# How to implementation DFT (discrete fourier transform) to intensity?

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MOHD on 17 Jun 2014
Edited: Star Strider on 18 Jun 2014
Here I am trying to calculate intensity of Xpolarized light by using DFT (discrete fourier
transform) instead of fft, by using DFT I am getting intensity in 4th quadrant only (Which is
shown in figure (1)). How can I get intensity in total plane. Can some help me in this regard
clear all;
clc;
lose all;
[kx,ky]=meshgrid(-1:2/21:1);
circ=sqrt(kx.^2+ky.^2)<1;
alp=asin(0.95);
k0=1/sin(alp);
kz=sqrt(k0^2-(kx.^2+ky.^2));
GX=sqrt(k0./kz).*((k0*ky.^2+kz.*kx.^2)./(k0*(kx.^2+ky.^2)));
GY=sqrt(k0./kz).*((kz-k0).*kx.*ky)./(k0*(kx.^2+ky.^2));
la=1;
lb=0;
EX=(GX.*la-rot90(GY.*lb, 3));
M=22;
N=22;
F=zeros(22,22);
for Xpx=1:M
for Xpy=1:N
F(Xpx,Xpy)=sum(sum(EX.*exp(1j*2*pi*(((Xpx.*kx)/M)+((Xpy.*ky)/N)))));
end
end
F=F/(M*N);
I1=F.*conj(F);
figure(1)
imagesc(I1),colormap gray;axis image; axis off;

Dishant Arora on 17 Jun 2014
Use the logarithmic scale to image the fourier transform. Fourier transform results in large dynamic range, thereby logarithmic scale makes it easy to see small signal components in the presence of large ones. Probably you can do:
imagesc(log(I))
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Dishant Arora on 18 Jun 2014
Edited: Dishant Arora on 18 Jun 2014
The kx and ky you are using inside the loop for dft calualation, shouldn't they be integers. They need to be indices not spatial coordinates. Make appropriate changes to your code and cross check with built in fft2. I tried and it works for me.