Patent Publication Number: US-10775163-B2

Title: Dielectric boundary surface estimation device

Description:
TECHNICAL FIELD 
     The present invention relates to a dielectric boundary surface estimation device for estimating a boundary surface between dielectrics having different dielectric constants using a radio wave. 
     BACKGROUND ART 
     A dielectric boundary surface estimation device is used for measuring a state in a dielectric utilizing a property of passing through an inside of the dielectric which is a property of a radio wave as a wave, and contributes to cancer detection and diagnosis of material deterioration of a construction. 
     In the cavity thickness investigating method disclosed in following Patent Literature 1, scattering from a dielectric boundary point is observed with S transform processing. In this method, not a boundary surface but only a boundary point of a dielectric is measured. As for measurement of the shape of a dielectric, an ellipsoid is simply applied on a basis of visual observation irrespective of S transform and no special plan is devised. 
     CITATION LIST 
     Patent Literatures 
     Patent Literature 1: JP 2015-197398 A (FIG. 37) 
     SUMMARY OF INVENTION 
     Technical Problem 
     In the cavity thickness investigating method disclosed in Patent Literature 1 described above, there is a problem that only presence of a boundary point which is a part of a dielectric boundary surface can be grasped, and it is not possible to grasp the boundary surface. In addition, in Patent Literature 1 described above, as a method of estimating the shape of a dielectric, a method of applying an ellipsoid in an environment in which synthetic aperture processing is not applied is adopted, so that the width of a dielectric boundary surface in the horizontal direction cannot be accurately estimated. 
     The present invention has been made to solve the above-described problem and an object thereof is to accurately estimate a width and a thickness of a dielectric boundary surface. 
     Solution to Problem 
     A dielectric boundary surface estimation device according to the present invention includes: a pre-processing wave data obtained by observing a dielectric by a radar device; a three-dimensional synthetic aperture processor performing three-dimensional synthetic aperture processing on the wave data pre-processed by the pre-processor; and a dielectric boundary surface estimator estimating a boundary surface between areas having different dielectric constants to each other using the wave data on which the three-dimensional synthetic aperture processing is performed by the three-dimensional synthetic aperture processor and calculating a width and a thickness of the boundary surface. The dielectric boundary surface estimator performs division of the wave data on which the three-dimensional synthetic aperture processor performs the three-dimensional synthetic aperture processing in an azimuth direction and an elevation direction, performs three-dimensional inverse Fourier transform on the wave data after the division, extracts a trajectory of low-dielectric constant side boundary points corresponding to a low-dielectric constant side boundary surface and a trajectory of high-dielectric constant side boundary points corresponding to a high-dielectric constant side boundary surface out of the wave data after the division subjected to the three-dimensional inverse Fourier transform, calculates a width of the high-dielectric constant side boundary surface or a width of the low-dielectric constant side boundary surface from the trajectory of the high-dielectric constant side boundary points or the trajectory of the low-dielectric constant side boundary points, and calculates a thickness from the high-dielectric constant side boundary surface to the low-dielectric constant side boundary surface on a basis of a distance between a center of the trajectory of the high-dielectric constant side boundary points and a center of the trajectory of the low-dielectric constant side boundary points. 
     Advantageous Effects of Invention 
     According to the present invention, since a dielectric boundary surface is estimated using wave data subjected to three-dimensional synthetic aperture processing, it is possible to accurately estimate a width and a thickness of a dielectric boundary surface. 
    
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         FIG. 1  is a functional configuration diagram illustrating a configuration example of a dielectric boundary surface estimation device according to a first embodiment of the present invention; 
         FIG. 2  is a hardware configuration diagram illustrating a configuration example of the dielectric boundary surface estimation device according to the first embodiment of the present invention; 
         FIG. 3  is a flowchart illustrating processing performed by a pre-processing unit of the dielectric boundary surface estimation device according to the first embodiment of the present invention; 
         FIG. 4  is a flowchart illustrating processing performed by a three-dimensional synthetic aperture processing unit of the dielectric boundary surface estimation device according to the first embodiment of the present invention; 
         FIG. 5  is a flowchart illustrating processing performed by a dielectric boundary surface estimating unit of the dielectric boundary surface estimation device according to the first embodiment of the present invention; 
         FIG. 6  is a view illustrating a situation when wave data stored in a wave data storing unit of the dielectric boundary surface estimation device according to the first embodiment of the present invention is observed; 
         FIG. 7  is a view illustrating the wave data after the three-dimensional synthetic aperture processing unit of the dielectric boundary surface estimation device according to the first embodiment of the present invention performed three-dimensional synthetic aperture processing; 
         FIG. 8  is a view illustrating the wave data after the dielectric boundary surface estimating unit of the dielectric boundary surface estimation device according to the first embodiment of the present invention performed aperture division and three-dimensional inverse fast Fourier transform; 
         FIG. 9  is a view illustrating a high-dielectric constant side boundary point trajectory and low-dielectric constant side boundary point trajectory calculated by the dielectric boundary surface estimating unit of the dielectric boundary surface estimation device according to the first embodiment of the present invention; and 
         FIG. 10  is a view illustrating widths and a thickness of a dielectric boundary surface calculated by the dielectric boundary surface estimating unit of the dielectric boundary surface estimation device according to the first embodiment of the present invention. 
     
