Patent Publication Number: US-2023152262-A1

Title: Dielectric Spectroscopic Measurement Device and Method

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This patent application is a national phase filing under section 371 of PCT application no. PCT/JP2020/015498, filed on Apr. 6, 2020, which is incorporated herein by reference in its entirety. 
    
    
     TECHNICAL FIELD 
     The present invention relates to a dielectric spectroscopic measurement apparatus and a method for measuring a complex permittivity of a slight amount of a liquid sample. 
     BACKGROUND 
     With the progression of aging, it has been a big issue of concern how to address lifestyle diseases. A test for blood sugar level or the like, which requires blood drawing, is a larger burden on patients. Accordingly, a non-invasive component concentration measurement apparatus not requiring blood drawing has attracted attention. 
     For a non-invasive component concentration measurement, a technology using a microwave-millimeterwave-band electromagnetic wave has been proposed. This technology has advantages including less in vivo scatter and a lower energy per photon as compared with optical measurement using a near-infrared light. Examples using a microwave-millimeterwave-band electromagnetic wave include a measurement technology using a resonance structure as described in Non-Patent Literature 1. In this technology, a measurement device with a high Q value, such as an antenna or a resonator, is brought into contact with a measurement sample, thereby measuring frequency characteristics in the vicinity of a resonance frequency. The resonance frequency is determined by a complex permittivity around the measurement device and, accordingly, a correlation between a shift amount of the resonance frequency and a component concentration is predicted, thereby estimating the component concentration from the shift amount of the resonance frequency. 
     As another measurement technology using a microwave-millimeterwave-band electromagnetic wave, a dielectric spectroscopy method as described in Patent Literature 1 has been proposed. In the dielectric spectroscopy method, an electromagnetic wave is applied into skin and the electromagnetic wave is absorbed in accordance with an interaction between blood components as measurement targets, such as glucose molecules and water, thereby observing an amplitude and a phase of the electromagnetic wave. A dielectric relaxation spectrum is calculated from the observed amplitude and phase with respect to a frequency of the electromagnetic wave. 
     The dielectric relaxation spectrum is typically expressed as a linear combination of relaxation curves on the basis of a Cole-Cole expression, based on which a complex permittivity is calculated. For a measurement of a biological component, the amount of a blood component, such as glucose or cholesterol, contained in the blood is correlated with the complex permittivity, and an electrical signal (with amplitude, phase) corresponding to a change therein is measured. A quantitative detection model is created by measuring in advance a correlation between a change in the complex permittivity and a component concentration, and quantitative detection is performed for determining the component concentration by comparing a change in the measured dielectric relaxation spectrum and the quantitative detection model. Irrespective of whether either of the measurement technologies is used, an improvement in measurement sensitivity can be expected by selecting a frequency band that has a strong correlation with a target component. Accordingly, it is important to measure a change in permittivity in advance by broadband dielectric spectroscopy in advance. 
     Among dielectric spectroscopy methods, a technology using a coaxial probe (an open-ended coaxial probe or an open-ended coaxial line) as described in Non-Patent Literature 2 is capable of using an easily available sample such as water for calibration of a measurement instrument. Further, this measurement technology eliminates the necessity of special machining of a material and makes it possible to measure a permittivity of a measurement sample by bringing the sample to measure into contact with a probe end surface. In view of the above, the measurement technology using the coaxial probe described in Non-Patent Literature 2 is suitable for measuring a sample difficult to machine, such as a living body or soil. 
     Citation List 
     Patent Literature 
     Patent Literature 1: Japanese Patent Laid-Open No. 2013-032933. 
     Non-Patent Literature 
     Non-Patent Literature 1: M. Hofmann et al., “Microwave-Based Noninvasive Concentration Measurements for Biomedical Applications”, IEEE Transactions on Microwave Theory and Techniques, vol. 61, no. 5, pp. 2195-2204, 2013. 
     Non-Patent Literature 2: J. P. Grant, “A critical study of the openended coaxial line sensor technique for RF and microwave complex permittivity measurements”, Journal of Physics E: Scientific Instruments, vol. 22, pp. 757-770, 1989. 
     SUMMARY 
     Technical Problem 
     However, a typical measurement using a coaxial probe, which is intended to accurately measure permittivity under conditions that a substance to measure has a sufficient thickness, is not capable of measuring permittivity in a case where a measurement target is thin unless a thickness of the measurement target is known. Further, in a case where a measurement target is multi-layered, a permittivity cannot be measured unless a permittivity or the like of a part of the measurement target is known. 
