Patent Publication Number: US-8982342-B2

Title: Method and apparatus for calculating a refractive index, material for calculating a refractive index, and a tomography apparatus

Description:
CLAIM OF PRIORITY 
     This application claims the benefit of Japanese Patent Applications No, 2012-053894, filed Mar. 11, 2012, and No. 2013-028580, filed Feb. 18, 2013, which are hereby incorporated by reference herein in their entirety. 
     BACKGROUND OF THE INVENTION 
     1. Field of the Invention 
     The present invention relates to (i) a calculation method and an apparatus for obtaining at least one of information regarding a refractive index and a thickness of a specimen by utilizing the fact that a propagation state of an irradiated electromagnetic wave changes due to the refractive index or a dielectric constant of the specimen, (ii) a material for calculating a refractive index, and (iii) a tomography apparatus. 
     2. Description of the Related Art 
     Calculation of the refractive index has been used widely in an optical band, and the calculation is also considered recently to be important for electromagnetic waves in a frequency band of a millimeter wave and a terahertz wave (30 GHz or higher and 30 THz or lower) (hereafter also referred to simply as a terahertz wave). This is because physical properties such as a refractive index and a dielectric constant of a specimen in this frequency band are different from those in the optical band, and that these characteristic properties can be used for identifying physical properties in a tomography apparatus, or the like. For instance, many biomolecules and pharmaceuticals have characteristic absorption spectra in this frequency band. As methods of calculating the refractive index in this frequency band, the following methods have been typically used. 
     As one of the methods, there is known a method of calculating the refractive index by irradiating a specimen with an electromagnetic wave in this frequency band, and comparing a waveform of a reflected wave thereof with the original waveform, for example, in a case without the specimen (see Japanese Patent Application Laid-Open No. H11-108845). According to this method, it is possible to map the refractive index in a depth direction of the specimen. Therefore, the method is one of important algorithms for forming a tomogram. 
     In addition, as a base of this algorithm, the original waveform to be compared with the waveform of the reflected wave is important. A waveform of an incident wave is used in the above-mentioned example, but various variations can be considered, depending on an optical system and the specimen. For instance, there is known a method in which a Fresnel reflection waveform on a surface of an attenuated total reflection (ATR) prism used in an optical system, called an attenuated total reflection spectroscopy, is used as the original waveform to be compared (see D. Woolard, W. Loerop, and M. Shur, translated by Omori and Hirose, “Terahertz Sensing Technology, vol. 1”, NTS publication (2006) chapter eight, page 289). In the optical system of the ATR spectroscopy, in which the ATR prism and the specimen contact closely with each other, it is possible to eliminate an influence of a refractive index of the ATR prism. Therefore, it is possible to obtain the refractive index of the specimen at high sensitivity. 
     In the frequency band of the millimeter wave and the terahertz wave (30 GHz or higher and 30 THz or lower), absorption by water, however, cannot be neglected. Therefore, the algorithm of Japanese Patent Application Laid-Open No. H11-108845, in which an approximation of neglecting electromagnetic wave absorption is used, is difficult to be applied to a specimen, such as a biomolecule, having a relatively large electromagnetic wave absorption. This is because Fresnel loss and absorption loss cannot be distinguished between the waveform of the reflected wave and the original waveform to be compared. Therefore, depending on the specimen, it is difficult for the conventional method to calculate a refractive index distribution or a dielectric constant distribution in the depth direction of the specimen. 
     SUMMARY OF THE INVENTION 
     The present invention has been made in view of the above-mentioned problem, and it is an object thereof to provide a technology for enabling mapping of a refractive index or a dielectric constant in the depth direction even for a specimen, such as a biological material, having a relatively large electromagnetic wave absorption. 
     According to an exemplary embodiment, the present invention provides a method of calculating a refractive index of at least a portion of a specimen by using electromagnetic wave measurement, the method including measuring a first scattered waveform from a structure of the specimen, measuring a second scattered waveform from a structure in which a material for calculating a refractive index is disposed on a surface of the specimen, and comparing intensities at corresponding portions of the first scattered waveform and the second scattered waveform. 
     Further features of the present invention will become apparent from the following description of exemplary embodiments, with reference to the attached drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a diagram illustrating a flowchart of a refractive index calculation algorithm according to Embodiment 1. 
         FIGS. 2A and 2B  are diagrams illustrating a positional relationship between a specimen and a material for calculating refractive index according to Embodiment 1. 
         FIG. 3  is a diagram illustrating a flowchart of a refractive index calculation algorithm according to Embodiment 2. 
         FIGS. 4A and 4B  are diagrams illustrating a structure of a specimen and a material for calculating refractive index according to Embodiment 3. 
         FIGS. 5A and 5B  are diagrams illustrating a structure of a specimen and a material for calculating refractive index according to Embodiment 3. 
         FIGS. 6A and 6B  are diagrams illustrating a refractive index calculation method according to Example 1. 
         FIG. 7  is a diagram illustrating a structure of a tomography apparatus according to Example 2. 
     
