optically even beyond the Rayleigh scattering regime. We developed a technique useful to measure the size of individual NPs by acquiring the axial variation of the iSCAT signal and fitting the theoretical PSF model to the axial profile of the iSCAT signal, which provides the information on the scattering dipole position, i.e., size of NPs in the present case.

The theoretical model used to fit the experimental data is a modified Török and Varga’s vectorial PSF theory. Our model accounts well for the factors that contribute to the iSCAT signal resulting from the interference between the scattered and reference fields. Our method turns out to be sensitive to small changes (within a few nanometers) in the size of NPs, which surpasses other optical methods such as NTA or DLS (Dynamic Light Scattering) in size sensitivity and single-particle characterization capability, not just ensemble size distribution. It also stands out amongst other size determination techniques for its instrumental simplicity and all-optical, contactless, nondestructive, and non-contaminating approach. The results presented here demonstrate that the axial profile-fitting method is a useful approach not only because it can be used to measure the size of NP covering a broader range from ∼ 10 nm to several hundred nanometers, well-beyond Rayleigh scattering limit [2,14] but also because it can be applied to NPs made of various materials. All taken together, we anticipate that our technique would be useful for characterizing NPs and stratified media.