Patent ID: 11965735
Assignee: PANASONIC INTELLECTUAL PROPERTY MANAGEMENT CO., LTD.
Field: Measurement (Instruments)
Classification: CPC G | IPC G

Claim 5:
6. The thickness measurement method according to claim 5, wherein
the solution function is represented by Eq. (1):, [
      
       Mathematical
       ⁢
          
       1
      
      ]
     
     ⁢
     

     
      
       T
       ⁡
       (
       
        r
        ,
        t
       
       )
      
      =
      
       A
       ⁢
       
        
         ∑
         
          n
          =
          
           -
           ∞
          
         
         ∞
        
         
        
         
          1
          
           
            
             
              (
              
               r
               
                L
                0
               
              
              )
             
             2
            
            +
            
             4
             ⁢
             
              n
              2
             
             ⁢
             
              B
              2
             
            
           
          
         
         ⁢
         
          exp
          ⁡
          (
          
           
            1
            2
           
           ⁢
           
            
             C
             ⁢
             
              F
              o
             
            
           
           ⁢
           
            
             
              
               (
               
                r
                
                 L
                 0
                
               
               )
              
              2
             
             +
             
              4
              ⁢
              
               n
               2
              
              ⁢
              
               B
               2
              
             
            
           
          
          )
         
        
       
      
     
    
   
   
    
     (
     1
     )
    
   
  
 

where T(r, t) is a temperature [K] of the surface of the measurement object; r is a distance [m] from the heated position on the surface; L0 is an initial value of the thickness [m]; L is the thickness [m] of the inspection object; t is a time [s]; Fo is the Fourier number; and A, B, and C are the respective parameters, and wherein
the three independent parameters A, B, and C are represented by Eqs. (2), (3), and (4), respectively:, [
   
    Mathematical
    ⁢
       
    2
   
   ]
  
  ⁢
  

  
   
    
     
      A
      =
      
       q
       
        2
        ⁢
        π
        ⁢
        k
        ⁢
        
         L
         0
        
       
      
     
    
    
     
      (
      2
      )
     
    
   
   
    
     
      B
      =
      
       L
       
        L
        0
       
      
     
    
    
     
      (
      3
      )
     
    
   
   
    
     
      C
      =
      
       
        α
        0
       
       α
      
     
    
    
     
      (
      4
      )
     
    
   
  
 

where q is a heat quantity [W] per unit time; k is a thermal conductivity [W/(m·K)] of the measurement object; a is a thermal diffusivity [m2/s] of the measurement object; and α0 is an initial value of the thermal diffusivity [m2/s].