    
    
     DESCRIPTION OF THE EMBODIMENTS 
     In the present invention, as an original waveform to be compared with a scattered wave, there is used a waveform in a case when a minute change is applied to an electromagnetic wave structure inside a specimen (a structure that affects a propagation state of an irradiated electromagnetic wave). Therefore, when constituting an apparatus, the apparatus structure includes a material for calculating refractive index applied to or disposed an a surface layer of the specimen for performing tomography. The material for calculation is a material affecting the specimen so as to slightly change the refractive index inside the specimen. For instance, there is a material being used, such as Vaseline® or urea ointment containing water or oil, or a wetting material, such as a nanocapsule used for drug delivery of an endermic drug, which permeates into a living organism, or the like, from the surface layer. Without being limited to a liquid, a mist or a vapor may be used. If the specimen is a living organism, water vapor is constantly evaporating from the surface of the living organism due to the metabolism of the organism. Therefore, it is also possible to slightly change the refractive index inside the specimen by using a blocking material, such as glass or plastic, covering the specimen as the material for calculation. It is preferred to use quartz, polyethylene, Teflon®, polyolefin, or the like, having permeability for the THz wave. 
     Hereafter, with reference to the drawings, embodiments and examples of the present invention are described. 
     Embodiment 1 
     A refractive index calculation method using electromagnetic wave measurement and a material for calculating refractive index according to this embodiment are described with reference to  FIGS. 1 ,  2 A, and  2 B.  FIG. 1  is a flowchart of a refractive index calculation algorithm according to this embodiment.  FIG. 2A  is a diagram of a layout of a specimen when Step  100  is performed, and  FIG. 2B  is a diagram of a layout of the specimen and the material for calculation when Step  110  is performed. Note that, a first layer  101 ′ and a second layer  102 ′ of  FIG. 2B  are the same, respectively, as a first layer  101  and a second layer  102  of  FIG. 2A . However, when a material for calculation  111  is a wetting material, for example, the welting material may permeate into the first layer  101  and the second layer  102 . Therefore, the first layer is denoted by  101 ′, and the second layer is denoted by  102 ′ in  FIG. 2B . 
     The algorithm of this embodiment includes Step  100  of measuring the scattered wave from the specimen structure, and Step  110  of measuring the scattered wave from the structure in which the material for calculating refractive index  111  is disposed on a surface of the specimen. The scattered wave includes a transmitted wave, a specular reflected wave and a diffuse reflected wave These steps may be performed in parallel or in series. If the wetting material as the material for calculation  111  dries slowly, it is preferred that Step  100  and Step  110  be performed in this order.  FIG. 1  illustrates a case in which the steps are performed in parallel. In either case, this algorithm needs the two data. The scattered wave obtained in Step  100  is referred to as a first scattered wave, and the scattered wave obtained in Step  110  is referred to as a second scattered wave. Analysis of these data is performed as described below. 
     First the refractive index of the first layer  101  of the specimen is calculated. For this purpose, this algorithm includes Step  121  of correcting a phase factor (phase rotation) of the first or second scattered wave. Step  121  is performed for correcting a phase shift due to the material for calculation  111 , and is performed easily by multiplying an amplitude of one of the scattered waves by Exp(j·n 111 ·k 0 ·d 111 ), because the thickness d 111  or the refractive index n 111  of the material for calculation  111  is known. Here, j is an imaginary unit, and k 0  is the wavenumber of the electromagnetic wave in a vacuum. In addition, if is possible to use one of the known thickness d 111  and refractive index n 111  so as to determine the other. 
