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Real-time Optical Detection of Single
Nanoparticles and Viruses using Heterodyne
Interferometry
Anirban Mitra1 andLukas Novotny1,2
Adapted from: Anirban Mitra and Lukas Novotny,“Real-time optical detec-tion of single nanoparticles and viruses using heterodyne interferometry,”Nano-Optics for Enhancing Light-Matter Interactions on a Molecular Scale,B. Di Bartolo et al. (eds.), Chapter 1, p.3–23, NATO Science for Peace andSecurity Series B: Physics and Biophysics (Springer, Dordrecht, 2013).
1. Department of Physics and Astronomy, University of Rochester, RochesterNY 14627
2. Institute of Optics, University of Rochester, Rochester, NY 14627
1 Introduction
Nanoparticles play a significant role in various fields such as biomedical imag-ing and diagnostics [1, 2, 3, 4], process control in semiconductor manufac-turing [5], explosives [6], environmental monitoring and climate change [7,8], and various other fields. Inhalation of ultrafine particulates in air hasbeen shown to have adverse effects, such as inflammation of lungs or pul-monary and cardiovascular diseases [9, 10]. Nano-sized biological agents andpathogens such as viruses are known to be responsible for a wide variety ofhuman diseases such as flu, AIDS and herpes, and have been used as biowar-fare agents [11, 12].
Rapid and accurate detection and characterization of viruses has becomeincreasingly important over the years. Accurate quantification of the pres-ence of human viruses such as HIV, herpes or influenza in blood samples isessential for clinical diagnosis and also for vaccine development. The abilityto distinguish between different kinds of viruses present in a sample is also
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highly desirable. For example, a single patient may be coinfected with mul-tiple viral pathogens such as HIV and HCV, and being able to identify andquantify both viruses is crucial for the patient to be treated appropriately.
Most of the existing virus particle quantification techniques either sufferfrom significant technical glitches or are extremely time and cost consum-ing. Techniques such as quantitative-PCR [13] only indirectly determine thenumber of viral particles in a sample, while the plaque titer method [14]quantifies only those which cause visible cell-damage. Quantitative ElectronMicroscopy (QEM) [15] is limited by its low resolution for small particles suchas viruses, whereas quantification by Image Enhanced Microscopy (IEM) [16]is unreliable due to experimentally unconfirmed efficiency of labeling withfluorescent dyes. At present there does not exist any virus quantificationmethod available to biologists which can quickly and reliably detect, quan-tify and characterize virus particles with single particle sensitivity.
In recent years several studies have focused on developing new and im-proved optical techniques for nanoparticle detection [17, 18, 19, 20, 21, 22, 23].Optical methods have proved particularly attractive because of their nonin-vasive nature and high sensitivity [24]. A lot of these methods have specif-ically concentrated on label-free viral biosensing. Optical techniques basedon sensing discrete resonance shifts in whispering gallery mode (WGM) mi-crocavities due to binding of single virus particles have proved really promis-ing [25, 26, 27, 28, 29], but they cannot be used to distinguish betweenviruses of different sizes present in a heterogeneous mixture. Other opticalsensing platforms such as those based on nanoplasmonics [30] or interferom-etry [31, 32] have proved to be sensitive to single viruses; but while some ofthem need to be run for a long time and hence are unsuitable for real-timesample characterization, others rely on extensive surface preparation stepsor availability of specific antibodies for the target viruses in a sample. Elec-trical sensors have been demonstrated to be able to detect single viruses insolution [33, 34], but they suffer from the drawback that they are extremelysensitive to changes in ionic strengths of the media [35]. A single label-freemethod which can quickly and accurately quantify levels of different virusespresent in clinically relevant samples without additional sample preparationsteps, has remained elusive for practical implementation.
Several optical methods for detection and characterization of nanoparti-cles that have been developed in the past have relied on light scattering [36],
2
since light scattering measurements are usually highly sensitive to small vari-ations in particle sizes or optical properties. Various optical particle counters(OPCs) have been developed, some of which such as the Flow Cytometer [37]are capable of detection single nanoparticles, while some others such as thosebased on Dynamic Light Scattering (DLS) [38] detect ensembles of parti-cles. However, the methods capable of single particle detection are usuallysensitive only for particles down to ∼ 200 nm in diameter. Methods such asDLS can be used to detect very small particles down to less than ∼ 10 nmdiameter, but they cannot attain single particle sensitivity.