     For example, assuming a non-invasive biological component application such as analysis of a sugar content in a fruit or estimation of an in vivo glucose concentration, in many cases, a site where a coaxial probe is to be brought into contact is supposed to have a two-layer structure including at least a barrier layer for retaining water and an in vivo layer containing a lot of water. In such a case, it is desirable that an influence of the barrier layer be reduced so that a component concentration estimated from an in vivo permittivity and permittivity information can be calculated. However, it is difficult to measure an in vivo material permittivity and a thickness of the barrier layer in advance and, accordingly, a typical technology using a coaxial probe is not capable of an accurate measurement. 
     Embodiments of the present invention can solve a problem as described above and an object thereof is to enable a multilayer measurement target to be accurately measured by a dielectric spectroscopy method using a coaxial probe. 
     Means for Solving the Problem 
     A dielectric spectroscopic measurement apparatus according to embodiments of the present invention includes: a first probe including a coaxial line and having an opened end as a detection end; a second probe including a coaxial line and having an opened end as a detection end, the second probe having a longer penetration length than the first probe; and a measurement instrument configured to determine, from a result of a measurement of a measurement object using the first probe and a result of a measurement of the measurement object using the second probe, a permittivity of a second medium of the measurement object in which a first medium on an outer-layer side that is thinner than a penetration length of the first probe and the second medium on a deep-layer side relative to the first medium are stacked on each other. 
     A dielectric spectroscopic measurement method according to embodiments of the present invention of determining, by a dielectric spectroscopy method using a first probe including a coaxial line and having an opened end as a detection end and a second probe including a coaxial line and having an opened end as a detection end, the second probe having a longer penetration length than the first probe, a permittivity ε s  of a second medium of a measurement object in which a first medium on an outer-layer side that is thinner than a penetration length of the first probe and the second medium on a deep-layer side relative to the first medium are stacked on each other, the dielectric spectroscopic measurement method includes: a first step of determining an actual measured value of permittivity of the first medium by a measurement of the measurement object using the first probe and determining an actual measured value Y measured  of admittance at the detection end of the second probe by a measurement of the measurement object using the second probe; a second step of determining, with use of a model of admittance at the detection end of the second probe with a permittivity ε 1  of the first medium and the permittivity ε s , a model value Y model  of admittance at the detection end of the second probe with an assumption that the permittivity ε 1  is defined as the actual measured value of permittivity and the permittivity ε s  is defined as a variable; and a third step of determining the permittivity ε s  at which the actual measured value Y measured  and the model value Y model  become equal. 
     Effects of Embodiments of the Invention 
     As described hereinbefore, according to embodiments of the present invention, the use of the first probe and the second probe, which has a longer penetration length than the first probe, enables a multilayer measurement target to be accurately measured by a dielectric spectroscopy method using a coaxial probe. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG.  1    is a configuration diagram illustrating a configuration of a dielectric spectroscopic measurement apparatus according to an embodiment of the present invention. 
         FIG.  2 A  is a side view illustrating a partial configuration of another dielectric spectroscopic measurement apparatus according to an embodiment of the present invention. 
         FIG.  2 B  is a bottom view illustrating a partial configuration of another dielectric spectroscopic measurement apparatus according to an embodiment of the present invention. 
         FIG.  3    is a characteristic diagram illustrating a decay rate of an electric field strength of each probe in a direction toward a measurement object. 
         FIG.  4    is a diagram of assistance in explaining a model configuration of the measurement object. 
         FIG.  5    is a flowchart for explaining a dielectric spectroscopic measurement method according to an embodiment of the present invention. 
         FIG.  6    is a characteristic diagram illustrating a result of a measurement by the dielectric spectroscopic measurement method according to an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS 
     Description will be made below on a dielectric spectroscopic measurement apparatus according to an embodiment of the present invention with reference to  FIG.  1   . The dielectric spectroscopic measurement apparatus includes a first probe  101 , a second probe  102 , and a measurement instrument  103 . 
     The first probe  101  includes a coaxial line and has an opened end as a detection end  101   a . The second probe  102  includes a coaxial line and has an opened end as a detection end  102   a . Further, the second probe  102  has a longer penetration length than the first probe  101 . With use of these probes, a permittivity of a measurement object  150  is to be measured as an electrical signal. 
     The measurement instrument  103  determines, from a result of a measurement of the measurement object using the first probe  101  and a result of a measurement of the measurement object using the second probe  102 , a permittivity of a second medium  152  of the measurement object  150  in which a first medium  151  on an outer-layer side that is thinner than the penetration length of the first probe  101  and the second medium  152  on a deep-layer side relative to the first medium  151  are stacked on each other. 