     Next, the algorithm includes Step  122  of comparing intensities of the first and second scattered waves as to the first layer  101 . The first and second scattered waves always have scattered waves of corresponding portions based on the same interface (for example, R 1  and R 0-1′ ), and thus an intensity ratio (for example, R 1 /R 0-1′ ) is obtained by selecting the surface on an incident side of the first layer  101  of the specimen. This intensity ratio is approximately equal to a Fresnel loss ratio of the related interface as shown by Expression (1). 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           
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     In Step  123  of determining the refractive index n 101  of the first layer  101  of the specimen, this relationship is used to calculate the refractive index. Note that, an imaginary part κ 101  is temporarily neglected, provided that n 101 &gt;&gt;κ 101  holds. The intensity ratio is used here, but it is possible to use a time domain waveform, or the like, to obtain an amplitude ratio, and accurately select a true solution from multiple solutions in a case of the intensity ratio. When the scattered wave is the reflected wave, a phase inversion relationship may be used for calculating a solution. In addition, at this time point, the thickness d 101  of the first layer of the specimen can be easily determined based on a relationship between the determined n 101  and The measured optical distance (namely, an interval between a peak position of the first scattered wave R 1  and a peak position of the second scattered wave R 1-2 ). In other words, a thickness of the specimen at a portion for which the refractive index is calculated can be calculated based on the refractive index of the specimen calculated by the refractive index calculation method of this embodiment. Therefore, this embodiment may be regarded as a thickness calculation method 
     When a minute change δn of the refractive index inside the specimen by the material for calculation  111  is not zero (No in determination  124 ), the process proceeds to a loop  125  of calculating a refractive index of the second layer  102  of the specimen (a loop proceeding to the (m+1)th layer of the specimen). The material for calculation  111  is a wetting material, for example, which permeates into at least the first layer  101 , and a minute change of the refractive index is given. Thus, the process can proceed to at least the second layer  102 . A refractive index of the second layer  102  of the Specimen is calculated. For this purpose, this algorithm includes Step  121  of correcting a phase factor of the first or second scattered wave. Step  121  is performed for determining a minute change δn of the refractive index by the material for calculation  111  (obtained by comparing an interval between the peak position of the first scattered wave R 1  and the peak position of the second scattered wave R 1-2  with an interval between a peak position of a second scattered wave R 0-1′ and a peak position of a third scattered wave R 1′-2′ ), and for correcting the minute change δn. Then, any one of the scattered wave amplitudes is multiplied by Exp(j·δn 101 ·k 0 ·d 101 ) as a trial, to determine the minute change δn so that a phase difference between the scattered waves (for example, R 1-2  and R 1′-2′ ) at the corresponding portions based on the same interface becomes zero. 
     Next, the algorithm includes Step  122  of comparing intensities of the first and second scattered waves as to the second layer  102 . The first and second scattered waves always have scattered waves based on the same interface (for example, R 1-2  and R 1′-2′ ) and thus an intensity ratio (for example, R 1-2 /R 1′-2′ ) is obtained by selecting the surface on an incident side of the second layer  102  of the specimen. This intensity ratio is approximately equal to a Fresnel loss ratio of the related interface as shown by Expression (2). 
     
