Patent ID: 11967116
Assignee: HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY
Field: Measurement (Instruments)
Classification: CPC G | IPC G

Claim 2:
3. The method of claim 1, wherein Step S2 comprises:
Step S21: converting the polarization cosine characterization equation into a linear form, I
   ⁡
   (
   
    t
    ,
    x
    ,
    y
   
   )
  
  =
  
   
    
     cos
     2
    
    ⁢
       
    t
    *
    
     
      I
      LP
     
     (
     
      x
      ,
      y
     
     )
    
    *
    
     [
     
      
       
        cos
        2
       
       ⁢
          
       θ
       ⁢
          
       
        (
        
         x
         ,
         y
        
        )
       
      
      -
      
       
        sin
        2
       
       ⁢
          
       θ
       ⁢
          
       
        (
        
         x
         ,
         y
        
        )
       
      
     
     ]
    
   
   +
   
    2
    ⁢
       
    cos
    ⁢
       
    t
    ⁢
       
    sin
    ⁢
       
    t
    *
    
     
      I
      LP
     
     (
     
      x
      ,
      y
     
     )
    
    ⁢
       
    sin
    ⁢
       
    θ
    ⁢
       
    
     (
     
      x
      ,
      y
     
     )
    
    ⁢
       
    cos
    ⁢
       
    θ
    ⁢
       
    
     (
     
      x
      ,
      y
     
     )
    
   
   +
   
    
    
     
      [
      
       
        
         I
         NLP
        
        (
        
         x
         ,
         y
        
        )
       
       +
       
        
         
          I
          LP
         
         (
         
          x
          ,
          y
         
         )
        
        *
        
         sin
         2
        
        ⁢
           
        θ
        ⁢
           
        
         (
         
          x
          ,
          y
         
         )
        
       
      
      ]
     
     ,
    
   
  
 

and bringing polarization image data obtained at different polarization angles into the linear form to obtain a matrix equation:, [
   
    
     
      
       
        cos
        2
       
       ⁢
          
       
        t
        1
       
      
     
     
      
       2
       ⁢
          
       sin
       ⁢
          
       
        t
        1
       
       ⁢
          
       cos
       ⁢
          
       
        t
        1
       
      
     
     
      1
     
    
    
     
      
       
        cos
        2
       
       ⁢
          
       
        t
        2
       
      
     
     
      
       2
       ⁢
          
       sin
       ⁢
          
       
        t
        2
       
       ⁢
          
       cos
       ⁢
          
       
        t
        2
       
      
     
     
      1
     
    
    
     
      ⋮
     
     
      ⋮
     
     
       
     
    
    
     
      
       
        cos
        2
       
       ⁢
          
       
        t
        n
       
      
     
     
      
       2
       ⁢
          
       sin
       ⁢
          
       
        t
        n
       
       ⁢
          
       cos
       ⁢
          
       
        t
        n
       
      
     
     
      1
     
    
   
   ]
  
  ⁢
  
   
   
    
     
      [
      
       
        
         
          
           
            I
            LP
           
           (
           
            x
            ,
            y
           
           )
          
          [
          
           
            
             cos
             2
            
            ⁢
               
            θ
            ⁢
               
            
             (
             
              x
              ,
              y
             
             )
            
           
           -
           
            
             sin
             2
            
            ⁢
               
            θ
            ⁢
               
            
             (
             
              x
              ,
              y
             
             )
            
           
          
          ]
         
        
       
       
        
         
          
           
            I
            LP
           
           (
           
            x
            ,
            y
           
           )
          
          ⁢
             
          sin
          ⁢
             
          θ
          ⁢
             
          
           (
           
            x
            ,
            y
           
           )
          
          ⁢
             
          cos
          ⁢
             
          θ
          ⁢
             
          
           (
           
            x
            ,
            y
           
           )
          
         
        
       
       
        
         
          
           
            I
            NLP
           
           (
           
            x
            ,
            y
           
           )
          
          +
          
           
            
             I
             LP
            
            (
            
             x
             ,
             y
            
            )
           
           ⁢
              
           
            sin
            2
           
           ⁢
              
           θ
          
         
        
       
      
      ]
     
     =
     
      [
      
       
        
         
          I
          ⁡
          (
          
           
            t
            1
           
           ,
           x
           ,
           y
          
          )
         
