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We present a novel scattering microscopy method to detect the orientation of individual silver nanorods and to measure their relative distances. Using confocal microscopy in combination with either the fundamental or higher order laser modes, scattering images of silver nanorods were recorded. The distance between two individual nanorods was measured with an accuracy in the order of 1 nm. We detected the orientation of isolated silver nanorods with a precision of 0.5 degree that corresponds to a rotational arch of about 1 nm. The results demonstrate the potential of the technique for the visualization of non-bleaching labels in biosciences.
©2007 Optical Society of America
1. Introduction
Fluorescence microscopy, utilizing organic labels, remains an unrivalled method for the non invasive detection in the interior of cells or other biological environments. Several techniques have been developed to increase the optical resolution[1, 2, 3], to determine the topology of fluorescent pointlike objects [4, 5, 7, 8] as well as to measure the size of fluorescent nano beads [6] and the size of polymerase-II active sites [9]. The bleaching of organic fluorescence labels, however, still limits the efficiency of advanced methods in fluorescence microscopy and stimulate the search of more efficient excitation/detection schemes [10].
Another approach for using optical microscopy in bioscience is to exploit nobel metal nanoparticles as non bleaching markers. The fast development of nanotechnology allows to produce [11, 12, 13], detect [14, 15, 16, 17] and characterize [18, 19] silver and gold nanopar-ticles of arbitrary shapes and size. Gold and silver nanoparticles are not toxic, they scatter light with high efficiency, they have their plasmon resonances in the visible, near infrared range and their luminescence signal does not bleach. In particular, gold clusters generate an enhanced and tunable luminescence signal [20] that permits to obtain a depth-resolved image of both live and fixed cells in a laser scanning microscope setup [21]. The plasmon coupling in single nobel metal particle pairs was used to monitor the intra-particle distance [22] and gold nanorods have been utilized as contrast agents for both molecular imaging and photothermal cancer therapy [23] as well as two-photon luminescence imaging agents in mouse ear blood vessels [24]. Recently we have reported about a novel technique to image the scattering patterns of metal nanoparticles [25, 26] by the combination of confocal scattering microscopy [27] and confocal interference microscopy [28]. Here, the interference between the light reflected at the sample interface and the light scattered by the metallic nanoparticles produce the image contrast.
In this article we investigate the precision of Confocal Interference Scattering Microscopy (CISM) in combination with either the fundamental or higher order laser modes. First, we determine the distance between three spatially isolated silver nanorods. The error associated with each measurement was found to be as low as 0.2 % of the detected distances in the range of 1μm. Second, the orientation of the same three nanorods was determined with an accuracy higher than one degree. Finally, we perform a rotational scan of a single silver nanorod. As a result, a manual rotation of the sample by one degree could be recognized from the measured and analyzed scattering images.
2. Material and methods
This section is dedicated to an overview of the sample preparation, the experimental setup,the basic theory of CISM signal generation and the data analysis algorithm.
2.1. Sample preparation
Fig. 1. AFM image of a spatially isolated silver nanorod. Inset left: Profiles of the particle taken along the white dashed lines. Inset right: Image of a representative silver nanorod cut from a transmission electron microscope-micrograph (its aspect ratio equals R ≃ 2). Note that the hight (short axis) of the imaged nanorod equals b = 25 nm.
We studied silver nanorods that were synthesized in solution according to [29]. Silver nanorods are characterized by their long axis a, their short axis b and their aspect ratio R = a/b. Using transmission electron microscopy (TEM) we found that b in our sample varies between 20 and 40 nm while R ranges between 1 and 4. In Fig. 1 inset right we present the image of a representative silver nanorod (R ≈ 2) that was cut from a TEM-micrograph.
For the optical experiments, we prepared samples with spatially isolated nanorods i.e. their mean relative distance was larger than 1 μm (see AFM image in Fig. 1). Briefly, diluted solutions of silver nanorods were spin coated on carefully cleaned glass cover-slides under optimized conditions. Afterwards the nanorods were covered with a layer of Poly(vinyl alcohol) (PVA) solution (1 %) having a thickness of several tens of microns to prevent oxidation and back reflection of the laser excitation light.