       
         
           
             
                 
             
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     In Expression (2), attenuation Exp(−2κ 101 ·k 0 ·d 101 ) of the scattered wave amplitude due to absorption by the first layer  101  of the specimen is cancelled in the denominator and the numerator, respectively. Therefore, the Fresnel loss and the absorption loss are separated. In Step  123  of determining the refractive index n 102  of the second layer  102  of the specimen, this relationship is used to calculate the refractive index. Here, in the same manner, an imaginary part κ 102  is temporarily neglected, provided that n 102 &gt;&gt;κ 102  holds. Note that, at this time point, the imaginary part κ 101  in the first layer  101  of the specimen can be restored. For instance, an intensity ratio of the first scattered wave between the scattered waves based on the front surface (for example, R 1 ) and the back surface (for example, R 1-2 ) of the first layer  101  is a function of n 101 , n 102 , and κ 101 . Because n 101  and n 102  are known at this time point, κ 101  can be determined. Therefore, the value κ that was temporarily neglected can be restored as necessary at the time point when the refractive index of the next layer is calculated. In this embodiment, refractive indexes can be determined sequentially until the m-th layer of the specimen by repeating the process. When the minute change δn of the refractive index of the m-th layer of the specimen is zero or small, the determination  124  is performed so as not to proceed to calculation of the refractive index of the (m+1)th layer  102  of the specimen. Finally, Step  130  is performed so as to form a tomogram by mapping the refractive indexes until the m-th layer of the specimen, and this algorithm is completed. Note that, it is preferred in this algorithm that an influence of the material for calculation  111  be larger on the front surface side of the specimen (n 111 &gt;δn 101 &gt;δn 102 &gt;δn 103  and so on). When the material for calculation  111  is a wetting material, for example, this assumption holds. This method can be performed, as illustrated in  FIGS. 2A and 2B , by acquiring the first scattered wave as to the specimen structure (including the first layer  101  and the second layer  102 ), and further by acquiring the second scattered wave as to the structure in which the material for calculating refractive index  111  is disposed on the surface of the same specimen. 
     Embodiment 2 
     A refractive index calculation method using electromagnetic wave measurement and a material for calculating refractive index according to Embodiment 2 are described with reference to  FIG. 3 .  FIG. 3  is a flowchart of a refractive index calculation algorithm according to this embodiment. This embodiment shows a modification example of Embodiment 1. There are variations of the refractive index calculation algorithm, and, for instance, the algorithm as illustrated in  FIG. 3  may be adopted. In addition to the method of Embodiment 1 in which the minute change δn of the refractive index inside the specimen by the material for calculation  111  is mainly considered, a minute change δd of the thickness of the layer inside the specimen is also considered in this embodiment. This embodiment is different from Embodiment 1 in Steps  221  and  226 . 
     In Step  221  of correcting a phase factor of the first or second scattered wave, the minute change δd of the thickness of the layer by the material for calculation  111  is also determined, and any minute change δd is corrected. For this purpose, either one of the scattered wave amplitudes is multiplied by Exp(j·δn 101 ·k 0 ·(d 101 +δd 101 )) as a trial, and a set of δn and δd is determined so that a phase difference between the scattered waves based on the same interlace (for example, R 1-2  and R 1′-2′ ) becomes zero. However, in this step, only the set of δn and δd can be determined. Therefore, a temporary value δn (determined in the manner as described in Embodiment 1) is used to perform Steps  122  and  123 . After that, the algorithm includes Step  226  of analyzing the scattered wave as for the (m-1)th layer of the specimen. Step  226  is performed for determining δn by another method. In this case, the Fresnel loss of the second scattered wave at the surface of the first layer  101 ′ (for example, R 0-1′ ) is expressed by following Expression (3). This relationship is used to calculate δn. 
     
       
         
           
             
               
                 