Optical detection of nanoscale biological agents (such as viruses) usinglight scattering is difficult due to their low scattering cross-section and lowindex contrast to the surrounding medium. Light scattering from a homoge-neous sphere has a rigorous solution, as derived by Mie [39]. In the limitingcase, particles much smaller than the wavelength of the excitation light canbe described by a dipolar polarizability α given by [36]
α = 4πεoR3 εp − εm
εp + 2εm, (1)
where R is the particle radius, and εp and εm are the dielectric permittivi-ties of the particle and the surrounding medium, respectively. An incidentoscillating electric field Eexc induces a dipole p in the particle parallel tothe incident field, given by p = αEexc. The induced dipole radiates (i.e.scatters) a secondary electric field Es ∝ αEexc. Evidently, α defines thescattering and absorption efficiencies and bears information on both particlesize (R) and composition (εp), and hence is highly significant in nanoparticlecharacterization. Nanoparticle detection techniques such as DLS probe theintensity of the scattered light I ∝ |Es|2, and hence the detector signalscales with |α|2 ∝ R6. The strong size dependence makes it extremelydifficult to detect small particles based on standard light scattering.
It would therefore be expected that a detection principle that hinges onan optical interaction mechanism that has a weaker size dependence thanstandard light scattering-based techniques would provide a better Signal toNoise Ratio (SNR) and hence would be sensitive to single particles of smallersizes. This is where interferometric detection [40, 41, 42] comes in. Unlikeother light-scattering based detection techniques, interferometric detectionexhibits a weaker size dependence and therefore provides significantly better
3
signal-to-noise for small particles. For interferometric detection, the detectorsignal is proportional to the amplitude of the scattered light |Es|, and hencescales with α ∝ R3. Interferometric detection can provide single particlesensitivity and has the potential for real-time detection [43, 44, 45, 46].
In real-time interferometric nanoparticle monitoring, particles typicallyare made to traverse a stationary laser focus, and the scattered field from asingle particle is combined with a reference field and recorded interferomet-rically with a photodetector. Using this standard (also called homodyne)scheme for interferometric detection, it has been shown that nanoparticlescan be detected in real-time with high sensitivity [43, 47]. However, thephase sensitivity of homodyne interferometric measurements makes it diffi-cult to accurately assess α of a target particle traversing a stationary laserfocus. Slight variations in the particle’s position have a significant influenceon the phase of the scattered field, thereby affecting the detector signal andhence the resolution of the measurement. This in turn makes it difficult toclearly distinguish between particles of slightly different sizes present in aheterogeneous mixture. In the following sections, we present a nanoparticledetection scheme based on heterodyne interferometry, using which amplitudeand phase of the interferometric signal from a nanoparticle can be effectivelydecoupled, hence improving the size resolution of particle characterization.Furthermore, combining heterodyning with differential detection greatly re-duces background and laser power noise, and helps achieve high detectionsensitivity.
2 Differential Optical Heterodyne Detection
Let us consider a detection scheme as illustrated in Fig. 1. A collimated ex-citation laser beam Eexc with frequency ω is incident on a high-NA invertedmicroscope objective, and is brought to a diffraction-limited tightly focusedspot at the interface of a nanofluidic channel [48] through which a nanopar-ticle solution is made to flow. Let the particle be located at r = (x, y, z), andthe flow direction be in the x-direction, transverse to the optical axis z. Thefocused electric field induces a dipole moment p in the particle, given by
p(r) = αEexc(r) , (2)
4
Er
Einc
Es_
Eexc
nanoparticles
nanofluidicchannel
SplitPhotodetector
objective lens
beam-splitter
yx
z
Pup
Pdown
max
r
p
(a)
(b)
Figure 1: (a) Heterodyne interferometric detection of the light scattered by ananoparticle or a virus (yellow) as it traverses a laser focus. The scheme employsan excitation laser (Eexc) with frequency ω that is reflected off a beamsplitter andfocused via an objective into a nanofluidic channel. The scattered light (Es) issuperimposed to a reference beam (Er) with frequency ω + ∆ω and directed ontoa split photodetector. (b) SEM micrograph of a series of nanofluidic channels inthe flow-cells used in the experiments. Scale Bar = 2µm.