2.2. Experimental setup
Fig. 2. Scheme of the optical setup (MC: Mode converter, SF: Spatial filter, BS: Beam splitter, L: Lens, MO: Microscope objective, SC: (x,y)-scanning stage, S: Sample). Inset (I): Intensity profiles in the focal regime of the excitation beams focused on a glass-PVA interface: Linearly polarized Gaussian mode (LPGM), left; azimuthally polarized doughnut mode (APDM), center; radially polarized doughnut mode (RPDM), right. (a)-(c): x and y in-focus intensity cross-sections (continuous/dotted line) taken from the images (d)-(f), (d)-(f): (x, y)-plane in-focus intensity profiles, (g)-(i): (x, z)-plane intensity profiles. Inset (II): Intensity profiles of the parallel beam for the three different modes. Note that the polarization is indicated by arrows.
All optical measurements were performed with a home-built inverted confocal microscope as sketched in Fig. 2. The 514 nm line of an Argon Ion laser served as primary light source. First the laser light passes through a linear polarizer. A mode converter (MC) followed by a spatial filter (SF) was placed in the path of the excitation beam transforming the linearly polarized Gaussian mode (LPGM) into higher order laser modes, i.e. an azimuthally polarized doughnut mode (APDM) or a radially polarized doughnut mode (RPDM) (for more details see [25, 26]). In short, the mode converter consists of a four-quadrant λ/2-retardation plate that rotates the polarization of an incoming linearly polarized laser beam [30]. The SF serves to remove distortions from the laser beam. The transversal intensity profiles of a well collimated LPGM, an APDM and a RPDM are shown in Fig. 2 inset (II). By rotating the mode converter through 90 degree one can switch between the two doughnut beams.
Fig. 3. CISM images of silver nanorods on a glass cover-slide covered by PVA and excited with an APDM (left) and a RPDM (right), respectively at 514 nm. (a), (b): Experimental data, the insets show the intensity profiles along the white dashed lines. (c), (d): Simulated data. Poissonian noise was added to account for the experimental conditions.
The collimated beam was reflected by a non polarizing 50:50 beam splitter (BS) and focused onto the sample surface with an immersion oil objective (NA = 1.25, 100x). Both the reflected light from the glass cover-slide and the scattered light from individual particles were collected with the same objective and focused onto a photon-counting avalanche photodiode (APD) that serves as a detector. Confocal images were produced by raster scanning the sample through the focal spot of the microscope objective.
2.3. Basics of CISM
In the following, we analyze the intensity distribution IF of the excitation beam within the focal volume (see Fig. 2 inset (I)) by investigating the fields above and below the glass-PVA interface (z=zint):
E f, E r and E t are the focused, reflected and transmitted fields at the glass-PVA interface, respectively. Note, that zint is the position of the interface on the optical axis (black dashed line through Fig. 2 inset (I) (g)-(i)). In Fig. 2 inset (I), the calculated intensity profiles of a LPGM, an APDM and a RPDM focused by a high numerical aperture objective (NA=1.25) onto the glass-PVA interface are shown together with the experimental coordinate system. Note that the intensity profile has rotational symmetry with respect to the z axis for the APDM and the RPDM whereas it is elongated on the polarization axis for the LPGM. The effect of the interference between E f and E r (for z ≤ zint) can be clearly noticed only in the case of LPGM.
The signal detected by the APD (IAPD) results from the superposition of the excitation light reflected at the interface E r and the field scattered by the nanoparticle E s:
The first term on the right-hand of Equation 4 is proportional to the square of the reflected field and represents the background intensity. The second term indicates the pure scattering signal. The third term results from the interference of the reflected and the scattered field at the interface and depends sensitively on their relative phase ϕ. In the case of nanoparticles having dimensions in the order of a few tens of nanometers the pure scattering signal can be neglected. The Mie theory indicates that E s is proportional to both the excitation field and the particle’s volume V [31]. Therefore, the pure scattering signal that scales as V 2 is more than one order of magnitude weaker compared to the interference term that is proportional to V and to E r.