                   
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     In this Step  226 , it is preferred to determine δn 101  in a recursive manner without neglecting κ 101  so that cancellation of significant digits does not occur. The method of determining κ 101  is performed as described above. When the material lor calculation  111  is a material such as water having a dielectric property similar to that of a biological material. δn becomes relatively small, and hence, it is considered that δd cannot be neglected. This embodiment is effective in this case. 
     Embodiment 3 
     A refractive index calculation method using electromagnetic wave measurement and a material for calculating refractive index according to Embodiment 3 are described with reference to  FIGS. 4A and 4B , and  FIGS. 5A and 5B .  FIG. 4A  is a diagram of a layout of the specimen when Step  100  is performed, and  FIG. 4B  is a diagram of a layout of the specimen and the material for calculation when Step  110  is performed. In addition,  FIG. 5A  is a diagram of layout of the specimen when Step  100  is performed, and  FIG. 5B  is a diagram of a layout of the specimen and the material tor calculation when Step  110  is performed. Note that, the first layer  101 ′ and the second layer  102 ′ of  FIGS. 4B and 5B  are the same, respectively, as the first layer  101  and the second layer  102  of  FIGS. 4A and 5A . However, when the material for calculation  111  is a wetting material, for example, the wetting material may permeate into the first layer  101  and the second layer  102 . Therefore, the first layer is denoted by  101 ′, and the second layer is denoted by  102 ′ in  FIGS. 4B and 5B . 
     This embodiment shows a modification example of Embodiment 1. There are variations of the layout of the specimen and the material for calculating refractive index. For instance, as illustrated in  FIGS. 4A and 4B , in a case when the material for calculation  111  is disposed on the surface of the specimen structure including the first layer  101  and the second layer  102  via a certain layer  112 , the algorithm of Embodiment 1 can be used as it is, by considering the specimen and the unknown layer  112  as an unknown specimen extended to include the unknown layer  112 . in a case of the wetting material  111 , the layer  112  may have an effect of promoting permeating. When materials for calculation  111 A and  111 B having different thicknesses are disposed on the surfaces of the specimen structures including the first layer  101  or  101 ′ as illustrated in  FIGS. 5A and 5B , it is possible to use one of the structures as the structure for the original waveform to be compared. When the material for calculation is a wetting material, it is considered that there occurs a difference of permeating depth due to the thickness. Therefore, by considering the specimen and the material for calculation (wetting material)  111 A as an unknown specimen extended to include the material for calculation (wetting material)  111 A in  FIG. 5A , the algorithm of Embodiment 1 can be used as it is. However, for this purpose, it is a precondition that a difference of the thickness δd 111  or the refractive index n 111  of the material for calculation  111 A is known. 
     A more specific refractive index calculation method, a material for calculating refractive index, and a tomography apparatus are described in the following examples. 
     Example 1 
     The refractive index calculation method and the material for calculating refractive index according to Example 1 are described with reference to  FIGS. 6A and 6B .  FIG. 6A  is a tomogram of the specimen according to this example.  FIG. 6B  shows time-base waveforms of the reflected waves from the specimen and from the material for calculating refractive index according to this example. 
     In this example, a piece of pig skin is used as the specimen. A pig skin includes an epithelium (including keratin)  101  and a corium  102 , and is similar to human skin. In addition, a terahertz time domain spectroscopic system (THz-TDS) is used for measuring a waveform of the scattered wave. As the terahertz wave, an electromagnetic wave pulse is used, which has a frequency of 0.5 THz at a highest intensity and a frequency band of approximately 4 THz. As the optical system, a general reflection system is used, so that the reflected wave from the specimen can he acquired. In this example, cream containing Vaseline® is used as the material for calculation  111 . The material for calculation  111  may be applied to only a portion of the specimen. Thus, the above-mentioned first scattered wave and second scattered wave can be obtained. 
       FIG. 6A  shows a tomogram of the pig skin acquired by the THz-TDS. In the image, the horizontal direction (x, y) represents a direction along the skin, and the vertical direction (z) represents a depth direction. This tomogram roughly includes three layers corresponding to the air, the epithelium, and the corium, arranged in order, from the top. In this example, at the point of x-y address (0, 6) in  FIG. 6A , data of the reflected wave from the skin itself is acquired. In addition, in an area near the point of x-y address (2, 4), data of the reflected wave from the skin on which Vaseline® is applied to have a thickness of 0.35 mm is acquired.  FIG. 6B  shows time-base waveforms thereof, which are denoted by Sample and Ref., respectively. The individual waveforms have their peaks, which indicate information of the individual interface. Further, the information of the individual interlace is as shown in Table 1. 
     
       
         
           
               
             
               
                 TABLE 1 
               
             
            
               
                   
               
               
                 Data of interfaces of specimen acquired by terahertz time 
               
               
                 domain spectroscopic system 
               
            
           
           
               
               
               
               
               
            
               
                   
                 Depth 
                 Amplitude 
                 Depth 
                 Amplitude 
               
               
                   
                 (Sample) 
                 (Sample) 
                 (Ref.) 
                 (Ref.) 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
               
            
               
                   
                 Vaseline 
                   
                   
                 0.657 
                 0.671 
               
               
                   
                 surface 
               
               
                   
                 Epithelium 
                 1.382 
                 −4.057 
                 1.696 
                 0.661 
               
               
                   
                 surface 
               
               
                   
                 Corium 
                 1.661 
                 2.893 
                 2.062 
                 0.809 
               
               
                   
                 surface 
               
               
                   
                   
               
               
                   
                 *Depth is optical distance in mm. 
               
