Confocal White Light Reflection Imaging for Characterization of Nanostructures

The ability to image nanostructures with a high spatial resolution as well as spectral resolution is very important for a host of both fundamental and practical studies (Grigorenko et al., 2005; Dixon et al., 1991; Verveer et al., 2007; Yoshifumi et al., 2006; Singh et al., 2007; Patel & McGhee, 2007; Laurent et al., 2006). Recently, optical imaging and spectroscopic studies of metal nanoarrays, individual metal nanostructures, and graphene (one monolayer thick carbon atoms packed into a two-dimensional honeycomb lattice, which is the basic building block for other sp2 carbon nanomaterials.) sheet have attracted much attention (Du et al., 2008, 2010; Laurent et al., 2005, 2006; Ni et al., 2007; Wang et al., 2010). As an example, scanning near-field optical microscope (SNOM) has provided high resolution and been widely used in nanostructure study. However, collecting an image by SNOM is very time-consuming and relies heavily on the equipment as well as the skill of the operator. SNOM is also ill-suited for spectroscopic measurements due to the weak signals. Comparatively, far-field techniques are simpler and generate much stronger signals, which have been successfully used to study localized surface plasmons (LSPs) of gold nanoparticle arrays (Laurent et al., 2005, 2006). Moreover, far-field white light scanning is a simple and low cost method, which also offers multiplewavelength advantage and is suitable to study spectral properties. White light confocal scanning microscopy has also been used to characterize material morphology, refractive index profile of fibers, etc (Ribes et al., 1995; Youk & Kim, 2006), where aperture or fiber were used as confocal pinhole. The best spatial resolution for normal confocal white light scanning optical microscope (not including that from a super continuum light source (Lindfors et al., 2004)) has been improved from 1.500 μm to about 0.800 μm (Youk & Kim, 2006). However, improvement of the spatial resolution is still much desired for the study of small-scale materials.


Introduction
The ability to image nanostructures with a high spatial resolution as well as spectral resolution is very important for a host of both fundamental and practical studies (Grigorenko et al., 2005;Dixon et al., 1991;Verveer et al., 2007;Yoshifumi et al., 2006;Singh et al., 2007;Patel & McGhee, 2007;Laurent et al., 2006). Recently, optical imaging and spectroscopic studies of metal nanoarrays, individual metal nanostructures, and graphene (one monolayer thick carbon atoms packed into a two-dimensional honeycomb lattice, which is the basic building block for other sp 2 carbon nanomaterials.) sheet have attracted much attention (Du et al., 2008(Du et al., , 2010Laurent et al., 2005Laurent et al., , 2006Ni et al., 2007;Wang et al., 2010). As an example, scanning near-field optical microscope (SNOM) has p r o v i d e d h i g h r e s o l u t i o n a n d b e e n w i d e l y u s e d i n n a n o s t r u c t u r e s t u d y . H o w e v e r , collecting an image by SNOM is very time-consuming and relies heavily on the equipment as well as the skill of the operator. SNOM is also ill-suited for spectroscopic measurements due to the weak signals. Comparatively, far-field techniques are simpler and generate much stronger signals, which have been successfully used to study localized surface plasmons (LSPs) of gold nanoparticle arrays (Laurent et al., 2005(Laurent et al., , 2006. Moreover, far-field white light scanning is a simple and low cost method, which also offers multiplewavelength advantage and is suitable to study spectral properties. White light confocal scanning microscopy has also been used to characterize material morphology, refractive index profile of fibers, etc (Ribes et al., 1995;Youk & Kim, 2006), where aperture or fiber were used as confocal pinhole. The best spatial resolution for normal confocal white light scanning optical microscope (not including that from a super continuum light source (Lindfors et al., 2004)) has been improved from 1.500 µm to about 0.800 µm (Youk & Kim, 2006). However, improvement of the spatial resolution is still much desired for the study of small-scale materials.
In this chapter, a new confocal white light reflection imaging technique is proposed by combining a confocal white light scanning microscope with a spectrometer. By decreasing the diameters of the incident light beam and the collection fiber, a spatial resolution of about 0.410 µm was achieved, which doubly enhances the previously reported best spatial resolution (~0.800 µm) of white light scanning and is even higher than those of laser scanning techniques (Rembe & Dräbenstedt, 2006;Gütay and Bauer, 2007). This system can provide both sample images extracted from reflection within a selective range of wavelength and their white light reflection spectra at each point. The simplicity in carrying out experiments makes this technique attractive, easy and fast. Metal nanoarrays, individual metal nanostructures (including single, dimer gold nanospheres and silver nanowires) and graphene sheet were characterized by the proposed system, demonstrating the strong capabilities in resolving nanometre structures, distinguishing different LSP resonant energies between different individual metal nanostructures and determining the graphene number layers, even the refractive index information of graphene.