    
    
     DESCRIPTION OF EMBODIMENTS 
     Hereinafter, in order to describe the present invention in more detail, some embodiments for carrying out the present invention will be described with reference to the accompanying drawings. 
     First Embodiment 
       FIG. 1  is a functional configuration diagram illustrating a configuration example of a dielectric boundary surface estimation device  100  according to a first embodiment of the present invention. As illustrated in the drawing, the dielectric boundary surface estimation device  100  includes a wave data storing unit  200 , a pre-processing unit  300 , a three-dimensional synthetic aperture processing unit  400 , a dielectric boundary surface estimating unit  500 , and an output data storing unit  600 . 
       FIG. 2  is a hardware configuration diagram illustrating a configuration example of the dielectric boundary surface estimation device  100  according to the first embodiment of the present invention. The wave data storing unit  200  in the dielectric boundary surface estimation device  100  is a storage device for input  11  and the output data storing unit  600  is a storage device for output  14 . The storage device for input  11 , the storage device for output  14 , and a memory  13  to be described later may be a nonvolatile or volatile semiconductor device memory such as a random access memory (RAM), a read only memory (ROM), an erasable programmable ROM (EPROM), a flash memory, and a solid state drive (SSD), or a magnetic storage medium such as a hard disk and a flexible disk. 
     The functions of the pre-processing unit  300 , the three-dimensional synthetic aperture processing unit  400 , and the dielectric boundary surface estimating unit  500  in the dielectric boundary surface estimation device  100  are implemented by a processing circuit. That is, the dielectric boundary surface estimation device  100  is provided with the processing circuit for reading wave data stored in the storage device for input  11 , pre-processing the wave data, performing three-dimensional synthetic aperture processing on the pre-processed wave data, estimating a boundary surface of the dielectric using the wave data subjected to the three-dimensional synthetic aperture processing, calculating a width and a thickness of the boundary surface, and storing the calculation result in the storage device for output  14 . The processing circuit is a processor  12  which executes a program stored in the memory  13 . The processor  12  is also referred to as a central processing unit (CPU), an arithmetic device, a microprocessor, a microcomputer or the like. 
     The functions of the pre-processing unit  300 , the three-dimensional synthetic aperture processing unit  400 , and the dielectric boundary surface estimating unit  500  are implemented by software, firmware, or a combination of software and firmware. The software or firmware is described as a program and stored in the memory  13 . The processor  12  implements the functions of the respective units by reading and executing the program stored in the memory  13 . That is, the dielectric boundary surface estimation device  100  includes the memory  13  for storing the program which is executed by the processor  12  to eventually execute steps illustrated in  FIGS. 3 to 5  to be described later. It may also be said that the program allows a computer to execute a procedure or a method of each of the pre-processing unit  300 , the three-dimensional synthetic aperture processing unit  400 , and the dielectric boundary surface estimating unit  500 . 
     Next, operation of the dielectric boundary surface estimation device  100  according to the first embodiment of the present invention will be described. 
       FIG. 3  is a flowchart illustrating processing of the pre-processing unit  300 .  FIG. 4  is a flowchart illustrating processing of the three-dimensional synthetic aperture processing unit  400 .  FIG. 5  is a flowchart illustrating processing of the dielectric boundary surface estimating unit  500 . 
       FIG. 6  is a view illustrating a situation when wave data stored in the wave data storing unit  200  is obtained by observation. Hereinafter, an operation example of the dielectric boundary surface estimation device  100  is described using the wave data obtained by observation in the situation illustrated in  FIG. 6 . 
     In an observation system  20  in  FIG. 6 , the dielectric to be observed is a space  31  having a dielectric constant of ε r,1 . In the space  31 , a space  32  having a relatively low dielectric constant of ε r,2  (ε r,2 &lt;ε r,1 ) is included. Transceivers  21  to  24  of a radar device are arranged in a space  30  having a dielectric constant of ε r,0  (ε r,0 &lt;ε r,1 ) lower than the dielectric constant ε r,1  of the space  31 . 
     The transceivers  21  to  24  transmit pulse-shaped radio waves  25  to  28  toward the space  31 . The transmitted radio waves  25  to  28  are scattered on a dielectric boundary surface  33  which is a boundary between the spaces  30  and  31  having different dielectric constants and on a dielectric boundary surface  34  which is a boundary between the spaces  31  and  32  having different dielectric constants. The transceivers  21  to  24  receive the radio waves  25  to  28  scattered on the dielectric boundary surfaces  33  and  34 . The radar device converts scattering information of the radio waves from the dielectric boundary surfaces  33  and  34  into three-dimensional voxel data on the basis of transmission/reception results of the radio waves  25  to  28  and outputs the voxel data to the dielectric boundary surface estimation device  100 . 
     The above observation may be performed by a plurality of transceivers  21  to  24 , or may be performed by moving one transceiver to the respective positions shown as the positions of the transceivers  21  to  24 . 
     Hereinafter, scattering information obtained by observing an inside of the dielectric by the radar device is referred to as wave data s(x, y, t). Note that x∈[−L x /2, L x /2] is defined as the azimuth direction, y∈[−L y /2, L y /2] is defined as the elevation direction, and t∈[0, T PRI ] is defined as the slant range direction. L x  represents an aperture length in the azimuth direction, L y  represents an aperture length in the elevation direction, and T PRI  represents a pulse repetition cycle. 
     The wave data storing unit  200  receives and stores wave data obtained by observing the inside of the dielectric by the radar device. The wave data stored in the wave data storing unit  200  is transferred to the pre-processing unit  300 . 
     The pre-processing unit  300  performs the pre-processing at steps ST 301  to ST 303  to be described below in detail on the wave data transferred from the wave data storing unit  200  and outputs the processed wave data to the three-dimensional synthetic aperture processing unit  400 . 
     At step ST 301 , the pre-processing unit  300  removes the DC component in the range direction from the wave data. Specifically, the pre-processing unit  300  estimates a range direction DC component s 0,t (x, y, t) in, consideration of a case where the wave data s(x, y, t) transferred from the wave data storing unit  200  is fixed decimal data and the like in accordance with equation (1). Subsequently, the pre-processing unit  300  obtains wave data s Dc,t (x, y, t) from which the range direction DC component is removed by removing the range direction DC component s 0,t (x, y, t) from the wave data s(x, y, t) using equation (2). 
     
