five_point.m

implement of IFSAR using matlab

clc; clear;
% frequency settings
c=3e8;
f0=5e9;                          % central frequency=5GHz 
k0=2*pi*f0/c;
BW=5e8;                          %  frequency=1G-9G
Nf=401;
df=BW/(Nf-1);
f=linspace(f0-BW/2,f0+BW/2,Nf);
k=2*pi*f/c;
% frequency settings

% target and antenna location
deta=5;
R0=1000;
Ri=[-9,-6,-3,0,3,6,9]+R0;
Zi=[1,3,5,7,9,11,13]; 
sigmai=[1,2,3,4,5,6,7];
Nx=length(sigmai);
% target and antenna location
r1=sqrt(Ri.^2+(-deta/2-Zi).^2);
r2=sqrt(Ri.^2+(deta/2-Zi).^2);
dr=r1-r2;

figure(1);stem((Ri-R0),Zi,'*'); grid on; title('original target'); xlabel('(Ri-R0)/m'); ylabel('z/m'); axis([-10 10 0 20]);
figure(2); stem(Zi,dr,'*'); title('dr-z'); xlabel('z/m'); ylabel('(r2-r1)/m'); grid on;

Es1=ones(1,Nf);
Es2=Es1;
for m=1:Nf
    Es1(m)=0; Es2(m)=0;
    for n=1:Nx             % number of target point
        Et1=sigmai(n)*exp(-j*k(m)*2*r1(n));
        Es1(m)=Es1(m)+Et1;
        Et2=sigmai(n)*exp(-j*k(m)*(r1(n)+r2(n)));
        Es2(m)=Es2(m)+Et2;
    end
end      

figure(3);plot(abs(Es1)); grid on; title('scattering field'); xlabel('index'); ylabel('Es');  

et1=fftshift(ifft(Es1));
et2=fftshift(ifft(Es2));

% %dx=c/(2*BW);                                           scale the axis
% dk=4*pi*df/c;
% xrange=1/(dk/2/pi);
% dx=xrange/(Nf-1);   % it is the same as "dx=c/(2*BW);
% x=-xrange/2:dx:xrange/2;                              % scale the axis

figure(4); plot(abs(et1)); grid on; axis tight; title('range profile1'); xlabel('x/m'); ylabel('et1'); axis([250 400 0 10]);
figure(5); plot(abs(et2)); grid on; axis tight; title('range profile2'); xlabel('x/m'); ylabel('et2'); axis([250 400 0 10]);


et12=conj(et1).*(et2);       % r2-r1=deta*z/R0
figure(6); plot(abs(et12)); grid on; axis tight; title('range profile12'); xlabel('x/m'); ylabel('et12'); axis([250 400 0 50]);

wraptheta=angle(et12(305:10:365));
unwraptheta=unwrap(wraptheta);
Rdiff=unwraptheta/k0;        % r2-r1=deta*z/R0
zmeasure=Rdiff*R0/deta;

figure(7); stem(wraptheta); title('wraped phase');
figure(8); stem(unwraptheta); title('unwraped phase');

figure(9);stem(Ri,zmeasure); ylabel('z/m');grid on; axis tight; title('hight of the target'); axis([980 1020 0 20]);