     The first probe  101  includes the coaxial line including an outer conductor  111  and an inner conductor  112  with a space between the outer conductor  111  and the inner conductor  112  filled with a dielectric layer  113  including a fluorine resin or the like. Electrical properties such as impedance and admittance of the measurement object  150  can be measured by the first probe  101  with use of a leakage electromagnetic field occurring between the outer conductor  111  and the inner conductor  112 , which are brought into contact with the measurement object  150  at the detection end  101   a . 
     Further, the detection end  102   a  of the first probe  101  can be provided with, for example, a fringe  114 . The disc-shaped fringe  114  can be provided at an end portion of the columnar first probe  101 . The fringe  114  is provided on the outer conductor  111 . A surface of the fringe  114  in a direction perpendicular to a waveguide direction of the coaxial line is, for example, wider than a region where the electric field strength of the leakage electric field from the detection end  101   a  becomes 1% or less of a maximum value. 
     The second probe  102  includes the coaxial line including an outer conductor  121  and an inner conductor  122  with a space between the outer conductor  121  and the inner conductor  122  filled with a dielectric layer  123  including a fluorine resin or the like. An outer diameter of the inner conductor  122  is larger than an outer diameter of the inner conductor  112 . Electrical properties such as impedance and admittance of the measurement object  150  can be measured by the second probe  102  with use of a leakage electromagnetic field occurring between the outer conductor  121  and the inner conductor  122 , which are in contact with the measurement object  150  at the detection end  102   a . 
     Further, the detection end  102   a  of the second probe  102  can be provided with, for example, a fringe  124 . The disc-shaped fringe  124  can be provided at an end portion of the columnar second probe  102 . The fringe  124  is provided on the outer conductor  121 . A surface of the fringe  124  in a direction perpendicular to a waveguide direction of the coaxial line is, for example, wider than a region where the electric field strength of the leakage electric field from the detection end  102   a  becomes 1% or less of a maximum value. 
     Further, as illustrated in  FIG.  2 A  and  FIG.  2 B , the first probe  101  and the second probe  102  can be integrated in a common fringe  104 . By virtue of such integration of the first probe  101  and the second probe  102  in the common fringe  104 , measurement regions (the detection end  101   a , the detection end  102   a ) of both can be brought close to each other. Such a configuration makes it possible to measure a heterogeneous material, a material with a narrow measurement region, or the like. 
     The measurement instrument  103  includes a first process unit  131 , a second process unit  132 , a third process unit  133 , a high-frequency measurement unit  134 , and a display unit  135 . The high-frequency measurement unit  134  sweeps a frequency within a predetermined range to generate an electromagnetic wave and supplies the electromagnetic wave to the first probe  101  and the second probe  102 . In addition, with the electromagnetic wave absorbed in the measurement object  150  at each of the first probe  101  and the second probe  102 , the high-frequency measurement unit  134  measures (observes) an amplitude and a phase of the electromagnetic wave. 
     It should be noted that the high-frequency measurement unit  134  is, for example, a vector network analyzer. Alternatively, a commercially available impedance analyzer, LCR meter, or the like is usable as the high-frequency measurement unit  134 . 
     The first process unit  131  first determines an actual measured value of permittivity of the first medium  151  from a measurement result measured by the high-frequency measurement unit  134  through the measurement of the measurement object  150  using the first probe  101 . The first process unit  131  also determines an actual measured value Y measured  of admittance at the detection end  102   a  of the second probe  102  from a measurement result measured by the high-frequency measurement unit  134  through the measurement of the measurement object  150  using the second probe  102 . 
     With use of a model of admittance at the detection end  102   a  of the second probe  102  with a permittivity ε 1  of the first medium  151  and a permittivity ε s  of the second medium  152 , the second process unit  132  determines a model value Y model  of admittance at the detection end  102   a  of the second probe  102  with an assumption that the permittivity ε 1  is the actual measured value of permittivity and the permittivity ε s  is a variable. 
     The third process unit  133  determines the permittivity ε s  at which the actual measured value Y measured  and the model value Y model  become equal. The display unit  135  displays a result determined by the third process unit  133 . 
     Next, the dielectric spectroscopic measurement apparatus according to the embodiment will be described in more detail. 
     A characteristic impedance of the coaxial line is represented by Expression (1) below. In Expression (1), Zo is a characteristic impedance (Ω) of the coaxial line, ε r  is a parameter indicating a relative permittivity of a dielectric layer in the coaxial line, a is a radius of an outer diameter of an inner conductor, and b is a radius of an inner diameter of an outer conductor. Further, a cutoff frequency of the coaxial line is represented by Expression (2) below. In Expression (2), fc is the cutoff frequency and v is the speed of light. Expressions (1) and (2): 
     