5
with α being the polarizability of the particle. The particle (the oscillatingdipole) scatters a field Es, which is given by
Es(r) = ω2 µ µ0←→G (r) p(r) (3)
where ω is the frequency of the incident field, µ and µ0 are the relativepermittivity of the medium surrounding the particle and the permittivity of
free space respectively.←→G is the far-field dyadic Green’s function [49],
←→G (r) =
exp(ikR− iωt)
4πR
[
I−RR/R2]
(4)
where k = nω/c with n being the index of refraction, and R = r∞ − r is thevector from dipole to the field point r∞. The field radiated by the dipole iscollected by the same objective lens characterized by a focal length f andnumerical aperture NA = n sin θmax, with θmax being the maximum collectionangle measured from the optical axis (c.f. Fig. 1). The dipole’s farfield canbe written from Eqs. 3 and 4 as
Es(r∞) =k2
εon2
exp(ikR− iωt)
4πR
[
I−RR/R2]
p . (5)
where we have used the fact that µ ≈ 1 for most mediums and that µ0 = 1c2 εo
.For r∞ located on the reference sphere of the lens and for small deviationsof the dipole from the focus r = 0, R can be expanded as
R = f − 1
f[xx∞ + y y∞ + z z∞] + .. (6)
Retaining only terms up to first-order in the phase and terms up to zeroth-order in the amplitude yields
Es(θ, φ) =k2 exp(ikf − iωt)
4πεon2f
[
I− r∞r∞/f 2]
p (7)
× exp(−ik[x sin θ sin φ + y sin θ cos φ + z cos θ])
where we expressed (x∞, y∞, z∞) in spherical coordinates (f, θ, φ). For ourpurposes k|r| < 1 and hence we expand the last exponential term to firstorder, i.e. exp(x) ≈ 1+x. This substitution makes a later integration over θand φ possible. Also, using the paraxial approximation, [I− r∞r∞/f 2 ]≈ 1 .
6
The lens collimates the field of the dipole and projects it on the plane of thedetector. In the detector plane the field can be represented as
Es(θ, φ) =k2 exp(ik[f + ∆z]− iωt)
4πεon2fp (8)
× (1 − ik[x sin θ sin φ + y sin θ cos φ + z cos θ])
where ∆z is the distance from the lens to the detector plane.
Let us now consider the reference field Er that is incident on the photodetec-tor, along with Es(θ, φ). In heterodyne interferometry, a frequency-shift ∆ωis introduced into the reference field (with respect to the excitation field),usually with the help of a pair of acousto-optic modulators [44]. The magni-tude of ∆ω is usually chosen to be relatively high (80 kHz for the experimentsdescribed below), so that the signal processing can be done beyond the rangetill which 1/f noise [50] can affect the signal-to-noise (SNR) of the system.The reference field can be written as
Er = Er ei(k∆z−[ω+∆ω]t−∆φ) np , (9)
where np is the unit vector in direction of p, ∆φ is a constant phase shift, and∆ω is the frequency shift introduced in the reference field. For nanoparticlesor viruses suspended in an aqueous medium, there is a refractive index differ-ence at the interface between the glass nanofluidic channel and the mediuminside. Since the excitation laser beam is tightly focused at this interface(Fig. 1), a part of if it is reflected back along the same path as the scatteredlight and interferes with the reference and the scattered fields. We will callthis field as the background field Eb in the rest of the article.
2.1 Differential detection with a split photodetector
We have seen above that even without any particle traversing the laser focus,the fields Er and Eb are incident of the surface of the photodetector, whichwould inevitably produce a background in the detector, unless the effect ofthis background is somehow negated. This is usually done by performingdifferential detection using a split photodetector or a pair of balanced pho-todiodes. In the experiments we will describe below, a split photodetectoris used for differential detection. A particle traversing the laser focus in the
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x-direction (c.f. Fig. 1) produces a position-sensitive signal in the y-directionon the detector surface, and two independent power readings Pup and Pdown
can be obtained out of the detector. Let us first consider the total intensityI of the light that is incident on the detector
I(θ, φ) ∝ |Es + Er + Eb|2 (10)
∝ |Es|2 + |Er|2 + |Eb|2 + 2 Re {E∗
r ·Es}+ 2 Re {E∗
b · Es}+ 2 Re {E∗
b · Er} .
The differential output of the detector is the difference of the intensitiesintegrated over the areas of the two halves of the detector
S = [Pup − Pdown] . (11)
By centering the reference and the background beams on the surface of thedetector in the absence of a particle at the laser focus, the contribution ofthe terms in Eq. 10 that do not contain Es can be eliminated. This is howa perfectly aligned split detector helps in background-free detection. So, thedifferential signal S from a perfectly centered detector is given by
S = |Es|2 + 2 Re
{∫
up
E∗
r ·Es da
}
+ 2 Re
{∫
down
E∗
b · Es da
}
(12)
−2 Re
{∫
down
E∗
r ·Es da
}
− 2 Re
{∫
down
E∗
b · Es da
}
where∫
upstands for integration over the top half of the detector, and
∫
down
over the bottom half. Now, since |Es|2 is much weaker than the rest of theterms in the above equation, we can neglect it. Let us also not consider theterms containing Eb for now (we will see later that their contribution will beeliminated after processing with a lock-in amplifier). Eq. 13 reduces to
S = 2 Re
{∫
up
E∗
r ·Es da −∫
down
E∗
r · Es da
}
. (13)
Introducing the expressions for Es and Er from Eqs. (8) and (9) and carryingout the integrations in Eq. (13) yields
S(r) =16π2
3εo
NA3 f
n5
x
λ3Er Re{np·p exp[i∆ω t + i∆φ]}, (14)
8
where we made use of the small angle approximation sin θ ≈ θ. We find thatthe signal depends linearly on the dipole’s deviation in the flow direction(x) measured from the geometric focus r = 0. Note that we consider thatthe particle moves in the x direction exactly through the center of the focus(hence y = 0 and z = 0).
