March 1, 2006 / Vol. 31, No. 5 / OPTICS LETTERS 625

Imaging and sizing of diamond nanoparticles

Yannick Colpin, Amanda Swan, Andrei V. Zvyagin, and Taras PlakhotnikPhysics, School of Physical Sciences, The University of Queensland, St. Lucia 4072, Queensland, Australia

Received September 9, 2005; revised October 24, 2005; accepted October 26, 2005

Typical disturbances of biological environment such as background scatter and refractive index variationshave little effect on the size-dependent scattering property of highly refractive nanocrystals, which are po-tentially attractive optical labels. We report on what is to our knowledge the first investigation of these scat-tering optical labels, and their sizing, in particular, by imaging at subvideo frame rates and analyzingsamples of diamond nanocrystals deposited on a glass substrate in air and in a matrix of weakly scatteringpolymer. The brightness of a diffraction-limited spot appears to serve as a reliable measure of the particlesize in the Rayleigh scattering limit. © 2006 Optical Society of America

OCIS codes: 120.5820, 290.5870, 110.2960, 170.3880.

In biological imaging, site-specific optical labelinggenerally classified as luminescent and scatteringprovides superb discrimination between the sites ofinterest and the crowded background of a biologicalspecimen. Luminescent optical labels include fluores-cent dyes1 and quantum dots. Scattering labels in-clude plasmon-resonant particles, also known asimmunolabels,2 whose excitation at the plasmon fre-quency renders an ultrabright appearance. The scat-tering cross section of an 80 nm diameter silversphere is typically 106-fold that of a single fluorescentdye.2 Individual gold particles of diameters as smallas 10 and 2.5 nm have been imaged by usinginterference confocal3 and phase-contrast thermal-absorption4 microscopy, respectively. Multiplexing ofoptical labels is usually realized spectrally, by dis-criminating size-tunable emission bands, as in quan-tum dots, or size-tunable absorption–scattering crosssections, as in metal nanoparticles.5

None of these optical labels is ideal: photoinstabil-ity, low cross section, and toxicity6 of the luminescentlabels present a problem, especially in the context oftracking individual labels.1 In the case of the scatter-ing labels, thermal perturbation of biological environ-ments (several degrees centigrade) (Ref. 4) and un-predictable catalytic properties of immunolabels aredisturbing issues for biologists.

Color-center nanocrystals (e.g., nitrogen vacancydefect in diamond7) represent a luminescent label en-capsulated within a scattering optical label and dis-play a blend of merits that are characteristic of bothclasses: high-contrast imaging due to the spectralseparation of excitation–emission bands, photostabil-ity, immunity to the environment, and strong elasticscattering owing to the high refractive index relativeto that of the biological medium. The scope of thisLetter, however, is limited to elastic-scattering as-pects of this new type of label, i.e., a scattering opti-cal label.

A very high refractive index of diamond (2.5) leadsto high scattering efficiency of a nanocrystal relativeto its size (�300-fold that of the same size cell or-ganelle embedded in cytoplasm). Moreover, refractiveindex variation in the cell ranging from 1.33 to 1.6(Ref. 8) marginally affects the scattering efficiency ofnanocrystals. The dramatic dependence of Rayleigh

0146-9592/06/050625-3/$15.00 ©

scattering on nanocrystal size provides an alterna-tive multiplexing paradigm and offers a uniquemethod of sizing individual nonabsorbing nanocrys-tals by conventional optical means. The state-of-the-art methods of nanoparticle sizing, e.g., dynamiclight scattering based on Doppler velocimetry ofBrownian motion,9 are capable of determining sizedistributions only in ensemble. Despite the enhancedresolution of near-field scanning optical microscopy,its sizing capacity is compromised by various re-ported imaging artifacts.10

Accurate sizing of spherical nanoparticles is en-tailed in the sixth-power dependence of their scatter-ing cross section in the Rayleigh limit on diametersgiven by

�s =�

24k4�n2 − 1

n2 + 2�2

d6, �1�

where n denotes the particle refractive index relativeto that of the immersion medium and k denotes thewavenumber in the medium. In comparison with theexact Mie scattering theory, the total scattering crosssection of a 100 nm diameter diamond nanocrystal isunderestimated by only 26% by employing Eq. (1),which yields only a 3% systematic error in terms ofparticle sizing, vanishing for smaller particles.