       
         
           
             
               
                 
                   
                     
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     At step ST 302 , the pre-processing unit  300  removes the DC component in the azimuth direction from the wave data. Specifically, the pre-processing unit  300  estimates the azimuth direction DC component s 0,t,x (x, y, t) in consideration of a case where the wave data s(x, y, t) transferred from the wave data storing unit  200  is fixed decimal data and the like in accordance with equation (3). Subsequently, the pre-processing unit  300  obtains wave data s DC,t,x (x, y, t) from which the DC components in the azimuth direction and the range direction are removed by removing the azimuth direction DC component s 0,t,x (x, y, t) from the wave data s DC,t (x, y, t) from which the range direction DC component is removed using equation (4). 
     
       
         
           
             
               
                 
                   
                     
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     At step ST 303 , the pre-processing unit  300  corrects attenuation of the wave when the radio wave passes through the inside of the dielectric by performing contrast correction on the wave data. Specifically, the pre-processing unit  300  defines a contrast correction function s CNT,x (x, y, t) in consideration of the attenuation, of the wave as shown in equation (5) for the wave data s DC,t,x (x, y, t) in which the DC, components in the azimuth direction and the range direction are removed. Subsequently, the pre-processing unit  300  performs the contrast correction on the wave data s DC,t,x (x, y, t) using equation (6) and obtains wave data s PRE (x, y, t) after the contrast correction. The pre-processing unit  300  outputs the pre-processed wave data s PRE (x, y, t) to the three-dimensional synthetic aperture processing unit  400 . 
     
       
         
           
             
               
                 
                   
                     
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     The three-dimensional synthetic aperture processing unit  400  performs three-dimensional synthetic aperture processing at steps ST 401  to ST 403  to be described in detail below on the pre-processed wave data output, by the pre-processing unit  300  and outputs the wave data after the processing to the dielectric boundary surface estimating unit  500 . 
     At step ST 401 , the three-dimensional synthetic aperture processing unit  400  performs three-dimensional Fourier transform for converting the pre-processed wave data into wave data in a frequency space. Specifically, the three-dimensional synthetic aperture processing, unit  400  performs three-dimensional fast Fourier transform (FFT) on the pre-processed wave data s PRE (X, y, t) received from the pre-processing unit  300  using equation (7) and converts the pre-processed wave data s PRE (x, y, t) into wave data s PRE (k x , k y , k) in the frequency space. 
     
