Abstract:
Provided are a system and a method for detecting a number of layers of few-layer graphene employing multispectral image reproduction process to provide rapid detection of numbers of layers of few-layer graphenes on transparent or non-transparent substrates. The application of the system and method in relevant industries expedites validation and/or verification of the number of layers of an FLG product and improves the quality control efficiency thereof.

Description:
BACKGROUND OF THE INVENTION 
       [0001]    1. Field of the Invention 
         [0002]    The present invention relates to a system for detecting the number of layers of a few-layer graphene, especially to a system with an image analysis and processing means. The present invention also relates to a method for detecting the number of layers of a few-layer graphene, especially to a method using an image analysis and processing means. 
         [0003]    2. Description of the Prior Art 
         [0004]    The visualization of graphene is regarded as an issue of increasing importance to the developing graphite technology, especially regarding confirming the number (“N”) of layers of a few-layer graphene (hereinafter “FLG”). Conventional techniques for distinguishing number of layers of FLG include: Raman spectroscopy, transmission spectroscopy, atomic force microscopy (hereinafter “AFM”) and optical microscopy. 
       A. Raman Spectroscopy and Transmission Spectroscopy 
       [0005]    As described in reference 17, Raman spectroscopy allows detection of number of layers of an FLG by changes in G-band Raman intensity and differences in 2D-band. 
         [0006]    Reference 19 further describes an application of Raman spectroscopy on a silica/silicon (SiO 2 /Si) substrate for counting the number of atomic layers of an FLG. The counting via Raman spectroscopy of the number of atomic layers of the FLG on a silica/silicon substrate is accomplished by examining the sum of intensities of phonon peaks for graphene and silicon so as to obtain information for the number of the layers of the FLG, even if the number of layers is larger than four (N&gt;4). 
         [0007]    It is also revealed in reference 18 that the transmittance of a single-layer graphene is 97.7%, which indicates that information for the number of the layers of an FLG may be obtained by examining the transmittance of the FLG. 
         [0008]    Validation of the information obtained with the aforementioned techniques based on Raman spectroscopy or transmission spectroscopy, however, requires verifications that are significantly time-consuming and labor-intensive. For example, it requires three hours to verify and accomplish a task for examining an FLG having an area of 50 μm 2 . In addition, the technique based on Raman spectroscopy bears certain vague zones within which the number of layers of an FLG cannot be determined. 
       B. Atomic Force Microscopy 
       [0009]    In accordance with reference 19, the thickness of a single-layer graphene is 0.34 nm. A technique based on AFM detects the roughness of the surface of an FLG and thereby obtains information of the number of layers of the FLG. It is to be noted that such a technique based on AFM also requires a significant amount of time to complete a measurement. 
       C. Optical Microscopy 
       [0010]    A technique based on optical microscopy, such as one described in reference 14, may be employed to more thoroughly analyze the color of an FLG on a dielectric layer or substrate made of silica, silicon, silicon nitride or aluminum oxide, so as to distinguish different thin-film-optical characteristics of FLGs having different numbers of layers. 
         [0011]    The technique reference 12 relates to a method for examining number of layers of an FLG on specific substrates via microscopic imaging skills. Reference 12 has found that it is possible and feasible to detect the number of layers of an FLG on a 300 nm layer of silicon, whereby the silicon layer is formed on a silica substrate. Furthermore, an FLG on a 100 nm layer of silicon is most visualizable in terms of determining the number of layers of the FLG. Reference 12 also indicates that a silica/silicon substrate with a 285 nm oxide layer significantly increases the visualizability of an FLG thereon, the rationale of which has been verified by color difference calculations. 
         [0012]    Reference 13 has discussed a multispectral optical microscopic method for distinguishing and measuring effective optical characteristics of a graphite of nanometer-level thickness as a basal material. Such basal material is formed on a silicon substrate on a thin insulation layer. Selecting suitable optical characteristics and a dielectric layer of proper thickness allows revealing of the contrast of an FLG and the substrate. The effective refractive index and optical absorption coefficient of a graphene oxide, thermally reduced graphene oxide as well as FLG are obtained by comparing the estimated and measured differences thereof. 
         [0013]    Reference 15 has demonstrated that the measurement for number of layers of FLGs on different substrates made of silicon carbide, silica/silicon, quartz, silicon and glass are subject to the different lattice constants and the electronic structures. Reference 15 has also indicated that an FLG on a substrate of quartz or silica/silicon demonstrates higher contrast of color difference. 
         [0014]    Reference 14 has disclosed a conventional technology using light sources of different wavelength ranges for color difference simulation of FLGs on silica/silicon substrate, silicon nitride substrate and aluminum oxide substrate. The conventional technology of reference 14 has taught that the silicon nitride substrate is a suitable substrate for an FLG to be identified, while the silica/silicon substrate and the aluminum oxide substrate are suitable for graphene thin films of average and high number of layers. 
         [0015]    Reference 16 is related to a color difference analyzing method performed on FLGs deposited on silica/silicon and silica/air substrates. Reference 16 has described the colors of FLGs and graphene-oxides deposited on different dielectric layers. Reference 16 has also presented analyses of thicknesses of materials, types of dielectric layers, and existence of back silicon substrates. It has been indicated that the graphene-oxide layer periodically alters its color with the increase of the thickness of the material. The graphene layer on the same substrate, however, has demonstrated saturated and constant color without periodical alternation. 
         [0016]    As the foregoing literatures have suggested, conventional technologies may employ optical microscopy, especially multispectral optical microscopy, to expedite imaging so as to provide a rapid and intuitive method for detecting number of layers of FLG. The conventional technologies employing optical microscopy, however, are not applicable without substrates of specific thicknesses. It is also to be noted that, these conventional technologies are not feasible with transparent substrates. 
         [0017]    Furthermore, conventional technologies that employ optical microscopy to examine number of layers of FLGs are indeed capable of visually recognizing the number of layers through microscopic means. For example, the number of layers of an FLG deposited on a 300-nm silica dielectric layer of a silicon substrate may be detected using the aforementioned conventional means. In order to make the conventional optical microscopic technologies feasible, it is, however, necessary to make the FLG with a method having increased steps and manufacture processes. 
         [0018]    The conventional optical microscopic technologies fail to visualize distinguishable contrast for examining numbers of layers of FLGs. For example, the contrast obtainable when observing a 5-layer FLG printed on a glass substrate with conventional optical microscopic means is barely visible for examining the number of layers of an FLG. 
