MATLAB: How to get spatial frequency from FFT

matt j

Hi,
I have got the first graph based on the following code. How can I get the second graph after performing FFT?
I1=0.7;
I2=0.5;
I3=0.3;
L1=200;
L2=170;
n1=1;
n2=1.444;
lam=(1.52:0.0001:1.56);
Q12=(4*pi*n1*L1)./lam;
Q23=(4*pi*n2*L2)./lam;
Q13=Q12+Q23;
I=I1+I2+I3+2*sqrt(I1*I2).*cos(Q12)+2*sqrt(I2*I3).*cos(Q23)+2*sqrt(I1*I3).*cos(Q13);
plot(lam*1000,I)

Best Answer

The Fourier transform neither knows nor cares whether the units of the independent variable are time, space, or anything else. It will do whatever you ask it to do (within limits, of course)
Try this: 
I1=0.7;
I2=0.5;
I3=0.3;
L1=200;
L2=170;
n1=1;
n2=1.444;
lam=(1.52:0.0001:1.56);
Q12=(4*pi*n1*L1)./lam;
Q23=(4*pi*n2*L2)./lam;
Q13=Q12+Q23;
I=I1+I2+I3+2*sqrt(I1*I2).*cos(Q12)+2*sqrt(I2*I3).*cos(Q23)+2*sqrt(I1*I3).*cos(Q13);
figure
plot(lam*1000,I)
L = numel(lam);
Ts = mean(diff(lam));
Fs = 1/Ts;
Fn = Fs/2;
FTI = fft(I)/L;
Fv = linspace(0, 1, fix(L/2)+1)*Fn * 1E-3;
Iv = 1:numel (Fv);
[pks,locs] = findpeaks(abs(FTI(Iv)));
figure
plot(Fv, abs(FTI(Iv)))
xlim([0  0.5])
xlabel('Spatial Frequency (nm^{-1})')
ylabel('Amplitude')
text(Fv(locs), abs(FTI(locs)), sprintfc('Peak %d',(1:numel(locs))), 'HorizontalAlignment','center', 'VerticalAlignment','bottom')
producing:
.
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