Instrumentation and experiment
The schematic diagram of the experimental setup was shown in Figure 1. Light from a normal white light source (Xenon lamp) was polarized after passing through a polarizer, which serves as the incident light and was focused onto the sample through a holographic beam splitter and an OLYMPUS microscope objective lens (100X, NA=0.95). A tuneable aperture with a minimum diameter of 200 µm was introduced in the incident light path to tune the spatial resolution of the optical system. Different nanostructure samples were placed on a translation stage which provides coarse movement along the x and y axes, while the fine movement is offered by a piezostage with 100 m travel distance along the x and y directions and 20 m along the z direction. The piezostage also works as a mapping stage.  (Du et al., 2008).
The reflected light from the sample was collected by the same lens and directed to a spectrometer through a fiber. Fibers with various core diameters of 100, 50 and 25 µm were www.intechopen.com adopted in this work. The collection fiber also works as a pinhole, which is confocal with the illuminated spot on the sample. The reflected light was directed to a 150 grooves/mm grating and detected by a TE-cooled charge-coupled device (CCD). Typical integration time for imaging was 100 ms/pixel. The stage movement and data acquisition were controlled using ScanCtrl Spectroscopy Plus software from WITec GmbH, Germany. To determine the spatial resolution of the confocal reflection imaging system, we referred to the scanning knife edge method (Veshapidze et al., 2006) by using a two-layer graphene sheet on SiO 2 /Si substrate as the edge (Ni et al., 2007). Thickness of a single layer graphene sheet is ~0.34 nm. The graphene sample was prepared by micromechanical cleavage on a silicon wafer with a 300 nm of SiO 2 capping layer (Novoselov et al., 2004). The optical microscope ( Figure  2a) was used to locate the graphene sheet, which thickness was further confirmed by Raman spectroscopy. Figure 2b gives the Raman spectra of the graphene sample while its Raman image plotted by the intensity of G band was shown as Figure 2c. Figure 2d plots the cross section of the Raman image from the dashed line in Figure 2c, showing distinct difference in the Raman G-band intensity from the different thicknesses of graphene sample. Hence, the 2layer graphene sheet can be identified easily, which provides an ideal edge sample because it has strong enough Raman signal with sharp edge, and most importantly it is thin such that there is no ambiguity in determining the spatial resolution caused by the edge effect.
The scanning confocal white light reflection spectrum by using 25 µm core diameter collection fiber and 200 µm diameter aperture was shown in Figure 3, which was fitted quite well with the following equation: where P is the total power for the incident white light beam, 0 x is the centre of the incident light beam and w is the desired 1/e 2 half width. Thus the full width at half maximum (FWHM) of the incident beam (spot size) can be obtained from 2ln2w , which was defined as the spatial resolution. Fig. 3. Typical intensity versus graphene edge position data with the best fitting to Eq. (1) superimposed to determine the white light spot size. The inset gives the spatial resolution fitting results along with the fitting errors by using different aperture and collection fiber sizes.
Through tuning the collection fiber core diameter (D1) and the aperture diameter (D2), different spatial resolutions were obtained from Eq. (1) as shown in the inset table of Figure 3. It reveals the best spatial resolution about 0.410 µm, obtained using the 25 µm core diameter collection fiber and setting the aperture diameter to 200 µm. This doubles the previously reported best spatial resolution (~0.800 µm) for white light scanning (Youk and Kim, 2006) and is even better than those of laser scanning techniques (Rembe & Dräbenstedt, 2006;Gütay and Bauer, 2007). It also indicates that the aperture size, and especially the diameter of collection pinhole (the diameter of the collection fiber in our case), plays a significant role in improving the system resolution. All the white light reflection images shown below were obtained by setting D1 and D2 to 200 µm and 25 µm, respectively, unless stated otherwise. Scanning electron microscope (SEM) images of samples were taken with field emission SEM (JEOL JSM-6700F).