         [0019]    To overcome the shortcomings, the present invention provides a system and a method for the detection of the number of graphene layers to mitigate or obviate the aforementioned problems, such as the time-consuming and labor-intensive verifications for the techniques based on Raman spectroscopy or transmission spectroscopy, the expensive instruments and time-consuming measurements of the technique based on AFM, and the restrictions on substrate thickness and transparency and the lack of visible contrast of the conventional technologies based on optical microscopy. 
       SUMMARY OF THE INVENTION 
       [0020]    The main objective of the present invention is to provide a system for the detection of the number of graphene layers. Another aspect of the present invention is to provide a method for the detection of the number of graphene layers. 
         [0021]    The system in accordance with the present invention has a visualization module, an acquisition module and a reproduction module. The visualization module holds and illuminates an FLG sample. The acquisition module performs an optical observation on the FLG sample. The reproduction module is operably connected to the acquisition module to provide information of detection of a number of layers of the FLG for reproducing a multispectral color image. 
         [0022]    The method in accordance with the present invention has a spectral database construction process and a multispectral image reproduction process. 
         [0023]    The spectral database construction process has a spectra-analyzing step, a principal component analysis (hereinafter “PCA”) step, and a database constructing step. In the spectra-analyzing step, spectral analyses are performed for FLGs of different numbers of layers on different substrates, based on which resulting information is obtained. In the PCA step, PCA is performed with the resulting information to obtain a distinguishing formula. In the database constructing step, a database is built based on the resulting information of the spectral analyses and the distinguishing formula to present a relationship between a number of layers of an FLG and the distinguishing formula. 
         [0024]    The multispectral image reproduction process has an acquisition step, an analyzing step, a categorizing step, an enhancing step, a reproducing step, and an examining step. In the acquisition step, an image of an FLG is acquired. In the analyzing step, the image is analyzed to obtain a transmission spectrum of the FLG. In the categorizing step, the transmission spectrum is categorized according to the aforementioned database constructed via spectral analysis and PCA so as to obtain a categorization result. In the enhancing step, a simulation spectrum is determined based on the categorization result. In the reproducing step, a color image is reproduced with the simulation spectrum. In the examining step, a number of layers of the FLG is determined by examining the color image. 
         [0025]    The system and the method in accordance with the present invention employ multispectral image reproduction process implemented with means such as optical microscopes and charge-coupled devices (hereinafter “CCD”) to provide rapid detection of numbers of layers of FLGs on transparent or non-transparent substrates. The application of the present invention in relevant industries expedites validation and/or verification of the number of layers of an FLG product and improves the quality control efficiency thereof. 
         [0026]    The present invention utilizes colorimetric means such as multispectral imaging based on spectra demonstrated owing to inter-layer destructive interference or inter-layer constructive interference. With PCA and quantification of spectral information, optical microscopic images of FLGs having different numbers of layers may be categorized into groups defined by the proportionality coefficient of a first PCA and a second PCA, so as to provide a system and a method for analyzing numbers of layers of FLGs. 
         [0027]    Specifically, the present invention employs multispectral imaging techniques combining PCA for threshold determination and obtains reproduced images of FLGs having different numbers of layers, in order to rapidly detect a number of layers of an FLG. 
         [0028]    As a result, the present invention mitigates or obviates the problems of the prior art and has overcome the restrictions of substrate thickness and structure. The present invention is capable of readily and correctively detecting numbers of layers of FLGs. Furthermore, the present invention employs multispectral optical microscopy, PCA, color corresponding conversion and linear regression to reproduce color for an FLG image without adjusting color alternation owing to illumination of microscopic imaging means. The straightforward and simple algorithms and the structure of the apparatuses for the method and system in accordance with the present invention have effectively implemented detection and analysis for FLGs, thereby saving the time and intense labor for the conventional technologies without relying on time-consuming measurements using expensive instruments such as AFM. In other words, the present invention indeed provides an effective, low-cost and time-saving technique to conveniently detect numbers of layers of FLGs. 
         [0029]    Other objectives, advantages and novel features of the invention will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0030]      FIG. 1  is a schematic diagram of a system in accordance with the present invention; 
           [0031]      FIG. 2  is another schematic diagram of the system in  FIG. 1 ; 
           [0032]      FIG. 3  is a grayscale image of an FLG on a glass substrate obtained using Raman spectroscopy analysis, whereby grayscales corresponding to numbers of layers of the FLG are marked with numerical symbols 0 to 5. 
           [0033]      FIG. 4  is a grayscale image of the FLG  FIG. 3  obtained using the system and method in accordance with the present invention, whereby grayscales corresponding to numbers of layers of the FLG are marked with numerical symbols 0 to 5. 
           [0034]      FIG. 5  is an image of a 3-layer FLG on a silica/silicon substrate; 
           [0035]      FIG. 6  is a top view of a 5-layer FLG on a glass substrate; 
           [0036]      FIG. 7  is a schematic diagram of the FLG in  FIG. 6 ; 
           [0037]      FIG. 8  is a schematic top view of the FLG in  FIG. 6 ; 
           [0038]      FIG. 9  is an image of the FLG in  FIG. 6 , whereby ribbon regions of different numbers of layers are marked with dash lines and symbols 1 LG to 5 LG (1-layer graphene to 5-layer graphene.) One square area within the 5 LG ribbon region is marked out, and so are four square areas respectively covering two ribbon regions of different layers; 
           [0039]      FIG. 10  is an image of the square area marked out in  FIG. 9  covering the 5 LG and 4 LG ribbons; 
           [0040]      FIG. 11  is an image of the square area marked out in  FIG. 9  covering the 4 LG and 3 LG ribbons; 
           [0041]      FIG. 12  is an image of the square area marked out in  FIG. 9  covering the 3 LG and 2 LG ribbons; 
           [0042]      FIG. 13  is an image of the square area marked out in  FIG. 9  covering the 2 LG and 1 LG ribbons; 
           [0043]      FIG. 14  is an image of the square area marked out in  FIG. 9  within the 5 LG ribbon; 
           [0044]      FIG. 15  is a flowchart of the process for determining the matrix of transformation between the information obtained by a spectrometer and the information obtained by an image-acquiring device; 
           [0045]      FIG. 16  is a flowchart of the process for obtaining a simulation spectrum; 
           [0046]      FIG. 17  is a spectral PCA chart for a 3-layer FLG on a silica/silicon substrate; 
           [0047]      FIG. 18  is a spectral PCA chart for a 5-layer FLG on a glass substrate; 
           [0048]      FIG. 19  is a Raman spectroscopic analysis chart for the FLG in  FIG. 17 ; 