The sign of this signal and, hence, the image contrast depend on the phase relation ϕ that is determined by the spectral dependence of the particle plasmon, the refractive index gradient at the glass-PVA interface, the particle’s material, its size and aspect ratio as well as the NA of the objective lens. As we shall see, all optical patterns studied in this work exhibit a negative image contrast.
In Fig. 3, the measured scattering patterns of silver nanorods that were acquired using an APDM and a RPDM are compared with the simulated ones. The simulations are based on a model for the analytical calculation of the field distribution for an APDM (RPDM) focused onto a glass/PVA interface. The model accounts for optical parameters as the NA of the focusing lens, the Fresnel coefficients at the glass/PVA interface, the refractive index of the surrounding medium as well as the polarizabilty tensor of the nanoscatterers following Mie theory. A detailed description of this model is subject of a further publication.
The intensity profiles taken along the white dashed lines in Figs. 3 (a) and (b) are shown in the insets. These profiles were extracted from the raw data and show contrasts that were typical for our measurements. Note that the experimental count rate of about 1 MHz is far above the dark count rate of our detector ∼ 100 Hz.
All the parameters necessary to calculate the simulated scattering patterns were determined experimentally. In particular, the aspect ratio R = 2 and the short axis length b = 25 nm have been derived from TEM and AFM images (see for example Fig. 1). For both excitation modes the simulated scattering patterns were calculated with the addition of Poissonian noise to improve modelling accuracy. As it will be shown in the next paragraph, this procedure also serves for testing the stability and the sensitivity of the fit algorithm that was used for the data evaluation. The comparison of the experimental and theoretical scattering patterns shows a good agreement and demonstrates that orientational information can be clearly obtained only in the case of an APDM.
In contrast to the results discussed in [25] and [26], the scattering pattern rendered by silver nanorods excited by a RPDM at 514 nm do not show a two lobe shape. The characteristic of the scattering patterns generated with a RPDM depends strongly on the optical properties of the metal particle and its surrounding media as well as the wavelength of the excitation light. Figures 3(b) and (d) show that the scattering patterns rendered by a RPDM will not provide more topological information than the ones produced by a LPDM. Thus,we will only discuss the data acquired using a LPGM and an APDM in the following.
2.4. Data analysis algorithm
In order to analyze the scattering patterns rendered by silver nanorods, we developed a two dimensional (2D) fit algorithm running on Matlab. This algorithm uses two different model functions, one for each excitation mode. These functions do not correspond to the theoretical expressions of the scattering patterns but they are useful to extract physical information from the entire image. Before we applied the fit algorithm we normalized the measured scattering patterns with respect to their intensity minimum.
In general, the fit algorithm performs a coordinate transformation between the coordinate system of the scanning set-up (axes x, y in Figs. 2 and 4) and the particle’s coordinate system that is aligned with respect to the main axes x 1, y 1 of the scattering pattern (see also Fig. 4 (b)). If the scattering pattern is spherical, these two systems are parallel. In the case where the scattering pattern is not spherical the coordinates x 1, y 1 are generated by rotating the axes x, y through an angle ϑ:
where (X 1, Y 1) are the coordinates of the origin of the particle’s reference system as shown in Fig. 4 (b).
The angle ϑ is included as a parameter in both model functions defined in Equations 7 and 8 and furnishes the information about the particle’s orientation.
The 2D scattering patterns acquired by means of a LPGM were analyzed using the following model function:
where A is the amplitude of the signal that is defined as the absolute difference between the signal intensity background and the signal intensity minimum. The w x1(y1)-values are proportional to the signal full-width-at-half-maximum (FWHM) values along the optical pattern main axes (see Fig. 4 (b)). The third term in Equation 7 is normalized with respect to the overall intensity minimum of the scattering pattern for maximizing the speed and the precision of the fit routine.