       
         
           
             Z0 =  
             
               
                 138.061 
               
               
                 
                   
                     
                       ε 
                       r 
                     
                   
                 
               
             
             log 
             
               b 
               a 
             
           
         
       
     
     
       
         
           
             fc =  
             
               v 
               
                 π 
                 
                   
                     
                       ε 
                       r 
                     
                   
                 
                 
                   
                     a 
                     + 
                     b 
                   
                 
               
             
           
         
       
     
     For example, the high-frequency measurement unit in the measurement instrument  103  is typically designed such that the characteristic impedance becomes 50 Ω or 75 Ω. Accordingly, the parameters a, b, and ε r  are designed such that an upper limit of a measurement frequency does not become the cutoff frequency fc or less and the characteristic impedance satisfies the above. For example, in a case where the upper limit of the measurement frequency is 50 GHz, the characteristic impedance is 50 Ω, and the dielectric layer between the outer conductor and the inner conductor is a fluorine resin (ε r  ≈ 2.2), a is 0.175 mm, and b is 0.8 mm. 
     While the characteristic impedances of the first probe  101  and the second probe  102  are designed to be the same in value, the outer diameter of the inner conductor  122  is designed to be larger than the outer diameter of the inner conductor  112 . It means that the first probe  101  and the second probe  102  have a structure that satisfies Expression (3). It should be noted that in Expression (3), numbers of the variables denote the first probe  101  and the second probe  102 . Expression (1): 
     
       
         
           
             
               
                 
                   
                     
                       
                         
                           a 
                           1 
                         
                       
                     
                     
                       ≠ 
                     
                     
                       
                         
                           a 
                           2 
                         
                       
                     
                   
                   
                     
                       
                         
                           b 
                           1 
                         
                       
                     
                     
                       ≠ 
                     
                     
                       
                         
                           b 
                           2 
                         
                       
                     
                   
                   
                     
                       
                         
                           
                             
                               b 
                               1 
                             
                           
                           ¯ 
                         
                       
                     
                     
                       ≅ 
                     
                     
                       
                         
                           
                             
                               b 
                               2 
                             
                           
                           ¯ 
                         
                       
                     
                   
                   
                     
                       
                         
                           a 
                           1 
                         
                       
                     
                     
                         
                     
                     
                       
                         
                           a 
                           2 
                         
                       
                     
                   
                 
               
             
           
         
       
     