Confocal white light reflection (CWLR) imaging for characterization of metal nanostructures
Following, we will discuss our proposed applications in (1) resolving gold nanoarrys, (2) distinguish the resonance energy difference between the isolated single and dimer gold nanoparticles' LSP and revealing the strength of the near-field coupling between individual gold nanospheres and their supporting SiO 2 /Si substrate, and (3) correlating the polarization dependent CWLR images of single silver nanowires with the nanowire polarization dependent excitation of surface plasmon (SP).

CWLR imaging for characterization of gold nanoarrays
Gold nanoparticle arrays were fabricated by nanosphere lithography (Jensen et al., 1999) on cover glass substrates. Polystyrene (PS) microspheres with diameter 1 µm and 0.500 µm were used as masks, which will self-assemble into monolayer spheres on substrates. Gold thin film with thickness of about 0.050 µm was deposited by DC coater sputtering, and then the spheres were lifted off. Fig. 4. The CWLR image at the wavelength of 0.480-0.520 µm for gold nanoarrays on cover glass which were fabricated by using 0.500 µm diameter PS as the lithographic mask. Figure 4 gave a typical 5.0 x 5.0 µm 2 CWLR image for the obtained gold nanoarrays on cover glass fabricated by using 0.500 µm diameter PS as a lithographic mask. The image was extracted from the white light reflection intensity between the wavelength of 0.480-0.520 µm from the samples. Owing to smaller reflection of the cover glass substrate than that of gold particles, hexagonal bright rings in the image of Figure 4 correspond to gold nanoparticles while black areas correspond to the cover glass. The periodicity for the gold particle arrays, which is 0.500 µm, can be clearly resolved, demonstrating the high resolution of our technique. However, the gold particle size and centre-to-centre distance between two nearest gold particles is measured to be about 0.150 µm and 0.100 µm, respectively, by SEM images (not shown), which are out of the range of the system's spatial resolution. This can explain why the image for six gold particles in one hexagonal cell merges to form a hexagonal ring. The dots in Figure 4 work just as a guide for the eye labelling where the particle is. Meanwhile, different defects in the sample as indicated by the rectangular circles in Figure 4 were imaged as well, which reveals that the present imaging method can also be used to test the sample quality, similar to reports elsewhere (Ormonde et al., 2004), but here with much higher spatial resolution.
For comparison, in Figure 5, we have also given the CWLR images for gold nanoarrays on cover glass fabricated by using 1 µm diameter PS as a lithographic mask. Similar to Figure 4, owing to the smaller reflection of the substrate than metal particles, hexagonal bright dots in images Figures 5a to 5f correspond to gold particles while black areas correspond to the cover glass. From the images, we found that the image at 0.480-0.520 µm gives us the best resolution. All the images in this chapter were selected by this way. The gold particle size and centre-to-centre distance between two nearest gold particles is measured to be about 0.300 µnm and 0.200 µm, respectively, by SEM images (not shown). From images in Figures 5a to 5(f), the six gold nanoparticles in one hexagon cell can be resolved clearly as labelled by pink dots in Figure 5a for guiding. The size of these six nanoparticles in CWLR images is spatial resolution determined, which is ~0.410 µm. From these images, it is very easy to obtain the white light reflection spectra for the substrate and gold particles, respectively, as shown in Figure 5g. The contrast spectra are defined as where sample I and substrate I refer to the white light reflection intensity of the sample and the substrate, respectively. The result was shown as Figure 5h, which confirms that gold particles always have larger reflection than that of the substrate, as well as the role of SP in reflection, which is discussed in detail in the next section. Fig. 5. The CWLR images (a-f) at different wavelength ranges for gold nanoarrays on cover glass fabricated by using 1 µm diameter PS as the lithographic mask while (g) and (h) are the reflected white light spectra and reflection contrast between the gold particle and substrate, respectively. Wavelength ranges for images (a) to (f) correspond to 0.440-0.480 µm, 0.480-0.520 µm, 0.520-0.560 µm, 0.560-0.600 µm, 0.600-0.640 µm and 0.640-0.680 µm, respectively.