           [0049]      FIG. 20  is a Raman spectroscopic analysis chart for the FLG in  FIG. 18 ; 
           [0050]      FIG. 21  is a chart of 2D-band and G-band ratio of Raman spectroscopic analysis for the FLG in  FIG. 18 ; 
           [0051]      FIG. 22  is a chart of layer-wise 2D-band and G-band ratio of Raman spectroscopic analysis for the FLG in  FIG. 18 ; 
           [0052]      FIG. 23  is a chart of transmission spectroscopic analysis of the FLG in  FIG. 17 ; 
           [0053]      FIG. 24  is a zoomed chart of the chart in  FIG. 23  within the range of 90% to 100% transmittance; 
           [0054]      FIG. 25  is a chart of reflection spectroscopic analysis of the FLG in  FIG. 17 ; 
           [0055]      FIG. 26  is a chart of transmission spectroscopic analysis of the FLG in  FIG. 18 ; and 
           [0056]      FIG. 27  is a chart of reflection spectroscopic analysis of the FLG in  FIG. 18 . 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     A. System for Detecting the Number of Layers of FLG 
       [0057]    With reference to  FIG. 1 , the system in accordance with the present invention comprises a visualization module  10 , an acquisition module  20  and a multispectral imaging reproduction module  30 . 
         [0058]    The visualization module  10  holds an FLG sample  40  and illuminates the FLG sample  40  with a light source by projecting a light allowing the FLG sample  40  to be optically observed. Specifically, the visualization module  10  comprises a platform member  11  and an illumination member  12 . Preferably, the visualization module  10  further comprises a magnification member  13 , which comprises a structure for magnifying an image of the FLG sample  40  held by the platform member  11  and providing an enlarged image thereof. 
         [0059]    The platform member  11  is for holding the FLG sample  40 . The illumination member  12  provides a light source from which a light is projected to the FLG sample  40  held by the platform member  11 . The magnification member  13  is mounted to the platform member  11  so as to magnify an image of the FLG sample  40  held. 
         [0060]    The visualization module  10  further comprises an optional filter member  14 . The filter member  14  is positioned in a light projecting path from the illumination member  12 . The filter member  14  filters a light from the illumination member  12  in order to provide a filtered light of a band suitable for detecting the FLG sample  40  held by the platform member  11 . The filter member  14  comprises filters, which include red, green, blue, cyan, magenta and yellow filters, to be used alternately or in combination. In addition, in absence of the optional filter member  14 , the illumination member  12  may be an illuminating means capable of using switchable light sources to provide lights of different colors, or lights of different bands. 
         [0061]    With reference to  FIG. 2 , the illumination member  12  of the visualization module  10 , other than comprising a reflective structure to reflectively project lights to the FLG sample  40  as having been shown in  FIG. 1 , may comprise a beaming structure that operates with a transparent platform member  11  for directly providing lights through the transparent platform member  11  to the FLG sample  40  for observation. Preferably, the illumination member  12  comprises a reflective structure as shown in  FIG. 1  and a beaming structure as shown in  FIG. 2  and is capable of switching the reflective structure and beaming structure. In other words, the illumination member  12  may comprise a reflective structure which projects a light reflectively to the platform member  11 , a beaming structure which directly provides lights through a transparent platform member  11 , or a switchable structure which comprises both the reflective structure and the beaming structure and is capable of switching the structures. 
         [0062]    The acquisition module  20  comprises a structure for performing an optical observation of the FLG sample  40 . Specifically, the acquisition module  20  is positioned in an output path of the visualization module  10  in which the FLG sample  40  is optically observed, and comprises a CCD member  22 , a lens member  21  and a capturing member  23 . 
         [0063]    The CCD member  22  comprises an array formed with rows and columns of photosensitive units for respectively recording digital signals as pixel information of an electronic image. The CCD member  22  receives an image of the FLG sample  40  of the platform member  11  which has been magnified by the magnification member  13 . 
         [0064]    The lens member  21  is operably connected to the CCD member  22  for focusing the magnified image at the CCD member  22 . Preferably, the lens member  21  focuses a light from the illumination member  12  through the FLG sample  40  at the CCD member  22 . 
         [0065]    The capturing member  23  is an image capturing means operably connected to the CCD member  22  for acquiring information of the magnified image focused by the lens member  21 , which may be a camera or a spectrometer. More preferably, the spectrometer is a spectrometer of model number CS1000A of Konica Minolta or a spectrometer of model number QE65000 of Ocean Optics. 
         [0066]    The reproduction module  30  is operably connected to the acquisition module  20  to provide information of detection of a number of layers of the FLG sample  40 . The reproduction module  30  receives information from the capturing member  23  for the magnified image of the FLG sample  40  and comprises an implementation for a spectral analyzing step  31 , an enhancing step  32  for color image categorizing, and a reproducing step  33 , so as to process and to display the magnified image of the FLG sample  40  for a user to intuitively and rapidly examine a number of layers of the FLG sample  40 . 
       B. Method for Detecting the Number of Layers of FLG 
       [0067]    The method in accordance with the present invention comprises a spectral database construction process and a multispectral image reproduction process, wherein the spectral database construction process builds a database of numbers of layers of FLGs, based on which a detection by a reproduced multispectral color image for a number of layers of an FLG is performed in the multispectral image reproduction process. 
         [0068]    1. The database construction process comprises a spectra-analyzing step, a PCA step and a database constructing step. 
         [0069]    (1) In the spectra-analyzing step, spectral analyses are performed for FLGs of different numbers of layers on different substrates, based on which resulting information is obtained. Specifically, the spectra-analyzing step comprises the following procedures: 
         [0070]    (1-a) Preparing FLGs formed on different substrates, for example, developing FLGs on silica/silicon substrates or glass substrates; 
         [0071]    (1-b) Obtaining images of the FLGs, for example, capturing images of the FLGs via an acquisition means such as a microscope and a camera; 
         [0072]    (1-c) Confirming the numbers of layers of the FLGs, for example, via Raman spectroscopy, transmission spectroscopy, or AFM; and 
         [0073]    (1-d) Performing spectral analyses of the transmission spectra of the FLGs and providing resulting information thereof. 
         [0074]    (2) In the PCA step, PCA is performed with the resulting information to obtain a distinguishing formula. Specifically, the PCA step comprises the following procedures: 
         [0075]    (2-a) Performing PCA for the FLGs of different numbers of layers on different substrates and obtaining a PCA result thereof; and 
         [0076]    (2-b) Based on the PCA result, a distinguishing formula as shown in the following Table 1 is determined for FLGs having different numbers of layers on different substrates, provided that y0 is the first principal component and y1 is the second principal component. 
         [0000]    
       