       
         
           
             
               
                 
                   
                     
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     At step ST 402 , the three-dimensional synthetic aperture processing unit  400  performs azimuth bulk compression to compensate a wave surface of the wave data to a spherical shape in the frequency space. Specifically, the three-dimensional synthetic aperture processing unit  400  obtains wave data S BULK (k x , k y , k) in which the wave surface of the wave data S PRE (k x , k y , k) is made uniform and the image of the wave data is focused by performs the azimuth bulk compression by calculating equation (8) on the wave data S PRE (k x , k y , k) after the three-dimensional FFT and.
 
 S   BULK ( k   x   ,k   y   ,k )= S   PRE ( k   x   ,k   y   ,k )·exp( jR   0   k   z )  (8)
 
     Note that, in equation (8), R 0  represents a focus distance, and is defined by, for example, equation (9-1). k z  represents a wave number defined by equation (9-2). 
     
       
         
           
             
               
                 
                   
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     At step ST 403 , the three-dimensional synthetic aperture processing unit  400  performs Stolt interpolation to orthogonalize a wave transmitting direction 2k of the wave data in the x axis and the y axis. The direction of a wave number vector means the wave surface and the wave transmitting direction, and the wave number vector 2k generally observed by the radar device can be orthogonally decomposed into the wave number vectors (k x , k y , k z ), for example. This means that equation (9-3) described above holds from the Pythagorean theorem. Although the wave number vectors k z  and k y  can be immediately defined to be orthogonal to each other on an antenna surface, k z  in equation (9-2) described above cannot be observed directly and can be observed only as a function of (k x , k y , 2k). Processing of interpolation using equation (9-2) described above from (k x , k y , 2k) to (k x , k y , k z ) to make a state in which the observable and definable wave numbers (k x , k y , 2k) are orthogonal is the Stolt interpolation processing. Specifically, the three-dimensional synthetic aperture processing unit  400  obtains wave data S SAR (k x , k y , k z ) after the three-dimensional synthetic aperture processing by performing the Stolt interpolation to convert the wave number space (k x , k y , k) to (k x , k y , k z ) for the wave data S BULK (k x , k y , k) after the azimuth bulk compression. The three-dimensional synthetic aperture processing unit  400  outputs the wave data S SAR (k x , k y , k z ) after the three-dimensional synthetic aperture processing to the dielectric boundary surface estimating unit  500 . 
       FIG. 7  is a view illustrating wave data  40  after the three-dimensional synthetic aperture processing is performed by the three-dimensional synthetic aperture processing unit  400 , that is, the wave data S SAR (k x , k y , k z ). The high-dielectric constant side boundary  41  in the wave data  40  after the three-dimensional synthetic aperture processing corresponds to the dielectric boundary surface  33  in the observation system  20  illustrated in  FIG. 6 . The low-dielectric constant side boundary  42  in the wave data  40  after the three-dimensional synthetic aperture processing corresponds to the dielectric boundary surface  34  in the observation system  20  illustrated in  FIG. 6 . 
     Note that the three-dimensional synthetic aperture processing performed by the three-dimensional synthetic aperture processing unit  400  is a technology well-known as the Omega-K system. 
     In addition, as an interpolation method performed at step  403 , other than the Stolt interpolation described above as an example, sinc interpolation or cubic interpolation may be used, for example. 
     The dielectric boundary surface estimating unit  500  calculates the width and the thickness of the dielectric boundary surface by performing dielectric boundary surface estimation processing at steps ST 501  to ST 509  to be described below in detail on the wave data after the three-dimensional synthetic aperture processing output by the three-dimensional synthetic aperture processing unit  400 , and outputs the calculation result to the output data storing unit  600 . 
     At step ST 501 , the dielectric boundary surface estimating unit  500  decomposes the dielectric boundary surface into a dielectric boundary point group by dividing the wave data after the three-dimensional synthetic aperture processing into a plurality of observation units from respective phase centers. Hereinafter, a process at step ST 501  is referred to as aperture division. Specifically, the dielectric boundary surface estimating unit  500  obtains wave data per aperture S SAR,n,m (k x , k y , k z ) after aperture division by dividing the wave data S SAR (k z , k y , k z ) after the three-dimensional synthetic aperture processing received from the three-dimensional synthetic aperture processing unit  400  by N in the azimuth direction and by M in the elevation direction using equation (10). 
     
       
         
           
             
               
                 
                   
                     
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     Note that, in equation (10), K Bcut,x  represents an effective bandwidth in the azimuth direction after the aperture division, and K Bcut,y  represents an effective bandwidth in the elevation direction after the aperture division. Further, n∈[0,N−1] and m∈[0,M−1]. Δk x  represents a pitch width of the aperture division in the azimuth direction and Δk y  represents a pitch width of the aperture division in the elevation direction. 
     When the bandwidths after the aperture division are represented by K B,x  and K B,y , the relationship in equation (11) is satisfied among K B,x , K B,y , K Bcut,x , and K Bcut,y .
 