CWLR imaging for characterization of individual gold nanospheres
Commercial gold nanospheres with a diameter of 50  5 nm (Corpuscular Inc) deposited on 200 nm silicon dioxide (SiO 2 ) films were chosen for CWLR imaging as well. Their confocal white light reflection images were constructed by extracting the light intensity from the corresponding reflection spectra for a selected wavelength range, too. The image at the wavelength of 510-550 nm was shown in Figure 6b as one example. As can be seen from the SEM image shown in Figure 6a, it consists of three isolated single spheres and one dimer where the two spheres are almost in contact with each other. The four dark spots in Figure  6b represent the images of the gold nanospheres, which correspond well to the SEM image. The size of the dark spots is about 410 nm, determined by the spatial resolution of the imaging system. Considering the resolution limitation, it is reasonable that the white light reflection images can not distinguish between single sphere and dimer spheres. For comparison, Figure 6d presented the CWLR imaging results for the spheres by setting D2 to 100 µm while keeping other experimental conditions the same. It can be seen that the images from the spheres severely overlap, confirming the higher spatial resolution by using a 25 µm core diameter collection fiber again.
www.intechopen.com (c) The contrast spectra for single (black lines) and dimer spheres for incident light parallel (solid lines) and perpendicular (dotted lines) to the dimer axis. (Du et al., 2008). Figure 6c plotted the contrast spectra for the single and dimer gold nanospheres after locating their positions. Two contrast dips (labelled 1 and 2, respectively) were observed from Figure 6. It is noticed that the position of dip 2 of isolated single spheres (at about 525 nm) coincides with that of the LSP of gold spheres with diameter 50 nm (Dijk et al., 2005). However, the same dip shows red shifts to 548 nm and 542 nm for the incident polarization parallel and perpendicular to the dimer axis, respectively. This results from the coupling effect between the two nanospheres of the dimer (Moores & Goettmann, 2006). The larger red shift for the parallel polarization than that of the perpendicular case is understandable considering the stronger coupling of the dimer for parallel polarization. Figure 6c also reveals a weak dip 1 for the single and dimer located at about 470 nm, which originates from the multi-polar SP excitation of the gold nanospheres. Firstly, SP excitation at about 470 nm has been observed for gold nanospheres with diameters close to 40 nm, although it was ascribed to false spectral lines that arose from using a 488 nm argon laser (Benrezzak et al., 2001). Secondly, similar multi-polar SP excitation has been reported for other isolated metal nanoparticles (Dijk et al., 2005). Moreover, the excitation of LSPs leads to the enhancement of the absorption of the nanospheres, which consequently has the effect of reducing the reflection intensity (Kawata, 2001), making the nanospheres dark in the corresponding images in Figure 6b. The different dip 2 position for the single and dimer spheres also reflects their different dipolar LSP resonant energies, further implying that the CWLR imaging method is capable of resolving the LSP energies for individual noble metal nanoparticles.
Then, to determine the decay length of the electromagnetic (EM) coupling between individual gold nanopspheres and its supporting substrate, different thicknesses (d) SiO 2 film on Si were obtained by annealing single-crystalline Si (d < 20 nm) in air or by RF sputtering SiO 2 (d > 20 nm) to serve as the substrate.    Figure 8c. The distance between different individual nanospheres chosen for study herein was selected purposely to be larger than 1m. Thus the EM coupling between them can be neglected. For convenience, herein the contrast is defined by the following Eq. (3), and hence their contrast images and the CWLR contrast spectra can be obtained.
Where AuNSP I and sub I refer to the CWLR intensity from the positions of the Au NP and the substrate, respectively. Adopting Eq. (3), the CWLR contrast spectra for individual gold nanoparticles were obtained. A typical CWLR contrast spectra of an individual Au nanosphere on SiO 2 /Si substrates was presented as Figure 8a along with its different CWLR www.intechopen.com images at different wavelength regions. The different wavelength regions constructing these contrast images were labelled by the rectangular bars on the left contrast spectra of Figure. 8a. Figure 8a presents an obvious peak at ~530 nm, which originates from the excitation of dipolar LSPs with the peak wavelengths corresponding to the dipolar LSP wavelengths (Du et al., 2008;Okamoto & Yamaguchi, 2003;Abe & Kajikawa, 2006;Pinchuk et al., 2004;Knight et al., 2009). The excitation of LSP enhances the light absorption by the nanosphere and reduces its reflection intensity (Kawata, 2001), then further leads to its higher contrast intensity relative to the substrate in the CWLR contrast images (Figure. 8b). As can be seen, with the selected wavelength region closer to the contrast peak position, the larger image contrast between the Au nanosphere and the substrate is obtained while the maximum contrast is reached at the LSP wavelength. Meanwhile, from the unequivocal one-to-one correspondence between the nanosphere in the contrast images ( Figure. 8b) and its SEM image ( Figure. 8c), we can locate the individual nanosphere we concern.