         
               
               
               
             
           
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 number of 
                   
               
               
                   
                 layers of FLG 
                 formula 
               
               
                   
                   
               
             
             
               
                   
                 1 
                 −1.9348 &lt; y0 &lt; −1.2234 
               
               
                   
                   
                 −0.0047 &lt; y1 &lt; 0.0292  
               
               
                   
                 2 
                 −1.1640 &lt; y0 &lt; −0.2308 
               
               
                   
                   
                 0.0134 &lt; y1 &lt; 0.0420 
               
               
                   
                 3 
                 −0.2308 &lt; y0 &lt; 0.4213  
               
               
                   
                   
                 0.0279 &lt; y1 &lt; 0.0560 
               
               
                   
                 4 
                 0.4952 &lt; y0 &lt; 1.6962 
               
               
                   
                   
                 0.0175 &lt; y1 &lt; 0.0584 
               
               
                   
                 5 
                 1.6962 &lt; y0 &lt; 2.4659 
               
               
                   
                   
                 −0.0415 &lt; y1 &lt; 0.0175  
               
               
                   
                   
                 −0.0415 &lt; y1 &lt; 0.0175  
               
               
                   
                   
               
             
          
         
       
     
         [0077]    (3) In the database constructing step, a database is built based on the resulting information of the spectral analyses and the distinguishing formula to present a relationship between a number of layers of an FLG and the distinguishing formula. 
         [0078]    2. The multispectral image reproduction process comprises an acquisition step, an analyzing step, a categorizing step, an enhancing step, a reproducing step, and an examining step. 
         [0079]    (1) In the acquisition step, an image of an FLG, of which a number of layers is to be detected, is acquired via an acquisition means such as a microscope and a camera. 
         [0080]    (2) In the analyzing step, the image is analyzed to obtain a transmission spectrum of the FLG. 
         [0081]    (3) In the categorizing step, the transmission spectrum is categorized according to the aforementioned database constructed via spectral analysis and PCA so as to obtain a categorization result. 
         [0082]    (4) In the enhancing step, a simulation spectrum is determined based on the categorization result. 
         [0083]    (5) In the reproducing step, a color image is reproduced with the simulation spectrum. 
         [0084]    (6) In the examining step, a number of layers of the FLG is determined by examining the reproduced color image which makes possible an intuitive and rapid examination process. 
         [0085]    Preferably, the method for detecting numbers of layers of FLGs is implemented in the reproduction module  30 . The reproduction module  30  applies the information received from the capturing member  23  of the magnified image of the FLG sample  40  to perform the aforementioned acquisition step for acquiring an image of the FLG sample. After analyzing the image in the analyzing step  31 , a categorization result is obtained in the categorizing step, so as to further enhance and reproduce the magnified image of the FLG sample  40  in the enhancing step  32  and reproducing step  33 , in order to provide a user with a reproduced and enhanced image to perform the examining step for detecting a number of layers of the FLG sample  40 . 
         [0086]    Take a 5-layer FLG on a glass substrate for example, in the case that the FLG in question is analyzed with Raman spectroscopy, a time-consuming and labor-intensive analyzing process would be unavoidable, which makes impossible an intuitive and rapid determination of the number of layers of the FLG. With reference to  FIG. 3 , there are considerably vague zones in the results obtained with technique based on Raman spectroscopy, within which the number of layers of the FLG is difficult to be determined. 
         [0087]    Conversely, the system and the method in accordance with the present invention rapidly distinguishes transmission spectra of FLGs and employs color image reproduction to expedite detecting processes for numbers of layers of FLGs, which significantly obviates the shortcomings of the conventional techniques of the prior art. 
       C. Examples 
     Example 1 
       [0088]    The instant example relates to preparation of an FLG. 
         [0089]    In the instant example, a copper foil is employed as a catalyst for developing large-area single-layer graphene thin films under a low pressure environment, using methane as a carbon source. Developed graphene thin films are then transferred with polymethylmethacrylate (PMMA) to substrates of various types, such as silica/silicon substrates or glass substrates. Details for preparing the FLG are within the scope of the prior art and thus are omitted here. 
         [0090]    With reference to  FIG. 5 , a 3-layer FLG is formed on a silica/silicon substrate. On the silica/silicon substrate there are zero-layer (marked with the symbol “0L”) regions, that is, bare substrate without being covered by graphene, and one-layer (marked with the symbol “1L”), two-layer (marked with the symbol “2L”) and three-layer (marked with the symbol “3L”) regions covered respectively by corresponding layers of graphene. 
         [0091]    With reference to  FIG. 6 , a 5-layer FLG formed on a glass substrate is extremely difficult to be directly observed with an optical microscope in terms of distinguishing numbers of layers of the FLG on the substrate. As shown in  FIG. 7 , in the instant example, the numbers of layers decrease from a center ribbon region to lateral regions. The ribbon regions are partitioned as shown in  FIG. 8  and areas as demonstrated in  FIG. 9  and  FIGS. 10 to 14  are selected for analyses. 
       Example 2 
       [0092]    The instant example relates to a matrix of transformation between a spectrometer and an image-acquiring device. The image-acquiring device employed in the instant example comprises an optical microscope and a CCD camera operably connected to the microscope. 
         [0093]    The spectrometer employed in the instant example is model number QE65000 spectrometer of Ocean Optics. The spectrometer is used to obtain transmission spectra of the 24 colors listed in Macbeth ColorChecker within the visible band of spectrum. 
         [0094]    A model is built by multispectral calculation based on the obtained transmission spectra of the 24 colors. The color differences between simulated colors and the image-acquiring device are shown in Table 2, which lists the 24 colors used to build modules for image reproduction as well as the 24 colors&#39; respective reflection spectra and the color differences between simulation colors and microscopic colors. In Table 2, the 24 colors are numbered and listed in reversed order of the indices in the Macbeth ColorChecker ( Journal of Applied Photographic Engineering  2:95-99 (1976)). A simulation spectrum is generated based on the simulated colors to find the correlation between the spectrometer and the image-acquiring device, for analyzing the differences of FLGs of different numbers of layers. 
         [0000]    
       