For simplicity, we assume that the exciting field Eexc is a Gaussian beam ofthe form
Eexc(x, y, z) =Eo eikz
(1 + 2 iz/kw2o)
e−
(x2+y2)
w2o
1
(1 + 2 iz/kw2o) , (15)
where wo is the beam waist radius. For high NA, Eq. (15) is only a roughapproximation and more accurate models for the focal fields are necessary[49]. The black curve in Fig. 2 shows the calculated signal S(r) for the pa-rameters used in the experimental validation described in the later sections.
If the terms containing Eb are retained in Eq. (13) and the next few steps ofthe analysis, the split detector signal would be given by
S(r) ∝ EsEr cos(∆ω t + ∆φ) + EsEb cos(∆φb) (16)
which is a simplified form of Eq. (14) where Es is the amplitude of the scat-tered field ; with an additional term for the interference between the scattered
0
-0.5
1
0-1 1 2-2-1
0.5
0
1
0.5
am
plitu
de
(arb
. un
its)a
mp
litu
de
(a
rb. u
nit
s)
time (ms)
Figure 2: Differential detector signal S(r) for a particle moving along x withspeed v = 1mm /sec through the focal plane of a laser beam (λ = 532nm,wo = 0.5µm),obtained via numerical calculations. The reference beam is frequencyshifted by 80 kHz. The red curve is the demodulated amplitude.
9
and the background fields, where ∆φb is the phase difference between the twofields. Processing of the split detector signal with a lock-in amplifier gets ridof the second term, as we will see below.
2.2 Signal Demodulation
At the output of the split detector, the heterodyne signature of a singlenanoparticle rides over carrier frequency ∆ω, and needs to be demodulated.A lock-in amplifier of suitable operating range and bandwidth is used todemodulate the signal. The lock-in amplifier is given a reference TTL signalwhich has a frequency equal to ∆ω, the modulation frequency of the detectoroutput signal. The phase-locked loop (PLL) in the lock-in amplifier locks aninternal reference oscillator to this external reference frequency, which resultsin a reference sinusoidal wave at ∆ω and a fixed phase shift of φref . The lock-in reference can be written as
Vlockin = VL cos(∆ω t + ∆φref). (17)
Now the lock-in amplifies the detector output signal and multiplies it by thelock-in reference using a Phase-Sensitive Detector (PSD) whose output isgiven by
Sx ∝ EsErVL cos(∆ω t + ∆φ) cos(∆ω t + ∆φref) (18)
+ EsEbVL cos(∆φb) cos(∆ω t + ∆φref),
where we have written the detector signal including the terms containing Eb,as in Eq. (16). Eq. (18) can be simplified to
Sx ∝1
2EsErVL [cos(∆φ−∆φref) + cos(2∆ω t + ∆φ + ∆φref)] (19)
+1
2EsEbVL [cos(∆ω t + ∆φref −∆φ
b) + cos(∆ω t + ∆φref + ∆φ
b).
The lock-in passes this output through a narrow-bandwidth low-pass filter,where the AC parts of the output are removed. This reduces Eq. (19) to
Sx ∝1
2EsErVL (cos(∆φ−∆φref). (20)
10
Note that all contribution of the terms containing Eb is removed, justify-ing the simplification used to obtain Eq. (13) in the previous section. Thephase dependency in Eq. (20) is removed by the lock-in with the help ofa second PSD, which essentially shifts the reference oscillator by 90o andthen multiplies with the detector signal. The output of this second PSD alsopasses through a narrow-bandwidth low-pass filter, where the AC parts ofthe output are removed. Performing similar derivation steps as for Sx we get
Sy ∝1
2EsErVL (sin(∆φ−∆φref). (21)
Sx and Sy are the the two output signals from the lock-in amplifier. Thephase-sensitivity of these signals can be eliminated by calculating
A = [S2x + S2
y ]1/2 ∝ [Er α Eexc]
2, (22)
where we have used the fact that Es ∝ α Eexc, where α is the particle’spolarizability and Eexc is the excitation electric field. It can be seen that thesignal amplitude A reflects α (which gives a measure of the particles’s size),and is phase-independent. The red curve in Fig. 2 corresponds to this signalamplitude A, which we get after demodulation of the raw detector signal(the black curve) using the lock-in amplifier. Here lies the big advantageof heterodyne interferometry when it comes to particle detection, which isthat the phase sensitivity of the detector signal can be eliminated and hencedetection accuracy can be improved over standard homodyne detection. Inhomodyne detection, only one of the phase-sensitive signals (Sx or Sy) wouldbe recorded, and hence particle detection accuracy is affected by phase. Thered curve in Fig. 3b shows the theoretically expected variation of the ho-modyne signal (considered to be Sx) for the parameters of the experimentsdescribed in the following sections.