To explore the near-field coupling between individual gold nanospheres and their supporting substrate further, we have measured the contrast spectra between individual Au nanospheres on SiO2/Si substrates with different thicknesses of SiO 2 on Si substrate. Several typical spectra were presented in Figure 9, in which the dipolar LSP peaks were guided by the dashed line. The second peak at shorter wavelength for cases of bare Si substrate and d = 6 nm corresponds to the multi-polar LSP excitation (Du et al., 2008). In what follows, we will mainly discuss the dipolar LSP (labelled as LSP for short in the following) wavelength (  ) behaviour as a function of the spacer SiO 2 film thickness d. Fig. 9. Comparative CWLR contrast spectra between individual Au nanospheres on SiO 2 /Si substrates (with SiO 2 film d nm) and on Si substrate. (Du et al., 2010). Figure 9 reveals that the LSP wavelengths of all the samples show an obvious red-shift compared to the LSP resonant wavelength for an isolated Au nanosphere with diameter about 50 nm in air, which is at about 520 nm (Noguez, 2007). This originates from the different dielectric function of the substrate from that of air and agrees well with the literature reports (Okamoto & Yamaguchi, 2003;Abe & Kajikawa, 2006;Pinchuk et al., 2004). Moreover, the dashed line in Figure 9 demonstrates that the LSP wavelength blue-shifts with d increasing. To see this more clearly, we have plotted the function of the resonant wavelength of these LSP modes versus d in Figure 10. The experimental data of  vs. d is noted to can be fitted with a single exponential decay function (the solid line) quite well. All these reflect the near-field EM interaction between the nanosphere and its supporting www.intechopen.com substrate, which dominates the corresponding LSP wavelength shift (Jain et al., 2007;Biring et al., 2008). Accordingly, the near-field EM coupling strength between them determines the magnitude of the dipolar LSP wavelength shift ( 0     ) compared to the LSP wavelength (  ) of the isolated nanosphere case. By bringing a metal nanoparticle into the vicinity of a flat substrate, nonhomogeneous optical response due to the polarizability of the substrate material is expected. Generally, with an external EM field, a charge polarization on the NP can be induced, which further causes a charge distribution on the substrate. Under the quasi-static approximation, this charge distribution can be seen as the image charge distribution (Okamoto & Yamaguchi, 2006;Noguez, 2007) of the nanoparticle and it can in turn affect the local EM field around the nanoparticle, and further their optical responses. Adopting the method proposed elsewhere (Okamoto & Yamaguchi, 2006;Wind et al., 1987), the extinction spectra of the concerned nanospheres were calculated by including both the dipole and higher multiple image-charge effects along with the Fresnel reflection effect at the nanosphere-substrate interface. The corresponding obtained function of the LSP wavelength () versus the spacer thickness (d) was plotted as the dashed line in Figure 10 as well for comparison. The calculation qualitatively verifies the decrease behaviour of the experimental data of versus d though it predicts a faster decay rate than the experimental results.
To quantify the near-field EM coupling strength between the individual nanosphere and its supporting substrate, the normalized LSP wavelength shift ( 0 /    ) was calculated as well by the quasi-static theory and for the experimental data. Experimentally,  0 is obtained by assuming that it equals to the LSP wavelength of the nanosphere on very thick SiO 2 film (take it as 200 nm). Through a simple linear transformation, both the experimental and theoretical data of versus d can be transferred into versus d/R. The obtained results were scaled according to the right y-axis (corresponds to the upper x-axis) in Figure 10. , the influence of the image-charges owing to the substrate presence is ignorable and the LSP wavelength approaches to the limit of the individual nanosphere in the background. Meanwhile, the faster decay rate of the shift predicted by the quasi-static theory is resulted from the limitation of the theoretical model, which ignores the retardation effect while such effect is more pronounced for larger nanoparticles (Okamoto & Yamaguchi, 2003;Noguez, 2007). The solid line in the right y-axis of Figure 10 presents the single exponential decay fitting by Eq. (4) to the experimental data with a, t and y 0 as the fitting parameters. It reveals a decay length t about 0.30 in units of d/R and the fitting goodness equals to 0.97. The fitting results are interestingly noted to qualitatively agree with the 'plasmon ruler' scaling theory for the near-field EM coupling between two component noble metal nanoparticles of a dimer (Jain et al., 2007). It points out that the decay length is about 0.20 in units of the 'Gap/Diameter' regardless of the nature of the component metal nanoparticles of the dimer (Jain et al., 2007). The similarity of the decay length in magnitude is owing to that the image-charges induced in the substrate can be just replaced by the actual charges induced in the other particle for the dimeric nanoparticle's case. The deviation between their decay lengths is understandable considering the different polarizabilities between the dimer and our case. Thus, the near-field coupling strength between the individual Au nanosphere and the Si substrate is revealed to exponentially decrease with the spacer (SiO 2 film) thickness and the decay length is about 0.3 in units of d/R.