         
               
               
               
             
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 No. 
                 Color 
                 Color difference 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 Black 
                 5.644917 
               
               
                 2 
                 Neutral 3.5 
                 4.009531 
               
               
                 3 
                 Neutral 5 
                 2.192149 
               
               
                 4 
                 Neutral 6.5 
                 1.652081 
               
               
                 5 
                 Neutral 8 
                 3.204953 
               
               
                 6 
                 White 
                 1.871073 
               
               
                 7 
                 Cyan 
                 5.15552 
               
               
                 8 
                 Magenta 
                 5.373234 
               
               
                 9 
                 Yellow 
                 3.81115 
               
               
                 10 
                 Red 
                 1.631564 
               
               
                 11 
                 Green 
                 5.384228 
               
               
                 12 
                 Blue 
                 5.495808 
               
               
                 13 
                 Orange yellow 
                 5.052626 
               
               
                 14 
                 Yellow green 
                 3.438659 
               
               
                 15 
                 Purple 
                 5.58387 
               
               
                 16 
                 Moderate red 
                 2.627343 
               
               
                 17 
                 Purplish blue 
                 4.59063 
               
               
                 18 
                 Orange 
                 3.64488 
               
               
                 19 
                 Bluish green 
                 2.233358 
               
               
                 20 
                 Blue flower 
                 4.568302 
               
               
                 21 
                 Foliage 
                 4.429298 
               
               
                 22 
                 Blue sky 
                 7.24369 
               
               
                 23 
                 light skin 
                 6.52435 
               
               
                 24 
                 Dark skin 
                 5.741196 
               
               
                   
               
             
          
         
       
     
         [0095]    In the instant example, a process as shown in  FIG. 15  is employed to determine the matrix of transformation between the information obtained by the spectrometer and the information obtained by the image-acquiring device in order to acquire the transmission spectrum for every pixel of each image. 
         [0096]    For convenience for analyzing, in the instant example the foregoing transmission spectra are sorted into a matrix of 401 rows and 24 columns (“401*24 matrix”). Each row of the 401*24 matrix stands for the intensity of corresponding wavelength, while each column stands for the number of the colors. 
         [0097]    Further with the process as shown in  FIG. 16 , a simulation spectrum is obtained. Six sets of eigenvectors (6*401) and corresponding six eigenvalues (6*24) are obtained via eigensystem and PCA, as shown in the following Equation 1. 
         [0000]      [α] T   =[D]   T   p inv[ E]   [Equation 1]
 
         [0098]    In Equation 1, “pinv” is a false inverse. The information simultaneously detected and acquired for these colors by the image-acquiring device with the optical microscopic environment is output in sRGB JPEG format. With computational calculation, the R, G and B values (0 to 255) of the color of each image information are obtained and converted into R srgb , G srgb  and B srgb  within a smaller scale of 0 to 1, which, with the following Equations 2 to 4, converts the foregoing RGB values into the XYZ tristimulus of CIE standard. 
         [0000]    
       
         
           
             
               
                 
                   
                     
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                                   ) 
                                 
                               
                             
                           
                         
                         ] 
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     Whereas 
                      
                     
                       : 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     2 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     [ 
                     T 
                     ] 
                   
                   = 
                   
                     [ 
                     
                       
                         
                           0.4104 
                         
                         
                           0.3576 
                         
                         
                           0.1805 
                         
                       
                       
                         
                           0.2126 
                         
                         
                           0.7152 
                         
                         
                           0.0722 
                         
                       
                       
                         
                           0.0193 
                         
                         
                           0.1192 
                         
                         
                           0.9505 
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     3 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     f 
                      
                     
                       ( 
                       n 
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               
                                 ( 
                                 
                                   
                                     n 
                                     + 
                                     0.055 
                                   
                                   1.055 
                                 
                                 ) 
                               
                               2.2 
                             
                             , 
                           
                         
                         
                           
                             n 
                             &gt; 
                             0.04045 
                           
                         
                       
                       
                         
                           
                             
                               ( 
                               
                                 n 
                                 12.92 
                               
                               ) 
                             
                             , 
                           
                         
                         
                           otherwise 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     4 
                   
                   ] 
                 
               
             
           
         
       
     
         [0099]    The reference white of the sRGB color space is defined as the reference white under standard illuminant D65 light source, which is different from the reference white of the reflective spectrum obtained with the spectrometer under a halogen light source. Thus the RGB values have to be adjusted via chromatic adaptation. In order to accurately estimate the spectral values of the colors, calibration of the image-acquiring device is also necessary. 
         [0100]    Similarly, the reflective spectrum obtained with the spectrometer is converted to the XYZ tristimulus of the CIE standard with the following Equations 5 to 8. 
         [0000]    
       
         
           
             
               
                 
                   X 
                   = 
                   
                     k 
                      
                     
                       
                         ∫ 
                         
                           380 
                            
                           
                               
                           
                            
                           nm 
                         
                         
                           780 
                            
                           
                               
                           
                            
                           nm 
                         
                       
                        
                       
                         
                           S 
                            
                           
                             ( 
                             λ 
                             ) 
                           
                         
                          
                         
                           R 
                            
                           
                             ( 
                             λ 
                             ) 
                           
                         
                          
                         
                           
                             x 
                             _ 
                           
                            
                           
                             ( 
                             λ 
                             ) 
                           
                         
                          
                         
                            
                           λ 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     5 
                   
                   ] 
                 
               
             
             
               
                 
                   Y 
                   = 
                   
                     k 
                      
                     
                       
                         ∫ 
                         
                           380 
                            
                           
                               
                           
                            
                           nm 
                         
                         
                           780 
                            
                           
                               
                           
                            
                           nm 
                         
                       
                        
                       
                         
                           S 
                            
                           
                             ( 
                             λ 
                             ) 
                           
                         
                          
                         
                           R 
                            
                           
                             ( 
                             λ 
                             ) 
                           
                         
                          
                         
                           
                             y 
                             _ 
                           
                            
                           
                             ( 
                             λ 
                             ) 
                           
                         
                          
                         
                            
                           λ 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     6 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     Z 
                     = 
                     
                       k 
                        
                       
                         
                           ∫ 
                           
                             380 
                              
                             
                                 
                             
                              
                             nm 
                           
                           
                             780 
                              
                             
                                 
                             
                              
                             nm 
                           
                         
                          
                         
                           
                             S 
                              
                             
                               ( 
                               λ 
                               ) 
                             