2.3 Experimental Validation of Predicted Signal
With the theoretical understanding of heterodyne interferometric detectiondeveloped in the preceding sections, we will now experimentally validate ourpredictions using an experimental scheme similar to that illustrated in Fig. 1.Instead of particles in solution flowing through nanofluidic channels, we usean immobilized 100 nm polystyrene sphere as a test particle. A drop of wateris used to cover the immobilized particle to mimic the surrounding medium
11
for a particle in solution. By means of a piezo scan stage, the particle is firstpositioned in the focus r = (x, y, z) = (0, 0, 0) of the stationary excitationbeam and then periodically scanned in the transverse x direction. The blackcurve in Fig. 3a shows the raw detector signal according to Eq. (16) and theblue curve is the corresponding demodulated signal amplitude A. The insetshows the oscillations at the carrier frequency ∆ω. Because of the presenceof the background field Eb, the raw detector signal exhibits a time-dependentbaseline (hence different from the black curve in Fig. 2, where we don’t con-sider Eb). The blue curve, however, can be directly compared to that ofthe theoretically predicted red curve in Fig. 2. While the width of the bluecurve is associated with the size of the laser focus and the particle velocity,its height reflects the particle polarizability α.
To characterize the influence of the phase on the signal strength for homo-dyne detection Sx , the experiment is repeated for different offsets (z=const.)along the optical axis, representing the typical range of particle trajectories.For each z position, the maximum value of Sx is evaluated. The result,shown in Fig. 3b, represents the signal variations in a standard homodynedetection scheme. Evidently the phase variations cause the signal to varyrapidly with z. Therefore, different particle trajectories affect the homodynesignal strongly, which diminishes the measurement accuracy and makes itdifficult to assess the particle size and polarizability. In heterodyne detec-tion, on the other hand, the phase can be eliminated. The resulting signalA = [S2
x + S2y ]
1/2, which corresponds to the envelope of the oscillating curveshown in Fig. 3b, no longer varies across the typical range of particle tra-jectories (highlighted stripe, which denotes the lateral extent of nanofluidicchannels). As will be discussed in the following, the elimination of phasevariations leads to improved measurement accuracy.
3 Characterization of the Performance of a
Heterodyne Detection Scheme
A given set of particle measurements will have a characteristic size distribu-tion, whose width represents the actual particle size distribution as well asthe measurement uncertainty. The width can be estimated as the standard
12
-1
0
-0.5
0.5
1
0-0.5-1.5 -1 0.5 1.51
-1
0
-0.5
0.5
1
0-0.5-1.5-2 -1 0.5 1.5 21
a
b
z (µm)
time (ms)
sig
na
l (a
rb. u
nit
s)si
gn
al
(arb
. un
its)
Figure 3: Experimental signals recorded with a test particle scanned through thelaser focus. (a) The black curve shows the raw detector signal according to Eq. (16)and the blue curve is the demodulated modulus A. The amplitude of A is a measurefor the particle polarizability α. Inset shows the oscillations at the carrier frequency∆ω. (b) Demonstration of the phase sensitivity of homodyne detection. The figureshows the maximum value of Sx recorded by scanning a test particle through thelaser focus in different transverse planes z = const. The shaded region correspondsto the width of the nanofluidic channels used in our experiments with particlesin solution. Phase variations across the nanochannel dimensions have a stronginfluence on the signal strength of Sx (homodyne detection). Dots: experimentaldata; red curve: theoretical curve.
13
deviation
σtotal =√
σ2system + σ2
trajectory + σ2size , (23)
which has several contributing terms. Here, σsystem is due to the system re-sponse, which is the distribution that would be obtained for a single particlecrossing the laser focus several times on the same trajectory, and σtrajectory
represents the signal variation due to the various trajectories a particle maytake. A heterodyne system eliminates the phase dependence of this variation,but the modulus A is also affected to a small degree. Finally, σsize representsthe actual distribution of particle sizes, which is the quantity we generallywish to determine.