     For example, in a case where the upper limit of the measurement frequency is 50 GHz, the characteristic impedance is 50 Ω, and the material of the dielectric layer is a fluorine resin (ε r  ≈ 2.2), a 1 , b 1 , a 2 , and b 2  are 0.175 mm, 0.8 mm, 0.33 mm, and 1.5 mm, respectively. It should be noted that in the embodiment, a 1  &lt; a 2  and b 1  &lt; b 2 . and the second probe  102  has a wide opening and is low in cutoff frequency. At this time, a decay rate of an electric field strength of each of the probes in a direction toward the measurement object  150  is as in  FIG.  3   . In  FIG.  3   , a dotted line represents characteristics of the first probe  101  and a dashed line represents characteristics of the second probe  102 . As illustrated in  FIG.  3   , the second probe  102  penetrates deeper. 
     Here, the first process unit  131  calculates the permittivity of the measurement object  150  from impedance, admittance, reflection coefficient, etc. measured by the high-frequency measurement unit  134 . For example, with use of a first reference substance, a second reference substance, and a third reference substance, permittivities of which are known in advance, the permittivity of the measurement object  150  is calculated by Expression (4) and Expression (5) below, or the like. Expressions (4) and (5): 
     
       
         
           
             
               
                 
                   
                     
                       ρ 
                       4 
                     
                     − 
                     
                       ρ 
                       1 
                     
                   
                 
                 
                   
                     
                       ρ 
                       3 
                     
                     − 
                     
                       ρ 
                       2 
                     
                   
                 
               
               
                 
                   
                     
                       ρ 
                       4 
                     
                     − 
                     
                       ρ 
                       2 
                     
                   
                 
                 
                   
                     
                       ρ 
                       1 
                     
                     − 
                     
                       ρ 
                       3 
                     
                   
                 
               
             
             = 
             
               
                 
                   
                     
                       y 
                       4 
                     
                     − 
                     
                       y 
                       1 
                     
                   
                 
                 
                   
                     
                       y 
                       3 
                     
                     − 
                     
                       y 
                       2 
                     
                   
                 
               
               
                 
                   
                     
                       y 
                       4 
                     
                     − 
                     
                       y 
                       2 
                     
                   
                 
                 
                   
                     
                       y 
                       1 
                     
                     − 
                     
                       y 
                       3 
                     
                   
                 
               
             
           
         
       
     
     
       
         
           
             
               y 
               i 
             
             = 
             
               ε 
               i 
             
             + 
             
               
                 
                   G 
                   0 
                 
               
               
                 j 
                 ω 
                 
                   C 
                   0 
                 
               
             
             
               ε 
               i 
               
                 5 
                 / 
                 2 
               
             
           
         
       
     
     Here, ρ 1  is a reflection coefficient determined as a result of a measurement of the first reference substance, ρ 2  is a reflection coefficient determined as a result of a measurement of the second reference substance, and ρ 3  is a reflection coefficient determined as a result of a measurement of the third reference substance. Further, ρ 4  is a reflection coefficient determined as a result of a measurement of a target substance. 
     Further, y 1  is a linear mapping of admittance determined as a result of a measurement of the first reference substance having a permittivity of ε 1 , y 2  is a linear mapping of admittance determined as a result of a measurement of the first reference substance having a permittivity of ε 2 , and y 3  is a linear mapping of admittance determined as a result of a measurement of the first reference substance having a permittivity of ε 3 . Further, y 4  is a linear mapping of admittance determined as a result of a measurement of the measurement object  150  having a permittivity of ε 4 . G o  denotes a characteristic impedance of a portion of each of the probes projecting outside with respect to the detection end. 
     The permittivity of the measurement object  150  is calculated by using the first reference substance, the second reference substance, and the third reference substance, each of which has a known permittivity, as calibration standards. Air, solid, liquid metal, water, or an organic solvent such as alcohol is usable as the calibration standards. 
     Here, the dielectric spectroscopic measurement apparatus (the second process unit  132 ) according to the embodiment provides an effective permittivity model for the object  150  as a material including a dielectric body  151   a  and a dielectric body  152   a  as illustrated in  FIG.  4   . Here, the effective permittivity is determinable by measurement. In  FIG.  4   , dp1 is a penetration depth of the first probe  101  and dp2 is a penetration depth of the second probe  102 . The penetration depth refers to a distance required for the electric field strength in  FIG.  3    to decay to a certain value, for example, any value in a range from 10% to 30%. ε 1  is an actual measured value determined by measurement using the first probe  101 . Further, ε s  is a permittivity of the second medium  152  in  FIG.  1   . It should be noted that in a typical coaxial probe method, with respect to an effective permittivity of the measurement object  150 , the measurement object  150  is assumed to be a dielectric body of a material that is uniform at the measured permittivity. 
     A model of admittance for measuring a two-layer medium including the above-described two types of dielectric bodies can be represented by, for example, Expression (6) below (see Reference Literature 1). Expression (6): 
     