                           
                            
                           
                             R 
                              
                             
                               ( 
                               λ 
                               ) 
                             
                           
                            
                           
                             
                               y 
                               _ 
                             
                              
                             
                               ( 
                               λ 
                               ) 
                             
                           
                            
                           
                              
                             λ 
                           
                         
                       
                     
                   
                    
                   
                     
 
                   
                    
                   
                     Whereas 
                      
                     
                       : 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     7 
                   
                   ] 
                 
               
             
             
               
                 
                   k 
                   = 
                   
                     100 
                     / 
                     
                       
                         ∫ 
                         
                           380 
                            
                           
                               
                           
                            
                           nm 
                         
                         
                           780 
                            
                           
                               
                           
                            
                           nm 
                         
                       
                        
                       
                         
                           S 
                            
                           
                             ( 
                             λ 
                             ) 
                           
                         
                          
                         
                           
                             y 
                             _ 
                           
                            
                           
                             ( 
                             λ 
                             ) 
                           
                         
                          
                         
                            
                           λ 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     8 
                   
                   ] 
                 
               
             
           
         
       
     
         [0101]    After chromatic adaptation undergone, the RGB values of the camera are converted into XYZ values as matrix [A]. The correlation between the spectrometer and the camera is obtained via 3-degree polynomial regression. The matrix of 3-degree polynomial regression is shown in Equation 9. 
         [0000]      [ C]=[A]p inv[ B]   [Equation 9]
 
         [0000]      Whereas: 
         [0000]      [ B]=[ 1, R,G,B,RG,GB,BR,R   2   ,G   2   ,B   2   ,RGB,R   3   ,G   3   ,B   3   ,RG   2   ,RB   2   ,GR   2   ,GB   2   ,BR   2   ,BG   2 ] T   [Equation 10]
 
         [0102]    The “R”, “G” and “B” are values obtained by the image-acquiring device corresponding to each color. The colors are converted from RGB to XYZ tristimulus of the CIE standard as matrix [β], and the matrix of transformation, [M], between the spectrometer and the image-acquiring device is obtained via Equation 11. 
         [0000]      [ M]=[α]p inv[β]  [Equation 11]
 
       Example 3 
       [0103]    The instant example relates to color-reproduction using simulation spectra. 
         [0104]    Every pixel of the image obtained by the spectrometer are multiplied by RGB to generate linear regression matrix [C], which gives corresponding XYZ values with calculation with Equations 2 to 4. The simulation spectrum of each color (380 nm to 780 nm band) is obtained via Equation 12. 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       [ 
                       Spectra 
                       ] 
                     
                     
                       380 
                       - 
                       
                         780 
                          
                         
                             
                         
                          
                         nm 
                       
                     
                   
                   = 
                   
                     
                       
                         [ 
                         E 
                         ] 
                       
                        
                       
                         [ 
                         M 
                         ] 
                       
                     
                      
                     
                       [ 
                       
                         
                           
                             X 
                           
                         
                         
                           
                             Y 
                           
                         
                         
                           
                             Z 
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     12 
                   
                   ] 
                 
               
             
           
         
       
     
         [0105]    With the technique of the present invention, the spectrum obtained with the spectrometer under halogen light source is divided by the spectrum obtained with the image-acquiring device under the image-acquiring illumination environment and then multiplied by a spectrum of a new substitution light source. The technique of the present invention makes possible the reproduction of colors under the substitution light source, which may be any light source. 
         [0106]    In order to confirm the feasibility of color reproduction, the error between the actual spectrum and the simulation spectrum is evaluated using color difference formulae in the instant example, a process of which is demonstrated as follows: 
         [0107]    A. The tristimulus XYZ values obtained with the spectrometer and the image-acquiring device are converted into chromatic coordinate values (L*, a*, b*) of the CIE 1976 space, whereas: 
         [0000]    
       
         
           
             
               
                 
                   
                     L 
                     * 
                   
                   = 
                   
                     
                       116 
                        
                       
                           
                       
                        
                       
                         f 
                          
                         
                           ( 
                           
                             Y 
                             
                               Y 
                               n 
                             
                           
                           ) 
                         
                       
                     
                     - 
                     16 
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     13 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     a 
                     * 
                   
                   = 
                   
                     500 
                      
                     
                         
                     
                     [ 
                     
                       
                         f 
                          
                         
                           ( 
                           
                             X 
                             
                               X 
                               n 
                             
                           
                           ) 
                         
                       
                       - 
                       
                         f 
                          
                         
                           ( 
                           
                             Y 
                             
                               Y 
                               n 
                             
                           
                           ) 
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     14 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     b 
                     * 
                   
                   = 
                   
                     200 
                      
                     
                         
                     
                     [ 
                     
                       
                         f 
                          
                         
                           ( 
                           
                             Y 
                             
                               Y 
                               n 
                             
                           
                           ) 
                         
                       
                       - 
                       
                         f 
                          
                         
                           ( 
                           
                             Z 
                             
                               Z 
                               n 
                             
                           
                           ) 
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     15 
                   
                   ] 
                 
               
             
             
               
                 
                   
                     f 
                      
                     
                       ( 
                       n 
                       ) 
                     
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             
                               n 
                               
                                 1 
                                 3 
                               
                             
                             , 
                           
                         
                         
                           
                             n 
                             &gt; 
                             0.008856 
                           
                         
                       
                       
                         
                           
                             
                               
                                 7.787 
                                  
                                 n 
                               
                               + 
                               0.137931 
                             
                             , 
                           
                         
                         
                           otherwise 
                         
                       
                     
                   
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     16 
                   
                   ] 
                 
               
             
           
         
       
     
         [0108]    B. The Euclid distance of two points in the CIE 1976 chromatic coordinate system (or the color difference) is calculated: 
         [0000]      Δ E   ab *=√{square root over ((Δ L *) 2 +(Δ a *) 2 +(Δ b *) 2 )}{square root over ((Δ L *) 2 +(Δ a *) 2 +(Δ b *) 2 )}{square root over ((Δ L *) 2 +(Δ a *) 2 +(Δ b *) 2 )}  [Equation 17]
 