In the following sections, we present experimental results obtained withthe above-introduced heterodyne detection scheme, that characterize the sys-tem response, σsystem, and the trajectory uncertainty, σtrajectory. Once thesequantities are known for a given experimental configuration, it is straight-forward to isolate the particle size distribution, σsize of a given sample ofnanoparticles.
3.1 System Response
To investigate the effect of the system’s response function in the performanceof the detection scheme, we use a single immobilized nanoparticle that is re-peatedly scanned through the laser focus. This configuration eliminates theproblems associated with particle heterogeneity and different particle trajec-tories.
Polystyrene spheres 75 nm in radius are immobilized on a microscopecover-slip, covered with a drop of water, and a single particle is scannedseveral times back-and-forth through the laser focus. Each detection event,corresponding to the particle passing through the laser focus, renders thesignals Sx(t) and Sy(t) as described by Eqs. (20) and (21), from which wecalculate the modulus A(t) = [S2
x+S2y ]
1/2. As seen in Fig. 3a (blue curve), theamplitude A(t) of an individual detection event has a characteristic double-peak structure. This information is used to distinguish detection events fromsystem noise. For each detection event we evaluate the maximum peak am-plitude of A(t) and use the resulting value as a data point in a histogram.A sufficiently large number of detection events generates a characteristic sig-
14
20
200
0120100806040
100
400
300
200
0
100
400
300
200
0
100
400
300
a b c
cou
nts
cou
nts
cou
nts
particle radius (nm)
20 120100806040
particle radius (nm)
20 120100806040
particle radius (nm)
Immobilized particle Trapped particle Ensemble of particles
σ = 8.1 nmσ = 3.9 nmσ = 0.7 nm
Figure 4: Experimental particle size distributions measured with the heterodyne
approach for (a) a single immobilized 75 nm polystyrene particle that is repeatedly
scanned through the laser focus, (b) a single 75 nm polystyrene particle electroos-
motically trapped in a nanochannel, and (c) an ensemble of 75 nm polystyrene
particles freely flowing through a nanochannel. The standard deviations for the
respective size measurements (reflecting the size resolutions in the measurements)
are indicated by the σ values.
nal distribution. The signal can be calibrated to the particle’s size becausethe signal magnitude scales linearly with the polarizability α (c.f. Eq. 1)and hence with the third power of particle size R. Fig. 4a shows a size his-togram obtained for an immobilized 75 nm polystyrene particle. In essence,this size distribution represents the system response function, and the widthof the distribution, 0.7 nm, defines the resolving power of the measurementapproach.
Homodyne detection yields a size distribution that is significantly wider,which can be demonstrated by plotting a histogram of sizes obtained fromthe signal Sx(t) [or Sy(t)] by itself. This increase in width originates fromthe fact that the homodyne signal is affected by phase variations due to in-terferometer instabilities and by small deviations in particle trajectories.
3.2 Particle Trajectories
Having quantified the system’s response, we next characterize the influenceof different particle trajectories and Brownian motion. As shown in Fig. 1,we use a flow-through scheme that employs a nanofluidic channel to directsingle nanoparticles through a stationary laser beam. The characterizationof particle trajectories requires that the particle size does not vary between
15
measurements. However, commercial nanoparticle solutions come with a fi-nite size distribution. In order to eliminate this ambiguity we implementedan electroosmotic recycling scheme, which allows the interrogation of thesame single particle over and over again.
The nanofluidic channels used in our experiments are fabricated in fusedsilica wafers using UV lithography. The nanochannels are 15 µm long, have a500 × 500 nm square cross-section, and are connected to two reservoirs [48].A single nanochannel is positioned in the laser focus by means of the scanstage. A nanoparticle solution is introduced into one of the reservoirs and aparticle flow is established using the electroosmotic effect [47].
To repeatedly interrogate the same nanoparticle, the electroosmotic volt-age is controlled by a feedback loop. The signal from a single particle travers-ing the laser focus is used to flip the electroosmotic voltage immediately af-ter the passage, causing the nanoparticle to reverse its direction of motionand pass through the laser focus again. In order for the trap to be stable,the particle’s passage time τ through the laser focus (size ∆x ≈ 500 nm)needs to be shorter than the timescale associated with Brownian motion, i.e.
τ < ∆x2/2D, where D is the diffusion coefficient. In water D ≈ 10−11 m2/sand hence τ < 8 ms. In our experiments τ ≤ 1 ms, which typically allows usto detect a single nanoparticle more than 104 times before it escapes due toBrownian motion.