The second model function has been used for fitting the scattering patterns of silver nanorods excited by an APDM:
where and (xj,yj) (j = 1,2,3) are three coordinate systems oriented parallel to the symmetry axes of the patterns and centered on the minima of their two lobes and on their median point, respectively. Including two Gaussian functions G(x1(2)) in Eq. 8 allowed us to fit scattering patterns having asymmetric intensity distributions, see e.g. Fig. 5 (a)-(c). As defined above, Ai (i = 1,2) are the relative amplitudes of the two scattering lobes values and the w x1(x2)-values are proportional to their FWHM values. Moreover w x3(y3) are the FWHM values of a first order Hermite-Gauss function that envelopes the entire pattern.
We verified the consistency and the stability of the fit algorithm on simulated scattering patterns calculated according to the procedure summarized in [25]. The model will be described in detail in a further publication. These simulations have been carried out assuming the aspect ratio R of the nanorods to be 2 and that the length of their short axis b equals 25 nm. For each excitation mode, the virtual particle was placed in the origin of the (x, y)-scanning reference the particle’s main axis was set parallel to the y-axis (ϑ = 90 degree). Poissonian noise was added to each simulated pattern to reproduce low photon counts conditions i.e. 100 photon counts for the signal peak. To simulate stochastic fluctuations of the detected signal, 15 different patterns were produced for each excitation mode. The results of this test are shown in Table 1 and in all cases, the absolute position r of the virtual silver nanorod was analyzed by the fit algorithm. In the case of an APDM, the absolute orientation of the simulated patterns was determined additionally. The results prove that the two model functions defined in Equations 7 and 8 are well-suited for analyzing CISM measurements with high precision.
Fig. 4. CISM images of the same three silver nanorods (1,2,3) using an LPGM (a) and a APDM (c). Left column: Experimental data. Right column: Patterns reproduced by the fit algorithm based on Equations 7 (b) and 8 (d).
Table 1. Simulated topological evaluations
3. Experimental topological studies
3.1. Distance measurements on silver nanorods
Three silver nanorods were spatially localized after an image acquisition process. Figures 4 (a) and (c) show scattering patterns of the same three particles that were measured employing a LPGM and an APDM as excitation beam. The particles are labelled as 1, 2 and 3. The total scanning area was 3×3 μm2 with a pixel size of 10 nm. In each excitation mode, 12 images were acquired. In the following, we investigate the relative distances Dij (i,j=1,2,3) between two different particles and the absolute orientation of all of them. The evaluations were performed using the 2D fit algorithm based on Equations 7 and 8. Figures 4 (b) and (d) show the pattern reproduced by fitting the model function to the experimental data. As a result, we obtained geometrical information from the experimental scattering patterns (e.g. the position of their minima) that were useful for determining the barycenter of each pattern. Here, the distance Dij between two particles was defined as the distance between the respective barycenters.
Table 2 contains the distance estimates D and the associated errors ΔD. The D-values represent the arithmetic averages of the 12 independent measurements and the ΔD-values the corresponding standard deviations. The results determined with a LPGM are in good agreement with the ones performed using an APDM. Here, a sub-pixel precision (ΔD < 10 nm) is achieved and the relative error ΔD/D associated with each distance measurement is below 1 %. Thus, both excitation modes are suitable for high precision distance measurements.
3.2. Orientational measurements on silver nanorods
In the previous Section, we showed that the combination of CISM and a LPGM allows one to determine the particle distance Dij with sub-pixel precision. In contrast, orientational information can not be obtained by analyzing the patterns shown in Fig. 4 (a). Obviously, these patterns are oriented similarly and they resemble the shape of the intensity distribution of a focused LPGM (see Fig. 2 inset I (d)). However, as already demonstrated in [25] the combination of CISM and higher order laser modes permits to determine the absolute orientation of individual metallic nanorods.