         [0109]    The color differences of the aforementioned 24 colors are as shown in Table 2. The average color difference is 4.21, which indicates that the instant example has demonstrated that the technique of the present invention is capable of providing an effect of color reproduction and thus suitable for the application of color display. 
       Example 4 
       [0110]    The instant example relates to PCA for principal component scores calculation for categorizing the spectra of a 3-layer FLG on a silica/silicon substrate and a 5-layer FLG on a glass substrate. 
         [0111]    With reference to  FIGS. 17 and 18 , the principal component scores simplify high-dimensional data into lower-dimensional data for analyses with a projection in an eigenvector space. The formula of principal component scores is as shown in Equation 18. 
         [0000]        y   j   =a   j1 ( x   1i   −  x     1 )+ a   j2 ( x   2i   −  x     2 )+ . . . + a   jp ( x   pi   −  x     p )  [Equation 18]
 
         [0112]    x 1i , x 2i  . . . x pi  are intensities corresponding to the first, second, . . . , p-th wavelengths, while  x   1 ,  x   2 , . . . ,  x   p  are average intensities corresponding to the first, second, . . . , p-th wavelengths. a j1 , a j2 , . . . , a jp  are coefficients of the eigenvector of the covariance matrix of the spectrum. 
         [0113]    As for PCA, the first principal component, being a general indicator, provides the most abundant information of the original data. The second principal component and the third principal component also demonstrate partial information of the original data, which are useful for further subdividing categorized groups. In order to gain a clear picture of the distribution of the data, succeeding PCA is performed for each group to demonstrate the range of the group in an ellipse as shown in Equation 19: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           ( 
                           
                             
                               
                                 a 
                                 1 
                               
                                
                               x 
                             
                             + 
                             
                               
                                 b 
                                 1 
                               
                                
                               y 
                             
                             + 
                             
                               c 
                               1 
                             
                           
                           ) 
                         
                         2 
                       
                       
                         d 
                         1 
                         2 
                       
                     
                     + 
                     
                       
                         
                           ( 
                           
                             
                               
                                 a 
                                 2 
                               
                                
                               x 
                             
                             + 
                             
                               
                                 b 
                                 2 
                               
                                
                               y 
                             
                             + 
                             
                               c 
                               2 
                             
                           
                           ) 
                         
                         2 
                       
                       
                         d 
                         2 
                         2 
                       
                     
                   
                   = 
                   1 
                 
               
               
                 
                   [ 
                   
                     Equation 
                      
                     
                         
                     
                      
                     19 
                   
                   ] 
                 
               
             
           
         
       
     