 K   B,x   =K   Bcut,x +( N− 1)Δ k   x ,
 
 K   B,y   =K   Bcut,y +( M− 1)Δ k   y   (11)
 
     At step ST 502 , the dielectric boundary surface estimating unit  500  performs three-dimensional inverse Fourier transform which converts the wave data per aperture obtained by the aperture division from a frequency domain to a spatial domain. Specifically, the dielectric boundary surface estimating unit  500  performs three-dimensional inverse, fast Fourier transform (IFFT) on the wave data per aperture S SAR,n,m (k x , k y , k z ) using equation (12) and converts it into wave data per aperture I SAR,n,m (x, y, z) of the spatial domain. 
     
       
         
           
             
               
                 
                   
                     
                       I 
                       
                         SAR 
                         , 
                         n 
                         , 
                         m 
                       
                     
                     ⁡ 
                     
                       ( 
                       
                         x 
                         , 
                         y 
                         , 
                         z 
                       
                       ) 
                     
                   
                   = 
                   
                     
                       1 
                       
                         
                           ( 
                           
                             2 
                             ⁢ 
                             
                                 
                             
                             ⁢ 
                             π 
                           
                           ) 
                         
                         3 
                       
                     
                     ⁢ 
                     
                       ∫ 
                       
                         ∫ 
                         
                           ∫ 
                           
                             
                               
                                 S 
                                 
                                   SAR 
                                   , 
                                   n 
                                   , 
                                   m 
                                 
                               
                               ⁡ 
                               
                                 ( 
                                 
                                   
                                     k 
                                     x 
                                   
                                   , 
                                   
                                     k 
                                     y 
                                   
                                   , 
                                   
                                     k 
                                     z 
                                   
                                 
                                 ) 
                               
                             
                             ⁢ 
                             
                               exp 
                               ⁡ 
                               
                                 [ 
                                 
                                   j 
                                   ⁡ 
                                   
                                     ( 
                                     
                                       
                                         
                                           k 
                                           x 
                                         
                                         ⁢ 
                                         x 
                                       
                                       + 
                                       
                                         
                                           k 
                                           y 
                                         
                                         ⁢ 
                                         y 
                                       
                                       + 
                                       
                                         
                                           k 
                                           z 
                                         
                                         ⁢ 
                                         z 
                                       
                                     
                                     ) 
                                   
                                 
                                 ] 
                               
                             
                             ⁢ 
                             
                               dk 
                               x 
                             
                             ⁢ 
                             
                               dk 
                               y 
                             
                             ⁢ 
                             
                               dk 
                               z 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
       FIG. 8  is a view illustrating wave data  50  after the dielectric boundary surface estimating unit  500  performs the aperture division and the three-dimensional IFFF. By the processes at steps ST 501  and ST 502 , a portion of the high-dielectric constant side boundary  41  in the wave data  40  after the three-dimensional synthetic aperture processing illustrated in  FIG. 7  is divided into a plurality of local small areas as shown in wave data per aperture  51 A to  51 G illustrated in  FIG. 8 . The wave, data per aperture  51 A to  51 G can be referred to as the dielectric boundary point group obtained by decomposing the dielectric boundary surface  33 . Similarly, a portion of the low-dielectric constant side boundary  42  in the wave data  40  after the three-dimensional synthetic aperture processing illustrated in  FIG. 7  is divided into, a plurality of local small areas as shown in wave data per aperture  52 A to  52 D illustrated in  FIG. 8 . The wave data per aperture  52 A to  52 D can be referred to as the dielectric boundary point group obtained by decomposing the dielectric boundary surface  34 . 
     Note that, although not illustrated in  FIG. 8  a portion other than the wave data Per aperture  51 A to  51 G and  52 A to  52 D in the wave data  50  is also divided into a plurality of local small areas as is the case with the wave data per aperture  51 A to  51 G and  52 A to  52 D. 
     At step ST 503 , the dielectric boundary surface estimating unit  500  extracts high-dielectric constant side boundary points exceeding a predetermined threshold from the wave data per aperture. At subsequent step ST 505 , the dielectric boundary surface estimating unit  500  records the extracted high-dielectric constant side boundary point group as a high-dielectric constant side boundary point trajectory. 
     Specifically, the dielectric boundary surface estimating unit  500  obtains a set of local maximum points of the wave data per aperture exceeding a threshold T, that is, a high-dielectric constant side boundary point trajectory (x top,n,m , y top,n,m , z top,n,m ) by calculating equation (13) for high-dielectric constant side boundary surface candidates {x + , y + |Re[I SAR,n,m (x, y, z)]≥T} exceeding the threshold T out of the wave data per aperture. 
     Note that, in next equation (13) and equation (14) to be described below, T represents a predetermined threshold, which is a value corresponding to signal power of the radio wave scattered on the dielectric boundary surface  33  on the high-dielectric constant side. 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         x 
                         