CWLR imaging for characterization of individual silver nanowires
Silver nanowire samples with a diameter about 100 nm were fabricated by a simple hydrothermal method (Wang et al., 2005) and deposited onto silicon for CWLR imaging. Two typical CWLR images of the silver nanowire were presented as Figures 11a and 11b, which clearly exhibits polarization dependent. By rotating 90 degree of the incident polarization, their contrast reverses from the comparison between Figures 11a and 11b. Even for the same bent nanowire, the different parts exhibits different contrast compared to the substrate. Owing to the larger reflectivity of silver than that of the substrate silicon, it is expected that the nanowires are brighter than the substrate under CWLR imaging system. However, this contradicts with the results of Figure 11, revealing that other factors besides material reflectivity contribute to the observed CWLR images.
It is known that the excitation of SPs of sliver nanowires is anisotropic (Schider et al., 2003), which is sensitive to the polarization direction of the incident light. This can account for the polarization dependence of the reflection images of Figure. 11, which also contribute to the different contrast for different parts of the same bent nanowire as well since for different parts of the same nanowire, the only difference lies in their different orientation relative to the incident light polarization direction. As the images shown in Figures 11a and 11b were extracted from the reflections in the range of 600 -640 nm, it is overlapped with one of the SP mode (500 -700 nm) (Kim et al., 2003;Mohanty et al., 2007) of the Ag nanowire, which www.intechopen.com experiences preferred excitation when the polarization of the incident light is parallel to the nanowire. Thus, this SP mode along the different material reflectivity contributes to the obtained polarization dependent CWLR images. It also demonstrates that the developed CWLR imaging system is able to correlate the polarization dependent CWLR images of single silver nanowires with the nanowire polarization dependent excitation of SP.

CWLR imaging for characterization of graphene
We also note that the proposed CWLR system is not limited to characterize metal nanostructures. It can also be extended to other samples, such as graphene sheet. In this part, we will show how the system was used to determine the number of graphene layers and to extract the corresponding refractive index.
The graphene's visibility strongly varies from one laboratory to another and it relies on experience of the observer though one can observe different colours/contrasts for graphene sheets of different thickness using the optical image with "naked eyes". Taking advantage of contrast spectra and image, this can be made quantitative and accurate. By combing Raman spectroscopy and optical images, graphene sheets with different layer numbers were first obtained as shown in Figure 12. Then, their contrast spectra were measured and plotted in Figure 12. For consistence with reference (Ni et al., 2007), the contrast spectra C( ) were obtained by using C( )= (R0( )-R( ))/ R0( ), where R0( ) is the reflection spectrum from the SiO 2 /Si substrate while R( ) is the reflection spectrum from graphene sheet. As revealed in Figure 12, the contrast spectrum of single layer graphene has a peak at about 550 nm, which makes the single layer graphene visible and is in green-orange range. Meanwhile, the peak position is almost unchanged with increasing number of layers up to ten. The contrast value for single layer graphene is about 0.09+0.005 and it increases with the number of layers, for example, 0.175+0.005, 0.255+0.010, and 0.330+0.015 for two, three, and four layers, respectively. For graphene of around ten layers, the contrast saturates and the contrast peak shifts towards red (samples a and b). For samples with larger number of layers (c to f), negative contrast occurs. This can easily be understood that these samples are so thick that the reflections from their surface become more intense than that from the substrate, resulting in negative value contrast.
Hence, different layer graphene gets different contrast value, which provides a standard for determining the number of layers for graphene. This can also be understood in terms of the Fig. 12. The contrast spectra of graphene sheets with different thicknesses, together with the optical image of all the samples. Besides the samples with 1, 2, 3, 4, 7 and 9 layers, samples a, b, c, d, e and f are more than ten layers and the thickness increases from a to f. The arrows in the graph show the trend of curves in terms of the thicknesses of graphene sheets. (Ni et al., 2007).
