Appendix

      
        MATLAB Function for Processing SAR Data
        
          
        
        
          
        
        
          
        
        
          function img = sar_lin(f,az_lin,iq_lin)
        
        
          
        
        
          
        
        
          % INITIALIZATION
        
        
          
        
        
          R=4*pi*f/3e8;% Transformation of Time Freqeuncy to Spatial Frequency
        
        
          A=pi/180*az_lin;% Transformation of Angle in degree to radians
        
        
          for j=1:147
        
        
          A(j)=A(j)-2*pi;% Adjustment so that all angular values are between 0 and pi
        
        
          end
        
        
          
        
        
          % Initialization of Cartesian Grid
        
        
          X=zeros(1,175);
        
        
          Y=zeros(175,1);
        
        
          for j=1:175
        
        
          X(j)=208+(j-1);
        
        
          Y(j)=208+(j-1);
        
        
          end
        
        
          
        
        
          val=zeros(175);% Initialize the matrix of values in the cartesian grid.
        
        
          
        
        
          
        
        
          
        
        
          
        
        
          % INTERPOLATOR
        
        
          
        
        
          for j=1:175
        
        
          
        
        
          j % Update on how far we are.
        
        
          
        
        
          for k=1:175
        
        
          
        
        
          r=sqrt(X(j)^2+Y(k)^2);
        
        
          a=atan(Y(k)/X(k));
        
        
          
        
        
          if (r>R(1) & r<R(512))
        
        
          
        
        
          % Data index of cartesian point
        
        
          J=ceil((r-R(1))*511/(R(512)-R(1)));
        
        
          K=ceil((a-A(1))*1540/(A(1541)-A(1))); 
        
        
          
        
        
          % Linearly interpolate the cartesian point with its 4 nearest neighbor polar data points.
        
        
          
        
        
          % Interpolate in R
        
        
          v0 = 1/(R(J+1)-R(J)) * ( iq_lin(J,K)*(R(J+1)-r) + iq_lin(J+1,K)*(r-R(J)) );
        
        
          v1 = 1/(R(J+1)-R(J)) * ( iq_lin(J,K+1)*(R(J+1)-r) + iq_lin(J+1,K+1)*(r-R(J)) );
        
        
          
        
        
          % Interpolate in THETA
        
        
          val(j,k) = 1/(A(K+1)-A(K)) * ( v0*(A(K+1)-a) + v1*(a-A(K)) );
        
        
          
        
        
          end
        
        
          
        
        
          end
        
        
          
        
        
          end
        
        
          
        
        
          
        
        
          % Plot the interpolated values
        
        
          figure(1)
        
        
          imagesc(abs(val)); 
        
        
          
        
        
          % Take the 2d inverse DFT to get the image
        
        
          img = ifft2(val);
        
        
          
        
        
          % Plot the image
        
        
          figure(2)
        
        
          imagesc(abs(img));