       
         
           
             
               
                 
                   Y 
                   
                     m 
                     o 
                     d 
                     e 
                     l 
                   
                 
                 
                   
                     
                       ε 
                       s 
                     
                   
                 
                 = 
                 
                   
                     j 
                     
                       k 
                       0 
                     
                     ε 
                     1 
                   
                   
                     
                       
                         
                           ε 
                           c 
                         
                       
                     
                     I 
                     n 
                     
                       
                         
                           b 
                           a 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           ∫ 
                           0 
                           ∞ 
                         
                         
                           
                             1 
                             
                               
                                 γ 
                                 
                                   p 
                                   1 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           
                             
                               J 
                               0 
                             
                             
                               
                                 ζ 
                                 a 
                               
                             
                             − 
                             
                               J 
                               0 
                             
                             
                               
                                 ζ 
                                 b 
                               
                             
                           
                         
                       
                       2 
                     
                   
                   ζ 
                 
                 d 
                 ζ 
               
             
             
               
                 + 
                 
                   
                     
                       ∫ 
                       0 
                       ∞ 
                     
                     
                       
                         1 
                         
                           
                             γ 
                             1 
                           
                         
                       
                     
                   
                 
                 
                   
                     2 
                     
                       
                         
                           ε 
                           s 
                         
                         
                           γ 
                           1 
                         
                         − 
                         
                           ε 
                           s 
                         
                         
                           γ 
                           s 
                         
                       
                     
                     
                       e 
                       
                         − 
                         2 
                         
                           γ 
                           1 
                         
                         d 
                         
                           p 
                           1 
                         
                       
                     
                   
                   
                     
                       
                         
                           ε 
                           s 
                         
                         
                           γ 
                           1 
                         
                         + 
                         
                           ε 
                           1 
                         
                         
                           γ 
                           s 
                         
                       
                     
                     − 
                     
                       
                         
                           ε 
                           s 
                         
                         
                           γ 
                           1 
                         
                         − 
                         
                           ε 
                           1 
                         
                         
                           γ 
                           s 
                         
                       
                     
                     
                       e 
                       
                         − 
                         2 
                         
                           γ 
                           1 
                         
                         d 
                         
                           p 
                           1 
                         
                       
                     
                   
                 
                 
                   
                     
                       
                         
                           
                             
                               
                                 
                                   J 
                                   0 
                                 
                                 
                                   
                                     ζ 
                                     a 
                                   
                                 
                                 − 
                                 
                                   J 
                                   0 
                                 
                                 
                                   
                                     ζ 
                                     b 
                                   
                                 
                               
                             
                           
                           2 
                         
                       
                       ζ 
                     
                     d 
                     ζ 
                   
                 
               
             
           
         
       