A characteristic time trace for a single electroosmotically trapped nanopar-ticle is depicted in Fig. 5a. The top curve (red) shows the periodic switchingof the electroosmotic potential, the center curve (blue) is the homodyne sig-nal Sx(t), and the bottom curve (black) is the heterodyne signal A(t). Asdiscussed earlier, the phase variations due to different particle trajectories arefully contained in Sx(t) but are eliminated in A(t). Therefore, as shown inFig. 5a, the variations between individual detection events are considerablylarger in the homodyne signal than in the heterodyne signal, supporting thehypothesis that the phase should be eliminated for accurate particle charac-terization.
The maximum value of A(t) for each particle passage is then evaluatedand a distribution of the values is established. The resulting histogram isshown in Fig. 4b. Since the same particle is detected repeatedly, the factorscontributing to signal variations are system noise and variations in particle
16
time (s)
particle radius (nm)
Heterodyne
Homodyne
200
0
100
400
300
cou
nts
20 120100806040
particle radius (nm)
cou
nts
20 120100806040
50
100
200
150
a b
σ = 3.9 nm
c
σ = 7.9 nm
Figure 5: Characterization of the influence of particle trajectories. (a) Timetrace for a single 75 nm polystyrene particle repeatedly passing through the laserfocus. The figure shows the periodic switching of the electroosmotic potential(top), the homodyne signal Sx(t) (center), and the heterodyne signal A(t) bottom.It is evident that the signal variations between detection events are lower for A(t)than for Sx(t), proving that the elimination of phase variations due to differentparticle trajectories improves the detection accuracy. (b and c) Comparison of thesize distributions obtained using the heterodyne (red) and the homodyne (green)signals. The effect of phase variations is clearly evident from the significantlygreater width of the distribution in the homodyne case.
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trajectories. The latter gives rise to a broadened size distribution as com-pared to the immobilized particle case shown in Fig. 4a. The width of thedistribution is evaluated to be σ = 3.9 nm. A comparison of the hetero-dyne distribution with that obtained with homodyne detection (Sx or Sy)is shown in Fig. 5b and c. The homodyne distribution in Fig. 5c is muchwider (σ = 7.9 nm) than the heterodyne distribution in Fig. 5b, becauseof phase variations due to different particle trajectories. This difference inwidth clearly illustrates the importance of eliminating the effect of phasevariations with heterodyne interferometry, hence improving the accuracy ofparticle characterization.
3.3 Ensembles of Single Nanoparticles
The particle distributions further broaden if different nanoparticles from par-ticle solutions are used. Having characterized the detector response and theinfluence of varying particle trajectories we now concentrate on the size dis-tribution of particles in a solution.
To detect different particles from solutions we open the feedback loopcontrolling the electroosmotic trapping. Under this condition, a constantelectroosmotic potential propels single nanoparticles through the nanochan-nel. Fig. 4c shows the recorded size distribution for ∼5000 different 75 nmpolystyrene spheres. The distribution is slightly asymmetric with a standarddeviation of σtotal = 8.1 nm, from which we determine the particle size uncer-tainty σsize according to Eq. (23). Now, σsystem = 0.7 nm is the contribution ofthe system response to the width (Fig. 4 a), and σtrajectory =
√3.92 − 0.72 nm
= 3.8 nm is the width associated with the variations in particle trajectories(Figs. 4 a,b). The size uncertainty is found to be σsize = 7.1 nm.
The optical detection scheme introduced here can be employed for mea-suring the homogeneity of particle samples and for testing the specificationsof commercially available particle solutions. Most particle sizing methodsmake use of surface immobilization, which is generally less effective for smallparticles as compared to larger ones. The variation in binding strength affectsthe measured particle size distributions and hence the specified standard de-viations. On the other hand, the present heterodyne detection scheme doesnot rely on immobilization, which makes the measured distributions morereliable. For example, the asymmetry of the measured distribution in Fig. 4c
18
is likely the result of the manufacturer’s filtering process, which is effectivefor the removal of large particles but less effective for the smaller ones.
4 Characterization of Nanoparticle Mixtures
Using the above method, it is possible to distinguish between nanoparticlesof different sizes or materials in the same solution. In this section we presentsome results obtained with mixtures of gold and polystyrene particles of dif-ferent sizes.
Figs. 6a and b show the particle size distributions recorded for a mixtureof polystyrene particles with mean radii of 50 nm and 75 nm, using the het-erodyne (red) and homodyne (green) signals. Using heterodyne detection,one can clearly resolve the two particle sizes, with very little overlap. On theother hand, the individual particle distributions are wider in the homodynecase, and hence the distributions partly overlap. This illustrates the supe-rior size resolution obtainable with heterodyne detection for a heterogeneousmixture of particles.