            
           
         
       
     
     For instance, Sample has a peak of amplitude −4.057 at point 1.382 in the depth direction. Because Sample includes the epithelium surface and the corium surface (an interface between the corium and the epithelium), there are ideally two peaks. Because Ref. includes the Vaseline® surface and the epithelium surface (an interface between the epithelium and the Vaseline®), and the corium surface (an interface between the corium and the epithelium), there are ideally three peaks. In  FIG. 6B , other unnecessary peaks are observed, but it is possible to determine whether they are ghosts or not based on horizontal continuity in the tomogram, or the like. In this example, peak detection is simply used. The above-mentioned algorithm of the present invention is applied to the data prepared in this way. 
     First, a phase factor shift due to the Vaseline® is corrected so as to calculate n vaseline . In this example, the following Expression is used:
 
(1.696−0.657)=2×n vaseline ×0.35.
 
     Thus, n vaseline =1.44 is determined. In the right side, “2” indicates a path count of an outward path and an inward path. Next, in order to determine nepithelium, an amplitude ratio of the epithelium surfaces of Sample and Ref. is compared with the square root of the right side of above Expression (1). As a result, n epithelium =1.37 is easily calculated. Because sign information is contained in a case of the amplitude ratio, the calculation is easier than in the case of the intensity ratio. In other words, it is possible to select a solution of the calculated refractive index based on the signs of the amplitudes at the corresponding portions of the two scattered waves. Thus, d epithelium =0.10 mm can also be determined. 
     Next, correction of the phase factor shift due to moisture of the Vaseline® in the epithelium is performed to calculate δn epithelium . In this example, the following Expression is used:
 
(2.062−1.696)−(1.661−1.382)=2×δn epithelium ×0.10 mm.
 
     Thus, δn epithelium  is 0.43. Otherwise, the following Expression is used to obtain the same result:
 
(1.661−1.382)/(2.062−1.696)=n epithelium +δn epithelium ).
 
     Next, in order to obtain n corium , an amplitude ratio of the corium surfaces of Sample and Ref. is compared with the square root of the right side of the above Expression (2). As a result, n corium =1.99 is easily calculated. As a result of applying this algorithm, the calculated information is as shown in Table 2. As described above first, not only the refractive index of the epithelium  101 , but also, the refractive index of the corium  102  can be calculated. When there is a layer under the corium  102 , the items indicated unknown can be calculated as a matter of course. 
     
       
         
           
               
             
               
                 TABLE 2 
               
             
            
               
                   
               
               
                 Calculated data of interfaces of specimen 
               
            
           
           
               
               
               
               
               
            
               
                   
                   
                 Refractive 
                   
                 Refractive 
               
               
                   
                 Thickness 
                 index 
                 Thickness 
                 index 
               
               
                   
                 (Sample) 
                 (Sample) 
                 (Ref.) 
                 (Ref.) 
               
               
                   
                   
               
            
           
           
               
               
               
               
               
            
               
                 Vaseline 
                 — 
                 — 
                 Known 
                 1.44 
               
               
                 Epithelium 
                 0.10 
                 1.37 
                 0.10 
                 1.79 
               
               
                 Corium 
                 Unknown 
                 1.99 
                 Unknown 
                 Unknown 
               
               
                   
               
               
                 *Depth is optical distance in mm. 
               
            
           
         
       