     
     In Expression (6), ε c  is a permittivity of an insulation body of the coaxial line, k o  is a wave number of a measurement frequency, ε 1  and γ 1  are a permittivity and a propagation constant of the outer-layer-side dielectric body, ε s  and γ s  are a permittivity and a propagation constant of the deep-layer-side dielectric body, J o (x) is a o-order Bessel function, and ζ is a variable with Hankel transform. Further, the penetration depth dp1 of the first probe  101  is designed to be larger than a thickness of the first medium  151 . This causes an influence of the permittivity and thickness of the outer layer, or first medium  151 , to be encompassed in the permittivity ε 1  determined by measurement using the first probe  101 , which makes it possible to treat the dielectric body  152   a  in the effective permittivity model illustrated in  FIG.  4 A  as having the same permittivity as the second medium  152 . 
     It should be noted that a model of admittance for measuring a two-layer medium including the above-described two types of dielectric bodies can also be represented by, for example, Expression (7) below (see Reference Literature 1). It should be noted that in Expression (7), M is a decay rate of a strength of the coaxial probe. Further, Expression (8) is used for an evaluation function. ε meas  is a measured effective permittivity. Expressions (7) and (8): 
     
       
         
           
             
               
                 
                   C 
                   
                     m 
                     o 
                     d 
                     e 
                     l 
                   
                 
                 = 
                 
                   C 
                   f 
                 
                 + 
                 
                   ε 
                   1 
                 
                 
                   C 
                   0 
                 
                 + 
                 
                   
                     
                       ε 
                       s 
                     
                     − 
                     
                       ε 
                       1 
                     
                   
                 
                 
                   C 
                   0 
                 
                 
                   e 
                   
                     
                       
                         
                             
                           
                             _ 
                             d 
                             p 
                             1 
                           
                         
                       
                       M 
                     
                   
                 
               
             
             
               
                 
                   C 
                   
                     m 
                     o 
                     d 
                     e 
                     l 
                   
                 
                 - 
                 
                   C 
                   
                     m 
                     e 
                     a 
                     s 
                     u 
                     r 
                     e 
                     d 
                   
                 
                 = 
                 
                   C 
                   f 
                 
                 + 
                 
                   ε 
                   1 
                 
                 
                   C 
                   0 
                 
                 + 
                 
                   
                     
                       ε 
                       s 
                     
                   
                 
               
             
           
         
       
     
     
       
         
           
             
               
                 − 
                 
                   ε 
                   1 
                 
               
             
             
               C 
               0 
             
             
               e 
               
                 
                   
                     _ 
                     d 
                     p 
                     1 
                   
                   M 
                 
               
             
             ∼ 
             
               
                 
                   C 
                   f 
                 
                 + 
                 
                   ε 
                   
                     m 
                     e 
                     a 
                     s 
                   
                 
                 
                   C 
                   0 
                 
               
             
             = 
             0 
           
         
       