                           top 
                           , 
                           n 
                           , 
                           m 
                         
                       
                       , 
                       
                         y 
                         
                           top 
                           , 
                           n 
                           , 
                           m 
                         
                       
                       , 
                       
                         z 
                         
                           top 
                           , 
                           n 
                           , 
                           m 
                         
                       
                     
                     ) 
                   
                   = 
                   
                     arg 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         max 
                         
                           
                             x 
                             + 
                           
                           , 
                           
                             y 
                             + 
                           
                           , 
                           z 
                         
                       
                       ⁢ 
                       
                         Re 
                         [ 
                         
                           
                             I 
                             
                               SAR 
                               , 
                               n 
                               , 
                               m 
                             
                           
                           ⁡ 
                           
                             ( 
                             
                               
                                 x 
                                 + 
                               
                               , 
                               
                                 y 
                                 + 
                               
                               , 
                               z 
                             
                             ) 
                           
                         
                         ] 
                       
                     
                   
                 
               
               
                 
                   ( 
                   13 
                   ) 
                 
               
             
           
         
       
     
     At step ST 504 , the dielectric boundary surface estimating unit  500  extracts low-dielectric constant side boundary points smaller than the predetermined threshold from the wave data per aperture. At subsequent step ST 506 , the dielectric boundary surface estimating unit  500  records the extracted low-dielectric constant side boundary point group as a low-dielectric constant side boundary point trajectory. 
     Specifically, the dielectric boundary surface estimating unit  500  obtains a set of local minimum points of the wave data per aperture smaller than the threshold T, that is, a low-dielectric constant side boundary point trajectory (X btm,n,m , Y btm,n,m , Z btm,n,m ) by calculating equation (14) for low-dielectric constant side boundary surface candidates {x − , y − |Re[I SAR,n,m (x, y, z)]&lt;T} smaller than the threshold T out of the wave data per aperture. 
     
       
         
           
             
               
                 
                   
                     ( 
                     
                       
                         x 
                         
                           btm 
                           , 
                           n 
                           , 
                           m 
                         
                       
                       , 
                       
                         y 
                         
                           btm 
                           , 
                           n 
                           , 
                           m 
                         
                       
                       , 
                       
                         z 
                         
                           btm 
                           , 
                           n 
                           , 
                           m 
                         
                       
                     
                     ) 
                   
                   = 
                   
                     arg 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     
                       
                         min 
                         
                           x… 
                           , 
                           y… 
                           , 
                           z 
                         
                       
                       ⁢ 
                       
                         Re 
                         ⁡ 
                         
                           [ 
                           
                             
                               I 
                               
                                 SAR 
                                 , 
                                 n 
                                 , 
                                 m 
                               
                             
                             ⁡ 
                             
                               ( 
                               
                                 
                                   x 
                                   - 
                                 
                                 , 
                                 
                                   y 
                                   - 
                                 
                                 , 
                                 z 
                               
                               ) 
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   14 
                   ) 
                 
               
             
           
         
       
     
       FIG. 9  is a view illustrating a high-dielectric constant side boundary point trajectory  51  and a low-dielectric constant side boundary point trajectory  52  calculated by the dielectric boundary surface estimating unit  500 . The high-dielectric constant side boundary point trajectory  51  is a set of local maximum points of the wave data per aperture  51 A to  51 G on the high-dielectric constant side exceeding the threshold. The low-dielectric constant side boundary point trajectory  52  is a set of local minimum points of the wave data per aperture  52 A to  52 D on the low-dielectric constant side smaller than the threshold. 
     Note that, in  FIG. 9 , the local maximum points of the wave data per aperture  51 A to  51 G and the local minimum points of the wave data per aperture  52 A to  52 D are indicated by the intersection of each of “x” marks. 
     At step ST 507 , the dielectric boundary surface estimating unit  500  calculates the width of the dielectric boundary surface using the obtained high-dielectric constant side boundary point trajectory  51 . Specifically, the dielectric boundary surface estimating unit  500  calculates the widths (Δx, Δy) of the dielectric boundary surface from the high-dielectric constant side boundary point trajectory  51  using equations (15) and (16). 
     