     
     The time-base waveform is used as an example in this example, but this is not a limitation. For instance, a waveform of an interferogram, or the like, may be used. Therefore, the system is not limited to the THz-TDS. When the interferogram is used, it is necessary to compare the intensity ratio instead of the amplitude ratio of the scattered wave. There are considered various methods of calculating the multiple solutions. For instance, there are considered a method involving selection using a database, or the like, and a method of giving auxiliary information such as thickness by another apparatus using an ultrasonic wave or light. As a matter of course, a known algorithm may be used at the same time. 
     In addition, the optical system may be a transparent system or a reflection system with a tilt angle. In this case, it is only needed to rewrite Expressions (1) and (2) appropriately by using Fresnel equations. Details thereof are omitted, but a case of the transparent system is as follows, for example. The first scattered wave is assumed to be the scattered wave containing a pulse after passing through the first layer  101  and the second layer  102  of the specimen, or a pulse after being reflected by the interface between the first layer  101  and the second layer  102 , and by the interface between the air and the first layer  101  so as to pass through the first layer  101 , and the second layer  102 . In addition, the second scattered wave is assumed to be the scattered wave containing a pulse after passing through the material for calculation  111  and the first layer  101  and the second layer  102  of the specimen, a pulse after being reflected by the interface between the material for calculation  111 , and the first layer  101  and by the interface between the air and the material for calculation  111  so as to pass through the material for calculation  111 , the first layer  101 , and the second layer  102 , or a pulse after being reflected by the interlace between the first layer  101  and the second layer  102 , and by the interface between the material for calculation  111  and the first layer  101 , so as to pass through the first layer  101  and the second layer  102 . As to the pulses after passing through multiple surfaces, including the same interface regarding the first and second scattered waves, an appropriate interface is selected so as to acquire the intensity ratio. Then, using the above-mentioned appropriately rewritten Fresnel equations, a measurement optical distance between pulses, and the like, the above-mentioned process is performed. In this manner, it is possible to calculate the refractive index, and the like, of the specimen layer by utilizing the transmitted light. 
     Example 2 
       FIG. 7  illustrates an example of a tomographic imaging apparatus with a refractive index calculation apparatus and a terahertz time domain spectroscopic system (THz-TDS), which are constituted by using the refractive index calculation method and the material for calculating refractive index described above. 
     Such a spectroscopic system itself is basically the same as a conventional one. This spectroscopic system includes a short pulse laser  700 , a half mirror  710 , an optical delay system (delay unit)  720 , an electromagnetic wave generation element (electromagnetic wave generation unit)  730 , and an electromagnetic wave detection element (electromagnetic wave detection unit)  740  as main elements. A pump beam  711  and a probe beam  712  irradiate the electromagnetic wave generation element  730  and the electromagnetic wave detection element  740 , respectively. A terahertz wave generated from the electromagnetic wave generation element  730 , to which a voltage is applied from a voltage source  731 , is guided by terahertz guides  713  and  715  to a specimen  750 . The terahertz wave containing internal information of the specimen  750  is guided by terahertz guides  714  and  716  and is detected by the electromagnetic wave detection element  740 . In this case, a current value detected by an ammeter  741  is proportional to the amplitude of the terahertz wave. In order to perform time resolution (namely, to acquire a time-base waveform of the electromagnetic wave), it is only needed to control irradiation timings of the pump beam and the probe beam by, for example, moving the optical delay system  720  tor changing an optical path length of the probe beam  712 . In other words, the delay time between generation of the electromagnetic wave by the electromagnetic wave generation element  730  and detection of the electromagnetic wave by the electromagnetic wave detection element  740  is adjusted. This is a scan in the depth direction in the tomography. 
     Using the apparatus according to the Example 2, if there is a discontinuous portion of material inside the specimen, a reflected echo pulse appears at a time position corresponding to the discontinuous part in the signal to be acquired. A tomogram can be acquired by scanning the specimen  750  in a one-dimensional manner, and a three-dimensional image, as illustrated in  FIG. 6A , can be acquired by scanning the specimen  750  in a two-dimensional manner. By connecting to an analysis system (signal processing unit)  770  such as a PC that can perform signal processing as described in Example 1, it is possible to map the refractive indexes inside the specimen. Further, the apparatus may include an application apparatus  760  as an application unit that can apply the material for calculating refractive index on the specimen with good control. As described above, the apparatus illustrated in  FIG. 7  includes the electromagnetic wave generation unit for generating the electromagnetic wave for irradiating the specimen, the electromagnetic wave detection unit for detecting the electromagnetic wave from the specimen, the delay unit for adjusting the delay time between the generation of the electromagnetic wave by the electromagnetic wave generation unit and the detection of the electromagnetic wave by the electromagnetic wave detection unit, and the refractive index calculation apparatus including the signal processing unit for processing the signal from the electromagnetic wave detection unit. Then, the signal processing unit performs processes including the process of calculating the refractive index of at least a portion of the specimen by comparing intensities at the corresponding portions of the first and second scattered waves measured by the electromagnetic wave detection unit. 
     In this way, it is possible to constitute the tomographic imaging apparatus, the refractive index calculation apparatus, or the like, by using the refractive index calculation method, the material for calculating refractive index, and the like, according to the present invention. 
     While the present invention has been described with reference to exemplary embodiments, it is to be understood that the invention is not limited to the disclosed exemplary embodiments. The scope of the following claims is to be accorded the broadest interpretation so as to encompass all such modifications and equivalent structures and function.