To demonstrate this method of nanoparticle sizing,we carried out an experimental study using an opti-cal microscope built in house. The imaging module ofthe microscope comprised a dry infinity-corrected ob-jective lens (100�, NA 0.9) followed by a singlet lensof focal length 200 mm. The module was configuredto image a top surface of the sample onto a low-noiseelectron-multiplying CCD (EM-CCD) camera (AndorTechnology, 512�512, pixel size 16 �m�16 �m,16 bit). A collimated Gaussian-profile laser beam(wavelength 532 nm, diameter 3.2 mm, power10 mW) was used to illuminate the sample placed ona prism at an incident angle of 60° under total inter-nal reflection condition to produce background-freeimages. The exposure time of the EM-CCD of 0.05 sensured its operation below the saturation. The over-all magnification of the imaging module was adjustedso that a diffraction-limited spot was oversampled by

a 3�3 pixel matrix. An image frame was acquired

2006 Optical Society of America

626 OPTICS LETTERS / Vol. 31, No. 5 / March 1, 2006

and transferred to a PC and processed using Matlab.The diamond nanocrystals (Warren Superabrasive)were characterized by a mean diameter, d̄=55 nm,with a standard deviation of �=20 nm. Two sampleswere fabricated on a 150 �m thin glass coverslip:samples 1 and 2 represented a monodisperse distri-bution of diamond nanoparticles in air and 100 nmthin polyvinyl alcohol, respectively.

When nanoparticles are situated on a dielectricplanar interface11 and illuminated with an evanes-cent wave, the detected photon number is given by

Nph = ����s�Racorr exp�− kzd/2�, �2�

where � stands for the photon flux �photons/s /m2�, �denotes the quantum efficiency of the sensor, and � isexposure time. �R denotes photon collection efficiencyfor an unbounded Rayleigh scatterer: 2�R=1− �1−NA2�1/2, where NA stands for numerical aperture ofthe collection optics. Note that �R is obtained by av-eraging contributions from two orthogonal polariza-tion states of the incident light. The exponential fac-tor describes the evanescent field attenuation at thecenter of a dielectric sphere, where kz stands for themodulus of the pure imaginary wave vector. �corr is aproduct of three factors: (1) enhancement of the scat-tering efficiency in the presence of an interface, pro-vided that the dipole is situated in the lower-refractive index medium (air, in the case of sample1)11; (2) a modified scatter diagram11 that integratedover acceptance angles of the objective lens andscaled against that of an unbounded Rayleigh scat-terer; and (3) the Fresnel coefficient generalized for acomplex wave vector.12 The calculation using givenparameters of our system yields values of �R=0.28and �corr�0.6.

First, we carried out a numerical experiment of thesample imaging. A 512�512 image was modeled as asparse random distribution of 3�3 pixel clusters.The cluster amplitude was apodized with a 2DGaussian function, which was truncated at the clus-ter edge at the 1/e function falloff. The maximumpixel brightness in the numerically generated clusterensemble was set to 6.5�104 photons per second(pps). The number of the generated clusters, N=1000, roughly corresponded to the typical numberof nanoparticles situated in the field of view undertypical experimental conditions. Integral amplitudesof these clusters were distributed as the sixth powerof a statistical variable, which obeyed the Gaussiandistribution, where d̄ and � were chosen to be 55 and20 nm, respectively. A background characterized byits mean value of 2000 pps and associated shot noiseof 45 pps was added to the simulated image. The re-sultant image is presented in Fig. 1(a) as an invertedgray-scale color map.

Isolated clusters of pixels (associated with par-ticles) were singled out on the thresholded image.Each cluster was characterized by a sum of pixel val-ues that formed this cluster. The resultant histogramof the recovered clusters is plotted in Fig. 1(b). We ob-served that the number of registered particles was

reduced by 25% of the original particle number, and

the mean value of the particle sizes was shifted by9% to the small-size end of the histogram with re-spect to the original numerically generated distribu-tion [dashed–dotted curve, Fig. 1(b)]. We found thatmerging several clusters accounted for the reductionof the recovered number of particles, which contrib-uted to the high end of the size spectrum. More im-portantly, signals from particles of the lower end ofthe size spectrum were likely to be buried under theshot noise. It was calculated that 30 nm particleswould give rise to signals with a signal-to-noise ratio(SNR) of unity, rendering them undetectable in 50%of the cases [Fig. 1(b)].

