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function[f1,dx1,dy1,x1,y1]=fresnel(f0,M,N,dx0,dy0,z,lambda) 
global lambda; 
k.=2*pi/lambda; 
du=1./(M*dx0);dv=1./(N*dy0); 
u=ones(N,1)*[0:M/2-1-M/2:-1]*du; 
v=[0:N/2-1-N/2:-1]'*ones(1,M)*dv; 
H=exp(-i*2*pi^2*(u.^2+v.^2)*z/k); 
f1=ifft(fft2(f0).*H); 
dx1=dx0;dy1=dy0; 
x1=ones(N,1)*[-M./2:M/2-1]*dx1; 
y1=[-N/2:N/2-1]*ones(N,1)*dy1; 
 
function[f1,dx1,dy1,x1,y1]=fresnell(f0,M,N,dx0,dy0,z,lambda) 
k=2*pi/lambda; 
x0=ones(N,1)*[-M/2:M/2-1]*dx0; 
y0=[-N/2:N/2-1]'*ones(N\1,M)*dy0; 
g=f0.*exp(i*0.5*k*(x0.^2+y0.^2)/z); 
G=fftshift(fft2(fftshift(g))); 
du=1./(M*dx0);dv=1./(N*dy0); 
dx1=lambda*z*du;dy1=lambda*z*dv; 
x1=ones(N,1)*[-M/2:M/2-1]*dx1; 
y1=[-N/2:N/2-1]'*ones(1,M)*dy1; 
f1=G.*exp(i*0.5*k*(x1.^2+y1.^2)/z); 
f1=f1./(i*lambda*z); 
clear; 
cm=0.01;um=1e-6; 
N=128; 
rx=0*cm*ones(N);ry=0*cm*ones(N);rz=3*ones(N); 
ox=1*cm*ones(N);oy=1*cm*ones(N);oz=2*ones(N); 
hx=2*cm;hy=2*cm; 
dhx=hx/N;dhy=hy/N; 
w=0.63*um; 
k=2*pi/w; 
x=dhx.*(ones(N,1)*[-N/2:N/2-1]); 
y=(dhy.*(ones(N,1)*[-N/2:N/2-1]))'; 
z=0*ones(N); 
d1=sqrt((rx-x).^2+(ry-y).^2+(rz-z).^2); 
d2=sqrt((ox-x).^2+(oy-y).^2+(oz-z).^2); 
ur=exp(i*k*d1)./d1; 
uo=exp(i*k*d2)./d2; 
p=abs(ur+uo).^2; 
p=mat2gray(p); 
figure; 
imshow(p); 
p1=p.*conj(ur); 
for f=1:6; 
    [f1,dx1,dy1,x1,y1]=fresnell(p1,N,N,dhx,dhy,f,w); 
    f1=abs(f1).^2; 
    f1=mat2gray(f1); 
    figure; 
    imshow(f1); 
end 
clear;clc; 
cm=0.01;um=1e-6; 
N=128; 
hx=1*cm;hy=1*cm; 
dhx=hx/N;dhy=dy/N; 
x=dhx.*(ones(N,1)*[-N/2:N/2-1]); 
y=(dhy.*(ones(N,1)*[-N/2:N/2-1]))'; 
p1=imread('anda.bmp'); 
figure;imshow(p1); 
z=4; 
w=0.63*um; 
k=2*pi/w; 
[f,dx1,dy1,x1,y1]=fresnel(p1,N,N,dhx,dhy,z,w); 
sit=pi/6; 
ur=exp(-j*k*y*sin(sit)); 
f1=f+ur; 
f1=abs(f1).^2; 
f1=mat2gray(f1); 
figure;imshow(f1); 
rp1=f1.*conj(ur); 
a=0.002;b=0.3; 
rp1=pure(rp1,a,b,x1,y1); 
[f,dx2,dy2,x2,y2]=fresnel(p1,N,N,dhx,dhy,z,w); 
f2=abs(f2)^2; 
f2=mat2gray(f2); 
figure;imshow(f2); 
 
 
 
clear;clc; 
cm=0.01;mm=0.001;um=1e-6; 
w=0.63*um; 
f=4; 
N=64; 
hx=1*cm;hy=1*cm; 
hdx=hx/N;hdy=hy/N; 
u=hdx.*(ones(N,1)*[-N/2:N/2-1]); 
v=(hdy.*(ones(N,1)*[-N/2:N/2-1]))'; 
A=imread('dot64dot.bmp');M=64; 
rx=1*cm;ry=1*cm; 
rdx=rx/N;rdy=ry/N; 
x1=rdx.*(ones(N,1)*[-N/2:N/2-1]); 
y1=(rdy.*(ones(N,1)*[-N/2:N/2-1]))'; 
r=2*cm/pi; 
xx=x1./r;yy=y1./r; 
x=r*sin(xx);y=r*sin(yy).*cos(xx);z=r*cos(yy).*cos(xx); 
k=1:N;l=1:N;h(k,1)=0; 
f1=(u.*u+v.*v);f1=pi*f1/(w*f*f);o=2*pi/(w*f); 
for k=1:N 
    for l=1:N 
        del=0 
        for m=1:M 
            for n=1:M 
                if A(m,n)~=0 
                     
del=A(m,n)*exp(j*(z(m,n)*f1(k,l)-o*(x(m,n)*u(k,l)+y(m,n)*v(k,l)))); 
                 h(k,l)=h(k,l)+del; 
                end 
            end 
        end 
    end 
end 
save h64r1h1; 
 
clear;clc; 
load h64rdian5.mat; 
dx=0.5*cm;dy=0.5*cm; 
figure;imshow(A); 
ex=exp(j*2*pi*(dx*u+dy*v)/(w*f)); 
h=3+real(h.*ex); 
figure;imshow(h); 
rec=fftshift(fft2(h)); 
rec=mat2gray(rec); 
figure:imshow(rec);