     
     Next, description will be made on a dielectric spectroscopic measurement method according to an embodiment of the present invention with reference to  FIG.  5   . This measurement method is a method to determine the permittivity ε s  of the second medium  152  of a measurement object, in which the first medium  151  on the outer-layer side that is thinner than the penetration length of the first probe  101  and the second medium  152  on the deep-layer side relative to the first medium  151  are stacked on each other, by a dielectric spectroscopic method using the first probe  101  and the second probe  102 . 
     First, in Step S 101 , a measurement surface, or outer surface, of the measurement object  150  (the first medium  151 ) is subjected to calibration so that the outer surface serves as a boundary surface between the probe and the measurement target. As a material having a known permittivity, air, metal, or pure water is used as a standard sample, thereby obtaining data for calibration. In a case where metal is not used as the standard sample, two types of organic solvents such as alcohol may be used instead. 
     Next, in Step S 102 , measurement using the first probe  101  and measurement using the second probe  102  are performed. 
     Next, in Step S 103 , the first process unit  131  determines the actual measured value of permittivity of the first medium  151  from a measurement result measured by the high-frequency measurement unit  134  through the measurement of the measurement object  150  using the first probe  101 . Further, the first process unit  131  determines the actual measured value Y measured  of admittance at the detection end  102   a  of the second probe  102  from a measurement result measured by the high-frequency measurement unit  134  through the measurement of the measurement object  150  using the second probe  102  (a first step). 
     Next, in Step S 104 , with use of a model of admittance at the detection end  102   a  of the second probe  102  with a permittivity ε 1  of the first medium  151  and a permittivity ε s  of the second medium  152 , the second process unit  132  determines a model value Y model  of admittance at the detection end  102   a  of the second probe  102  with an assumption that the permittivity ε 1  is the actual measured value of permittivity and the permittivity ε s  is a variable (a second step). The model of admittance can be a model represented by, for example, Expression (6). 
     Next, in Step S 105 , the permittivity ε s  of the second medium  152  is determined by an inverse problem analysis where the actual measured value Y measured  and the model value Y model  become equal (a third step). 
     A dielectric spectroscopic spectrum can be obtained by repeatedly performing the above-described Step S 101  to Step S 105  for a number of times corresponding to predetermined frequency points. 
       FIG.  6    illustrates a result of an actual measurement by the above-described measurement method. The measurement object  150  includes a polyethylene sheet as the first medium  151  and normal saline as the second medium  152 . In  FIG.  5   , a solid line represents the actual measured value Y measured  determined by the actual measurement and a dotted line represents the model value Y model  determined with Expression (6) as a model. It is demonstrated that the admittance at the detection end  102   a  of the second probe  102  is successfully expressed with accuracy by the model value Y model  with Expression (6) as the model. 
     It should be noted that a measurement instrument in a dielectric spectroscopic measurement apparatus according to the above-described embodiment may be provided by computer equipment including a CPU (Central Processing Unit), a main storage, an external storage, a network connection apparatus, etc. so that the CPU is caused to work in accordance with a program developed in the main storage (run the program), thereby implementing the above-described functions (the dielectric spectroscopic measurement method). The above-described program is a program for a computer to perform the dielectric spectroscopic measurement method described in the above-described embodiment. Further, the functions may be distributed among a plurality of pieces of computer equipment. 
     Further, the measurement instrument in the dielectric spectroscopic measurement apparatus according to the above-described embodiment may include a programmable logic device (PLD) such as an FPGA (field-programmable gate array). For example, logic elements of the FPGA may be provided with a first process unit, a second process unit, a third process unit, and a fourth process unit as individual circuits, thereby being able to function as a measurement instrument. The first process unit, the second process unit, the third process unit, and the fourth process unit can each be written in the FPGA with a predetermined writing apparatus connected. Further, the writing apparatus connected to the FPGA enables the above-described circuits written in the FPGA to be seen. 
     As described hereinbefore, according to embodiments of the present invention, the use of the first probe and the second probe, which has a longer penetration length than the first probe, enables a multilayer measurement target to be accurately measured by a dielectric spectroscopy method using a coaxial probe. 
     It should be noted that embodiments of the present invention are not limited to the exemplary embodiments described hereinbefore and it is obvious that a lot of modifications and combinations are achievable by a person having ordinary skill in the art within the technical scope of the present invention. 
     Reference Literature 1: Kok Yeow You, “RF Coaxial Slot Radiators: Modeling, Measurements, and Applications”, ISBN: 9781608078226.  
     
       
         
           
               
               
             
               
                 Reference Signs List 
               
             
            
               
                 
                   101 
                 
                 First probe 
               
               
                 
                   101 
                   a 
                 
                 Detection end 
               
               
                 
                   102 
                 
                 Second probe 
               
               
                 
                   102 
                   a 
                 
                 Detection end 
               
               
                 
                   103 
                 
                 Measurement Instrement 
               
               
                 
                   111 
                 
                 Outer conductor 
               
               
                 
                   112 
                 
                 Inner conductor 
               
               
                 
                   113 
                 
                 Dielectric layer 
               
               
                 
                   114 
                 
                 Fringe 
               
               
                 
                   121 
                 
                 Outer conductor 
               
               
                 
                   122 
                 
                 Inner conductor 
               
               
                 
                   123 
                 
                 Dielectric layer 
               
               
                 
                   124 
                 
                 Fringe 
               
               
                 
                   131 
                 
                 First process unit 
               
               
                 
                   132 
                 
                 Second process unit 
               
               
                 
                   133 
                 
                 Third process unit 
               
               
                 
                   134 
                 
                 High-frequency measurement unit 
               
               
                 
                   135 
                 
                 Display unit 
               
               
                 
                   150 
                 
                 Measurement object 
               
               
                 
                   151 
                 
                 First medium 
               
               
                 
                   152 
                 
                 Second medium