In experimental measurements of diamond nano-crystal samples, the maximum signal of1,600,000 pps/particle on the glass substrate (sample1) was obtained, which corresponded to the particlesize cutoff of 110 nm estimated theoretically by d=C�Nph�1/6, where C was derived by using Eqs. (1)and (2).

Image processing of the experimental data yieldedresults presented in a histogram [Fig. 2(b)] charac-terized by d̄=57±1 nm and �=17 nm. As was thecase with the recovered particle size distribution inthe numerical experiment, the histogram is skewedtoward the high end of the size spectrum, indicatingthat small particles were not detected due to noise,which was believed to be due to scattering from sur-face irregularities. The signal profile is shown in Fig.2(c). Based on image analysis, the minimum detect-able size was estimated to be 37 nm. The manufac-turer distribution is also plotted as a dashed–dotted

Fig. 1. (a) Numerically generated image of cluster distri-bution; (b) histogram of the recovered cluster distribution.Theoretical curve of original Gaussian distribution (dash-dotted curve).

curve in Fig. 2(b). To facilitate comparison with the

March 1, 2006 / Vol. 31, No. 5 / OPTICS LETTERS 627

experimental data, the area under the histogramswas made equal. We note good agreement betweenthese distributions, with the only discrepancy at thehigh end of the particle size spectrum attributed tothe size distribution artifact due to the spin-coating-based sample fabrication.

To investigate the immunity of the nanoparticlesizing method to environmental perturbation of therefractive index, we imaged and analyzed sample 2,which represented diamond nanoparticles uniformlydispersed in a polyvinyl alcohol thin film. Despite thepresence of the scattering background, the originaldiamond nanoparticle distribution was faithfully re-covered, yielding 56±1 for d̄ and 16 nm for �. Theminimum detectable particle diameter was estimatedto be 40 nm.

In conclusion, we have demonstrated that diamondnanocrystals open new opportunities in optical imag-ing, especially in applications where the size of opti-

Fig. 2. (a) Image of sample 1, (b) histogram of sample 1.The manufacturer particle size distribution (shown by thedashed–dotted curve), (c) signal amplitude profile. SignalsA and B correspond to 75 and 55 nm particles, respectively.The image processing threshold is marked by the dashed–

dotted line.

cal labels represents an important parameter, as inthe case of the tracking of kinesin-drivenmovements.13 The dramatic Rayleigh-law depen-dence of the optical signals versus the particle sizesis the core concept of a new method for sizing indi-vidual dielectric nanocrystals. The method has beensuccessfully tested experimentally by imaging andanalyzing samples of diamond nanocrystals depos-ited on a glass substrate in air and in weakly scatter-ing polymer. The brightness of a diffraction-limitedspot serves as a reliable measure of the particle size.Either the noise floor fluctuation or form-factor-induced birefringence bears little effect on the sizingaccuracy. For example, the signal from a 39 nm diam-eter particle is prominent on the background of40,000 pps �SNR=2�, whereas a 37 nm particle isbarely detectable �SNR=1�. For practical applica-tions of nanocrystal-based optical labels, their detec-tion sensitivity on the crowded cellular backgroundneeds to be enhanced. The promise of image process-ing for detecting extended samples, e.g., 25 nm livemicrotubules,14 was demonstrated two decades ago.To our best knowledge, however, this Letter reportsthe lowest detectable limit for dielectric spheroidalparticles, pushed down to 37 nm. The applicationscope of bright dielectric nanocrystals is envisaged inoptical labeling of weakly scattering biological speci-mens.

A. V. Zvyagin (zvyagin@physics.uq.edu.au) is alsoaffiliated with Biomedical Engineering, School of In-formation Technology and Electrical Engineering,The University of Queensland. This project was sup-ported by UQ Research Development Grant2004001587.

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