         [0114]    a 1 , b 1 , a 2 , b 2  are coefficients of the eigenvector of the inverse covariance matrix of the group, whose physical meaning is rotation around the coordinate axis. c 1 , c 2  are the averages of the data of the group. Since all the data with the group are projected in PCA, it is necessary to relocate the center of the ellipse back to the original space due to the projection of the original data occurring during the PCA. d 1  and d 2  are eigenvalues of the covariance matrix, whose physical meanings are half of the major and minor axes of the ellipse. 
       Example 5 
       [0115]    The instant example relates to confirmation of the effect of the present invention with Raman spectroscopic analyses. 
         [0116]    Raman Effect may be used to observe molecular structures, molecular vibration and rotation energy levels, may be located within a molecule functional groups or chemical bonds, and quantitatively analyze complex molecular mixtures. Raman scattering is due to the vibration or rotation of matrix molecules that initiate energy interchange between incident photons and matrix molecules and alter the frequency of the reflected scattering light. 
         [0117]    The instant example employs the microscopic Raman spectrometer of model number Invia 1000 system of Renishaw, which focuses a laser beam through optical microscopic lens at a sample and allows a scattering light to enter the same microscopic lens and to obtain a spectrum therefrom for further analysis. 
         [0118]    The aforementioned Raman spectrometer is used with a 8.6 mW 633 nm red laser beam. A 40× objective lens is used to detect Raman signals. 
         [0119]    As described in reference 22, the Raman shift of an FLG are primarily shown at 1582 cm −1  of G-band and 2676 cm −1  of 2D-band. The Raman spectroscopic analysis chart for the 3-layer FLG on a silica/silicon substrate is shown in  FIG. 19 , and the Raman spectroscopic analysis chart for the 5-layer FLG on a glass substrate is shown in  FIG. 20 , from which it is evident that FLGs having different numbers of layers demonstrate different Raman shifts, wherein G-band signal intensities increase along with the increase of the number of layers, while the 2D-band signal intensities more significantly shift as the numbers of layers increase. 
         [0120]    In the instant example, the Raman analyses performed with the 3-layer FLG on silica/silicon substrate as shown in  FIG. 5  give the results as shown in  FIG. 19 , which verify the detection results of the techniques of the present invention match the results of Raman analyses. 
         [0121]    As for the 5-layer FLG on glass substrate as shown in  FIGS. 6 to 14 , the results of the techniques of the present invention also match the 2D-band and G-band results of Raman analyses as shown in  FIGS. 20 and 21 . With further reference to  FIG. 22 , Raman analyses performed on different square-areas also concur with the results obtained with the techniques of the present invention. Comparing aforementioned  FIGS. 3 and 4 , it is evident that the present invention makes possible an intuitive and rapid detection of numbers of layers of FLGs, which is superior to the convention methods based on Raman spectroscopy. 
       Example 6 
       [0122]    The instant example relates to confirmation of the effect of the present invention with transmission spectroscopic analyses. 
         [0123]    Ultraviolet-visible (“UV-Vis”) spectroscopy is a method that employs UV-Vis band of continuous electromagnetic spectrum as a light source for illuminating a sample so as to examine the relative intensity of absorbance. 
         [0124]    Qualification analyses may be performed with UV-Vis spectroscopy, and quantitative analyses are also possible according to Lambert-Beer&#39;s Law. When the wavelength is small, a solvent demonstrates strong absorbance, or end-absorbance. The tests are performed within the transparent limitation of the end-absorbance. 
         [0125]    With reference to  FIGS. 23 and 26 , the transmission spectrometer is used to verify that FLGs having different numbers of layers on different substrates demonstrate different transmission spectra. As shown in  FIGS. 23 and 24 , the transmission spectroscopic analyses of the 3-layer FLG on silica/silicon substrate concur with the result of the techniques of the present invention. The results of reflective spectroscopic analyses as shown in  FIG. 25  also concur with the result of the techniques of the present invention. 
         [0126]    Furthermore, with reference to  FIG. 26 , transmission spectroscopic analyses give concurring results with the result obtained with the techniques of the present invention. With further reference to  FIG. 27 , the results of reflective spectroscopic analyses also concur with the result of the techniques of the present invention. 
         [0127]    As described above, the present invention combines multispectral analysis with PCA to effectively expedite the examination of optical microscopic image of FLG for determining the number of layers thereof. The techniques of the present invention have been verified with conventional methods. For example, the reflection of the specific band increases with the increase of number of layers concurs with Raman analyses. It is evident that the present invention provides techniques for intuitive and rapid detection of numbers of layers of FLGs under low-cost and effective conditions. 
         [0128]    Even though numerous characteristics and advantages of the present invention have been set forth in the foregoing description, together with details of the structure and features of the invention, the disclosure is illustrative only. Changes may be made in the details, especially in matters of shape, size, and arrangement of parts within the principles of the invention to the full extent indicated by the broad general meaning of the terms in which the appended claims are expressed. 
       REFERENCES 
       [0129]    The following references are cited and incorporated as part of the specification.
   [1] H. C. Neto, F. Guinea, N. M. R. Peres, K. S. Novoselov and A. K. Geim: The electronic properties of graphene. Reviews of Modern Physics, 81, 109-162 (2009)   [2] K. S. Kim, Y. Z. Houk Jang, S. Y. Lee, J. M. Kim, K. S. Kim, J. H. A. P. Kim, J. Y. Choi and B. H. Hong: Large-scale pattern growth of graphene films for stretchable transparent electrodes. Nature, 457, 706-710 (2009)   [3] D. L., MARC B. M. L. SCOTT GILJE, R. B. KANER AND G. G. WALLACE: Processable aqueous dispersions of graphene nanosheets. Nature Nanotechnology, 3, 101-105 (2008)|doi:10.1038/nnano.2007.451   [4] Z. N. Ying W. T. Yu, and Z. Shen: Raman Spectroscopy and Imaging of Graphene. Nano Res 1, 273-291(2008)   [5] N. Mohanty, D. Moore, Z. Xu, T. S. Sreeprasad, A. Nagaraja, A. A. Rodriguez1 &amp; V. Berry: Nanotomy-based production of transferable and dispersible graphene nanostructures of controlled shape and size. Nature communications, 3, article number: 844 (2012)   [6] Maher F. El-Kady et al: Laser Scribing of High-Performance and Flexible Graphene-Based Electrochemical Capacitors. Science 335 (6074), 1326-1330 (2012)   [7] Jae Hun Seol, et al: Two-Dimensional Phonon Transport in Supported Graphene. Science, 328 (5975), 213-216 (2010)   [8] H. Yang, et al: Graphene Barristor, A Triode Device with a Gate-Controlled Schottky Barrier. Science, 336 (6085), 1140-1143 (2012)   [9] Y. W., H. W. Tong, X. F. Xu, B. Ozyilmaz, and K. P. Loh: Interface Engineering of Layer-by-Layer Stacked Graphene Anodes for High-Performance Organic Solar Cells. Adv. Mater. 23 (13), 1514-1518 (2011)   [10] W. Z., C. T. Lin, K. K. Liu, T. Tite, C. Y. Su, C. H. Chang, Y. H. Lee, C. W. Chu, K. H. Wei, J. L. Kuo, and L. J. Li: Opening an Electrical Band Gap of Bilayer Graphene with Molecular Doping. ACS NANO, VOLS NO. 9 7517-7524(2011)   [11] S. Lee, K. Lee, C. H. Liu and Z. Zhong: Homogeneous bilayer graphene film based flexible transparent conductor. Nanoscale, 4, 639-644 (2012). DOI: 10.1039/c1nr11574j (2011)   [12] P. Blake, E. W. Hill, A. H. Castro Neto, K. S. Novoselov, D. Jiang et al: Making graphene visible, Appl. Phys. Lett., 91, 063124 (2007)   [13] I. J. Matthew Pelton, R. P. Dmitriy A. Dikin, S. S. Ovich, S. W. Rotone, M. Hausner, and R. S. Ruoff: Simple Approach for High-Contrast Optical Imaging and Characterization of Graphene-Based Sheets, Nano Letters, 7 (12), 3569-3575 (2007)   [14] L. Gao, W. Ren, F. Li, and H. M. Cheng: Total Color Difference for Rapid and Accurate Identification of Graphene, ACS Nano 2 (8), 1625-1633 (2008)   [15] Y. Y. Wang, Z. H. Ni, T. Yu, Z. X. Shen, H. M. Wang, Y. H. Wu, W. Chen, and A. T. Shen: Raman Studies of Monolayer Graphene: The Substrate Effect, J. Phys. Chem 10637-10640(2008)   [16] I. J., J. S. Rhyee, J. Y. Son, R. S. Ruoff and K. Y. Rhee: Colors of graphene and graphene-oxide multilayers on various substrates. Nanotechnology, 23, 025708 (2012)   [17] Z. H. Ni, H. M. Wang, J. Kasim, H. M. Fan, T. Yu, Y. H. Wu, Y. P. Feng, and Z. X. Shen: Graphene Thickness Determination Using Reflection and Contrast Spectroscopy. Nano Lett., 7 (9), 2758-2763 (2007)   [18] Y. W. Zhu, S. Murali, W. Cai, X. Li, Ji Won Suk, J. R. Potts, and R. S. Ruoff: Graphene and Graphene Oxide: Synthesis, Properties, and Applications. Adv. Mater., 22 (35), 3906-3924 (2010)   [19] Y. K. Koh, M. H. Bae, D. G. Cahill, N. E. Pop: Reliably Counting Atomic Planes of Few-Layer Graphene (n&gt;4). ACS Nano, 5 (1), 269-274 (2011)   [20] W. Liu, H. Li, C. Xu, Y. Khatami, K. Banerjee: Synthesis of high-quality monolayer and bilayer graphene on copper using chemical vapor deposition, Carbon, 49 (13), 4122-4130 (2011)   [21] J. S. Park, A. Reina, R. Saito, J. Kong, G. Dresselhaus, M. S. Dresselhaus: G band Raman spectra of single, double and triple layer graphene, Carbon, 47 (5), 1303-1310 (2009)   [22] M. S. Dresselhaus, G. Dresselhaus, R. Saito, A. Jorio: Raman spectroscopy of carbon nanotubes, Physics Reports, 409 (2), 47-99( 2005 )   [23] A. C. Ferrari, J. C. Meyer, V. Scardaci, Casiraghi, M. Lazzeri, F. Mauri, S. Piscanec, D. Jiang, K. S. Novoselov, S. Roth, and A. K. Geim: Raman Spectrum of Graphene and Graphene Layers, Physical Review Letters, 97, 187401 (2006)