Fresnel reflection theory. Consider the incident light from air (n 0 = 1) onto a graphene, SiO 2 , and Si tri-layer system. The reflected light intensity from the tri-layer system can then be described by (Blake et al., 2007;Anders, 1967):  (Kelly, 1981, Dresselhaus, 1996. The refractive index of graphene is used as a fitting parameter. The thickness of SiO 2 , d 2 , is 285 nm, with a maximum 5% error. The refractive index of SiO 2 , n 2 , is wavelength dependent (Palik, 1991). The Si substrate is considered as semi-infinite and the refractive index of Si, n 3 , is also wavelength dependent (Palik, 1991). The reflection from SiO 2 background, R0(λ), was calculated by setting n 1 = n 0 = 1, and d 1 =0.
www.intechopen.com The contrast simulated by using both n G (blue triangles) and n z (red circles), the fitting curve for the simulations (blue and red lines), and our experiment data (black thick lines), respectively, for one to ten layers of graphene. (Ni et al., 2007).  (c) The cross section of contrast image, which corresponds to the dash lines. (Ni et al., 2007).
The optimized simulation result is shown in Figure 13a reveals a refractive index of single layer graphene n z = 2.0-1.1i, whereas the simulation result using the bulk graphite value of n G (2.6-1.3i) shows large deviation from our experimental data. Using the optimized refractive index n z , we have calculated the contrast of one to ten layers' graphene also as shown in Figure 13b, which agree well with the experimental data with the discrepancy being only 2%. By using this technique, the thickness of unknown graphene sheet can be determined directly by comparing the contrast value with the standard values shown in Figure 13b. Alternatively, it can be obtained using the following equation: www.intechopen.com C = 0.0046+0.0925N-0.00255N 2 (9) where N (≤10) is the number of layers of graphene.
In order to demonstrate the effectiveness of the contrast spectra in graphene thickness determination, we carried out the CWLR imaging, too. As shown in Figure 14a, distinct contrast for different thicknesses of graphene can be observed from the image. It is worth noting that the contrast image measurement can be done in a few minutes. Figure 14b and 14c show contrast along the two dash lines on the image. The contrast value for each thickness agrees well with those shown in Figure 13. Using Eq. (9), the N values along the two dash lines are calculated, where the N along the blue line is: 0.99, 1.93, and 3.83; and along the red line is: 0.98, 2.89 and 3.94. Again our results show excellent agreement.
Accordingly, by the proposed CWLR system, both the layer number of graphene and the refractive index of single layer graphene can be achieved. It does not need a single layer graphene as reference as that in Raman. It is also noted that the proposed system can be used to get information about the optical conductivity of some bilayer grapene sheet (Wang et al., 2010), which is not shown here.

Conclusion
In this chapter, we have proposed a far-field CWLR imaging system by combing a small aperture and a small collection fibre core diameter, which is fast, non-destructive and user friendly. It is demonstrated to provide a high spatial resolution about 410 nm, which is capable of resolve two nearest gold nanoparticles with the size and centre-to-centre distance in-between about 300 nm and 200 nm, respectively. Individual single, dimer gold nanospheres, silver nanowires, and graphene sheet were characterized by the imaging system as well. Apart from the dipolar LSP, excitation of multi-polar LSP of individual gold nanospheres was revealed. Compared to the resonance energy of single gold nanosphere, the resonance energy of the dimer is red-shifted due to the EM coupling between the two component nanospheres of the dimer. The near-field EM coupling effect between individual Au nanospheres and the supporting SiO 2 /Si substrate was also studied by the CWLR imaging method, which reveals a decay length of 0.30 in units of / dR for the coupling strength, qualitatively agreeing well with the 'plasmon ruler' scaling theory. The anisotropic excitation of LSP of single silver nanowire was revealed to get contribution to the polarization dependent images besides their essential reflectivity difference from that of the substrate. It is also demonstrated that the CWLR spectra method provides a standard to identify the thickness of graphene sheet on Si substrate with ~300 nm SiO 2 capping layer, from which the refractive index (n z = 2.0-1.1i) of graphene below ten layers can also be easily determined. As the CWLR imaging can be preformed at different wavelength, we also expect its other interesting applications such as biomaterial mapping and plasmonic studies in the future.