       
         
           
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     x 
                   
                   = 
                   
                     
                       max 
                       m 
                     
                     ⁢ 
                     
                       [ 
                       
                         
                           
                             max 
                             n 
                           
                           ⁢ 
                           
                             x 
                             
                               top 
                               , 
                               n 
                               , 
                               m 
                             
                           
                         
                         - 
                         
                           
                             min 
                             n 
                           
                           ⁢ 
                           
                             x 
                             
                               top 
                               , 
                               n 
                               , 
                               m 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   15 
                   ) 
                 
               
             
             
               
                 
                   
                     Δ 
                     ⁢ 
                     
                         
                     
                     ⁢ 
                     y 
                   
                   = 
                   
                     
                       max 
                       m 
                     
                     ⁢ 
                     
                       [ 
                       
                         
                           
                             max 
                             n 
                           
                           ⁢ 
                           
                             y 
                             
                               top 
                               , 
                               n 
                               , 
                               m 
                             
                           
                         
                         - 
                         
                           
                             min 
                             n 
                           
                           ⁢ 
                           
                             y 
                             
                               top 
                               , 
                               n 
                               , 
                               m 
                             
                           
                         
                       
                       ] 
                     
                   
                 
               
               
                 
                   ( 
                   16 
                   ) 
                 
               
             
           
         
       
     
     At step ST 508 , the dielectric boundary surface estimating unit  500  calculates a thickness of a space between the dielectric boundary surfaces using the obtained high-dielectric constant side boundary point trajectory  51  and low-dielectric constant side boundary trajectory  52 . Specifically, the dielectric boundary surface estimating unit  500  calculates the distance from the center of the high-dielectric constant side boundary point trajectory  51  to the center of the low-dielectric constant side boundary point trajectory  52  using equation (17) as a thickness Δz between the dielectric boundary surfaces. 
     
       
         
           
             
               
                 
                   
                     
                       Δ 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       z 
                     
                     = 
                     
                       { 
                       
                         
                           z 
                           
                             btm 
                             , 
                             n 
                             , 
                             m 
                           
                         
                         - 
                         
                           z 
                           
                             top 
                             , 
                             n 
                             , 
                             m 
                           
                         
                       
                       } 
                     
                   
                   ⁢ 
                   
                     
 
                   
                   ⁢ 
                   
                     
                       
                         wherein 
                         ⁢ 
                         
                             
                         
                         ⁢ 
                         n 
                       
                       = 
                       
                         N 
                         2 
                       
                     
                     , 
                     
                       m 
                       = 
                       
                         M 
                         2 
                       
                     
                   
                 
               
               
                 
                   ( 
                   17 
                   ) 
                 
               
             
           
         
       
     