However, the original combination of CISM and higher order laser modes permits to determine the orientation of individual silver nanorods. We fitted the model function described by Equation 8 to the scattering patterns shown in Fig. 4 (c). The angle ϑ (between the scanning reference system and the particle’s reference system as defined in Equations 5 and 6) is a fit parameter and a direct measure of the particle’s orientation. In Table 3, the results of the orientational measurements performed using an APDM are shown.
The results show that using an APDM, one can determine the orientation of an individual silver nanorod with a rotational error as small as 0.4 degree. As an example, for a particle having a long axis a = 100 nm, a rotation of 0.4 degree corresponds to a maximal rotational arch of about 0.8 nm. In other words, with CISM it is possible to detect a rotational arch of about 1 nm between two consecutively recorded patterns. By using conventional fluorescence microscopy techniques, these changes could never be detected.
Table 3. Orientation of the three silver nanorods imaged in Fig. 4(d) using an APDM.
3.3. Rotational resolution of CISM
Fig. 5. CISM images of the same silver nanorod excited with an APDM. The sample is rotated from picture to picture by around 10. (a)-(c): Experimental data. (d)-(f): Fitted patterns reproduced by the model function defined in Eq. 8. To guide the eye the measured angle α 0,1,2 is indicated. (g): Plot of the measured angle α versus the adjusted angle α’.
In a further experiment we demonstrate that CISM in combination with an APDM is suitable for detecting particle rotations of about one degree. The sample was mounted on a rotation stage fixed on top of the microscope objective.
After localizing an individual silver nanorod, a first scattering pattern was recorded (the overall scan area was 2×2 μm2). Afterwards, the rotation stage was rotated by one degree and a new scattering pattern was acquired. This procedure was repeated 19 times. Thus, the particle was expected to rotate through 19 degree with respect to the optical axis.
In Fig. 5 (a)-(c), three representative scattering patterns are shown: The initial pattern (a), the tenth (b) and the last one (c). The rotation α of about ten degrees between neighbored patterns can hardly be seen by eye (we help the reader drawing reference axes in Fig. 5 (a)-(f)). With the support of the data analysis algorithm, however, these and even smaller rotations can be detected and measured. Figures 5 (d)-(f) show the fitted patterns reproduced by the model function defined in Eq. 8.
In Fig. 5 (g), the measured rotations (α) are plotted versus the adjusted ones (α’) for all 20 confocal scans. The continuous line represents the best linear fit to the experimental data. The vertical error bars represent the rotational error associated with each measurement and were set to 0.4 degree (see Δϑ in Table 3). The horizontal error bars were set to 0.5 degree, i.e. one half of the rotational increment. The data presented in Fig. 5 demonstrate that the combination of CISM and an APDM allows to measure particle rotations of less than one degree.
3.4. Conclusion
We have performed topological measurements on silver nanorods excited either by a Gaussian laser beam or by higher order laser modes. We determined the distance between two particles down to 500 nm with a precision of 2.5 nm. By combining CISM and higher order laser modes, the 2D orientation of an individual nanorod was measured using one single scattering pattern. The precision associated with this measurement was found to be in the order of one degree. With the same accuracy, we followed stepwise the 19 degree rotation of an isolated silver nanorod.
Ongoing research is aimed to measure additionally the particle orientation with respect to the optical axis. Depending on the size and shape of the metallic nanoparticle as well as the excitation wavelength, the scattering patterns generated using a RPDM allow even for extracting 3D orientational information.
Since the scattering efficiency of metallic nanoparticles, is orders of magnitude higher than the scattering efficiency of intra-cellular biological objects, we believe that CISM can be used to image metallic nanorods within living cells. Using CISM for biological and biomedical applications recommends implementation in commercial confocal microscope setups. In this case, a faster detector with lower sensitivity, e. g. a photomultiplier, would be favorable.
Acknowledgments
We thank Frank Wackenhut for helping us in the confocal measurements. Financial support was given by the Research Center for Micro- and Nanochemistry and -Engineering (Universität Siegen, Germany) and the Deutsche Forschungsgemeinschaft (Me 1600/6-1/2).
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