        
       
       
        
         
          I
          ⁡
          (
          
           
            t
            2
           
           ,
           x
           ,
           y
          
          )
         
        
       
       
        
         ⋮
        
       
       
        
         
          I
          ⁡
          (
          
           
            t
            n
           
           ,
           x
           ,
           y
          
          )
         
        
       
      
      ]
     
    
    ,
   
  
 

where t=[t1 t2 . . . tn] represents different polarization angles, an, X
   =
   
    [
    
     
      
       
        
         cos
         2
        
        ⁢
          
        
         t
         1
        
       
      
      
       
        2
        ⁢
           
        sin
        ⁢
           
        
         t
         1
        
        ⁢
           
        cos
        ⁢
           
        
         t
         1
        
       
      
      
       1
      
     
     
      
       
        
         cos
         2
        
        ⁢
           
        
         t
         2
        
       
      
      
       
        2
        ⁢
           
        sin
        ⁢
           
        
         t
         2
        
        ⁢
           
        cos
        ⁢
           
        
         t
         2
        
       
      
      
       1
      
     
     
      
       ⋮
      
      
       ⋮
      
      
       ⋮
      
     
     
      
       
        
         cos
         2
        
        ⁢
           
        
         t
         n
        
       
      
      
       
        2
        ⁢
           
        sin
        ⁢
           
        
         t
         n
        
        ⁢
           
        cos
        ⁢
           
        
         t
         n
        
       
      
      
       1
      
     
    
    ]
   
  
  ,, independent variable matrix in sample data is, β
     ^
    
    (
    
     x
     ,
     y
    
    )
   
   =
   
    [
    
     
      
       
        
         
          I
          LP
         
         (
         
          x
          ,
          y
         
         )
        
        [
        
         
          
           cos
           2
          
          ⁢
             
          θ
          ⁢
             
          
           (
           
            x
            ,
            y
           
           )
          
         
         -
         
          
           sin
           2
          
          ⁢
             
          θ
          ⁢
             
          
           (
           
            x
            ,
            y
           
           )
          
         
        
        ]
       
      
     
     
      
       
        
         
          I
          LP
         
         (
         
          x
          ,
          y
         
         )
        
        ⁢
           
        sin
        ⁢
           
        θ
        ⁢
           
        
         (
         
          x
          ,
          y
         
         )
        
        ⁢
           
        cos
        ⁢
           
        θ
        ⁢
           
        
         (
         
          x
          ,
          y
         
         )
        
       
      
     
     
      
       
        
         
          I
          NLP
         
         (
         
          x
          ,
          y
         
         )
        
        +
        
         
          
           I
           LP
          
          (
          
           x
           ,
           y
          
          )
         
         ⁢
            
         
          sin
          2
         
         ⁢
            
         θ
         ⁢
            
         
          (
          
           x
           ,
           y
          
          )
         
        
       
      
     
    
    ]
   
  
  ,, a coefficient matrix to be solved is a, Y
     ^
    
    (
    
     x
     ,
     y
    
    )
   
   =
   
    [
    
     
      
       
        I
        ⁡
        (
        
         
          t
          1
         
         ,
         x
         ,
         y
        
        )
       
      
     
     
      
       
        I
        ⁡
        (
        
         
          t
          2
         
         ,
         x
         ,
         y
        
        )
       
      
     
     
      
       ⋮
      
     
     
      
       
        I
        ⁡
        (
        
         
          t
          n
         
         ,
         x
         ,
         y
        
        )
       
      
     
    
    ]
   
  
  ,, dependent variable matrix in the sample data and I(ti, x, y) represents an intensity value of a pixel point with coordinates (x, y) in an i-th polarized subimage, where i=1,2, . . . , n;
Step S22: substituting the matrix X and the matrix Ŷ into {circumflex over (β)}(x, y)=(XTX)−1XTŶ(x , y) to compute the coefficient matrix {circumflex over (β)}(x, y) of any pixel point; and
Step S23: solving the parameter matrix [ILP (x, y) INLP(x, y) θ(x, y)] of polarization cosine characterization of any pixel point according to the coefficient matrix {circumflex over (β)}(x, y) to obtain a linear polarization intensity image ILP, a non-linear polarization intensity image INLP, and a polarization angle distribution picture θ of the polarization imaging target.