       FIG. 10  is a view illustrating the widths (Δx, Δy) and the thickness Δz of the dielectric boundary surface calculated by the dielectric boundary surface estimating unit  500 . The widths (Δx, Δy) of the dielectric boundary surface indicated by an, arrow in  FIG. 10  correspond to widths of the dielectric boundary surface  34  being the boundary between the space  31  which is the dielectric to be observed and the space  32  included in the space  31  in  FIG. 6 . The thickness Δz between the dielectric boundary surfaces indicated by an arrow in  FIG. 10  corresponds to a thickness of the space  31  from the dielectric boundary surface  33  to the dielectric boundary surface  34  in  FIG. 6 . 
     At step ST 509 , the dielectric boundary surface estimating unit  500  records a calculation result of the widths and the thickness of the dielectric boundary surface. In addition, the dielectric boundary surface estimating unit  500  transfers the recorded calculation result to the output data storing unit  600 . 
     The output data storing unit  600  receives the calculation result of the widths and the thickness of the dielectric boundary surface transferred from the dielectric boundary surface estimating unit  500  and the wave data after the three-dimensional synthetic aperture processing and stores them. The output data storing unit  600  can output the stored calculation result and wave data to the outside. 
     The output data storing unit  600  may receive the wave data S SAR (k x , k y , k z ) after the three-dimensional synthetic aperture processing directly from the three-dimensional synthetic aperture processing unit  400  or via the dielectric boundary surface estimating unit  500 . 
     As is apparent from above, according to the first embodiment, a dielectric boundary surface estimation device  100  includes: a pre-processing unit  300  pre-processing wave data obtained by observing a dielectric by a radar device; a three-dimensional synthetic aperture processing unit  400  performing three-dimensional synthetic aperture processing on the wave data pre-processed by the pre-processing unit  300 ; and a dielectric boundary surface estimating unit  500  estimating a boundary surface between areas having different dielectric constants to each other using the wave data on which the three-dimensional synthetic aperture processing is performed by the three-dimensional synthetic aperture processing unit  400  and calculating a width and a thickness of the boundary surface. Since the position of the dielectric boundary surface is estimated using the wave data subjected to the three-dimensional synthetic aperture processing, it is possible to estimate the widths and the thickness of the dielectric boundary surface with high accuracy. 
     Further, according to the first embodiment, the dielectric boundary surface estimating unit  500  performs division of the wave data on which the three-dimensional synthetic aperture processing unit  400  performs the three-dimensional synthetic aperture processing in an azimuth direction and an elevation direction, performs three-dimensional inverse Fourier transform on the wave data after the division, extracts a low-dielectric constant side boundary point trajectory  52  corresponding to a dielectric boundary surface  34  on the low-dielectric constant side and a high-dielectric constant side boundary point trajectory  51  corresponding to a dielectric boundary surface  33  on the high-dielectric constant side out of the wave data after the division subjected to the three-dimensional inverse Fourier transform, calculates a width of the dielectric boundary surface  34  on the low-dielectric constant side from the high-dielectric constant side boundary point trajectory  51 , and calculates a thickness from the dielectric boundary surface  33  on the high-dielectric constant side to the dielectric boundary surface  34  on the low-dielectric constant side on a basis of a distance between a center of the high-dielectric constant side boundary point trajectory  51  and a center of the low-dielectric constant side boundary point trajectory  52 . By dividing the dielectric boundary surface into trajectories of points on the basis of the aperture division processing, position estimation accuracy of the dielectric boundary surface can be further improved. 
     Note that, although the space  31  including the space  32  of the lower-dielectric constant inside is the observation target in the first embodiment, the dielectric boundary surface estimation device  100  may also be used when the dielectric constant of the space  32  is higher than the dielectric constant of the space  31 . 
     Even when the dielectric constant of the space  32  is higher than the dielectric constant of the space  31 , that is, when ε r,0 &lt;ε r,1 &lt;ε r,2  is satisfied, the dielectric boundary surface estimation device  100  can calculate the widths and the thickness of the dielectric boundary surface by performing the processing illustrated in  FIGS. 3 to 5 . In this calculation, in the description at steps ST 503  to ST 508 , “high-dielectric constant side” is replaced with “low-dielectric constant side”, “low-dielectric constant side” is replaced with “high-dielectric constant side”, “local maximum point” is replaced with “local minimum point”, and “local minimum point” is replaced with “local maximum point”. 
     Thus, when the dielectric constant of the space  32  is higher than the dielectric constant of the space  31 , the dielectric boundary surface  33  in  FIG. 6  is on the low-dielectric constant side and the dielectric boundary surface  34  is on the high-dielectric constant side. When calculating the widths of the dielectric boundary surface  34  which is the boundary between the space  31  and the space  32 , the dielectric boundary surface estimating unit  500  uses the set of the local minimum points of the wave data per aperture which are smaller than the threshold, that is, the low-dielectric constant side boundary point trajectory. 
     According to the first embodiment, the three-dimensional synthetic aperture processing unit  400  performs three-dimensional Fourier transform on the wave data pre-processed by the pre-processing unit  300 , performs azimuth bulk compression to make a wave surface uniform on the wave data subjected to the three-dimensional Fourier transform, and thereafter performs interpolation to orthogonalize a wave transmitting direction. By improving locality of the wave by the three-dimensional synthetic aperture processing, the position estimation accuracy of the dielectric boundary surface can be further improved. 
     Also, according to the first embodiment, the pre-processing unit  300  removes a DC component in a range direction and a DC component in an azimuth direction from the wave data obtained by observing the dielectric by the radar device, and corrects attenuation of the wave when passing through the dielectric. It is possible to further improve the position estimation accuracy of the dielectric boundary surface by removing the DC component of the wave data and correcting contrast. 
     Note that, in the present invention, any component of the embodiment may be modified, or any component of the embodiment may be omitted without departing from the scope of the invention. 
     For example, in the configuration example in  FIG. 1 , the dielectric boundary surface estimation device  100  is provided with the wave data storing unit  200  and the output data storing unit  600 , but the wave data storing unit  200  and the output data storing unit  600  are not necessarily required. That is, the dielectric boundary surface estimation device  100  may have any configuration as long as it can receive wave data from the outside, calculate the widths and the thickness of a dielectric boundary surface, and output the calculation result to the outside. 
     INDUSTRIAL APPLICABILITY 
     The dielectric boundary surface estimation device according to the present invention calculates the widths and the thickness of a dielectric boundary surface using the wave data subjected to the three-dimensional synthetic aperture processing, so that it is suitable for a dielectric boundary surface estimation device used for detecting cancer, diagnosing material deterioration of a construction and the like. 
     REFERENCE SIGNS LIST 
       11 : Storage device for input,  12 : Processor,  13 : Memory,  14 : Storage device for output,  20 : Observation system,  21  to  24 : Transceiver,  25  to  28 : Radio wave,  30  to  32 : Space,  33 ,  34 : Dielectric boundary surface,  40 ,  50 : Wave data,  41 : High-dielectric constant side boundary,  42 : Low-dielectric constant side boundary,  51 : High-dielectric constant side boundary point trajectory,  52 : Low-dielectric constant side boundary point trajectory,  51 A to  51 G,  52 A to  52 D: Wave data per aperture,  100 : Dielectric boundary surface estimation device,  200 : Wave data storing unit,  300 : Pre-processing unit,  400 : Three-dimensional synthetic aperture processing unit,  500 : Dielectric boundary surface estimating unit,  600 : Output data storing unit.