In order to test the capability of the detection scheme in resolving the dis-tributions of similar particles with slightly different sizes, we used a mixtureof of gold nanoparticles with mean radii of 30 nm, 40 nm, and 50 nm. Thesize distributions obtained using the heterodyne (red) and homodyne (green)signals are shown in Fig. 6c and d respectively. The heterodyne detectionscheme resolves the particles although the individual distributions are largelyoverlapping, whereas in the homodyne case joint particle distribution is toobroad to identify individual particle peaks.
5 Detection and Classification of Viruses
We have demonstrated above that heterodyne interferometry can be usedvery effectively to detect single nanoparticles in solution with high sensitivityand selectivity. Now we explore the possibilities of detecting and distinguish-ing between viruses in solution using heterodyne interferometry.
The size of most human viruses is in the range of 20−200 nm [51], which is
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Figure 6: Particle size distributions for mixtures of particles flowing through
a nanochannel, obtained using the heterodyne and homodyne detection schemes
. (a and b) Size distributions for a mixture of 50 nm and 75nm polystyrene
nanoparticles.(c and d) Size distributions for a mixture of 30 nm, 40 nm, and
50 nm gold nanoparticles. Heterodyne : red histograms, and Homodyne : green
histograms.
20
well suited to the capabilities of the heterodyne detection scheme. In generalit is difficult to detect nanoscale biological particles such as single virusesin solution using scattering based techniques due to their weak refractiveindex contrast (refractive index of a virus particle n ∼ 1.5 [52]) with thesuspending medium, which is predominantly water-based (n = 1.33 for wa-ter). We show below that heterodyne detection helps overcome this difficulty.
Using the heterodyne detection technique, we could successfully detectHIV, Influenza, Sindbis, Vaccinia, Parainfluenza(Sendai), and Baculovirusin separate samples on the single virus level. For virus detection usingnanofluidic channels, a pressure-driven flow scheme [44] was used insteadof electroosmotic flow. The velocity profile and flow-speed control of the twomethods are similar, but electroosmotic flow tends to heat the buffer solutionof the viruses [53]. When added to heating due to the light focus, this cancause the formation of vapor bubbles [54] and decomposition of the sample,which clogs the nanofluidic channels and disrupts the measurement process.Pressure-driven flow does not heat the buffer solution.
In Fig. 7 shows some representative results for virus detection using theheterodyne detection scheme. Fig. 7a shows the size distribution recordedfor a sample of HIV virus (ADA strain). To calibrate the HIV size distribu-tions, the mean radius of HIV particles is taken to be 50 nm, as determinedfrom TEM measurements [55]. In Fig. 7b we show the size distribution for asample of Sindbis virus. For calibration purposes, the mean radius of Sindbisvirus particles is assumed to be 35 nm according to TEM measurements [56].
To demonstrate the ability to distinguish between HIV and Sindbis virusesin solution, the size distribution for a mixture of the two viruses is recorded. Fig. 7c shows that the two virus types can be resolved. The size distri-bution is calibrated with respect to the mean size of a HIV virus particle(50 nm). Note, that according to this calibration, the mean size of Sindbisviruses turns out to be ∼ 35 nm, which is in good agreement with the TEMmeasurements, and indicates that the optical properties (εp) of the two virustypes are similar. The results indicate that it is possible to distinguish by sizeindividual viruses in a mixture of different virus types, provided we know,for calibration purposes, the mean size of at least one virus type.
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Figure 7: Size distributions for different virus types. (a) HIV (ADA strain)and (b) Sindbis virus. (c) Size distribution for a mixture of HIV and Sindbisviruses.
22
6 Conclusions
In this article we have presented heterodyne interferometry as an effectivemethod for accurate characterization of nanoparticles, including those of bio-logical importance such as viruses. It has been established from both theoret-ical and experimental standpoints that heterodyne interferometric detectionis more viable than other presently available label-free techniques, when itcomes to accurate real-time characterization of nanoparticles in solution. Ithas been shown that such a system can detect single viruses in a sample andalso distinguish between different kinds of virus types in a heterogeneous mix-ture. Such a real-time single particle detection scheme can also be used toaccurately determine the concentration of nanoparticles present in a sample,which can be of great importance for virological research where the infectionlevels due to a viral pathogen need to be determined. It can be anticipatedthat these abilities will find application in label-free biosensing, environmen-tal contamination and quality control, and also for clinical research.
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