# Fraunhofer diffraction and Fourier Transform

1. May 25, 2010

### bcjochim07

1. The problem statement, all variables and given/known data
In lab, I obtained a single slit diffraction pattern and recorded an image of it. The slit width is known to be 0.000134 m. We are supposed to compare our experimentally-obtained diffraction pattern to the result of taking a Discrete Fourier Transform of the aperture in MATLAB.

2. Relevant equations

3. The attempt at a solution

Here is my MATLAB code:

E=[-100000:25:100000];
F=zeros(1,8001);
for n=1:8001;
F(n)=0.000134*(sin(pi*0.000134*E(n)))/(pi*0.000134*E(n));
end;
plot(E,abs(F))

Here, E corresponds to spatial frequency (m^-1). I'm plotting the power spectrum as a function of E. Qualitatively, the MATLAB result looks very similar to the experimental result, as one would expect. But can I compare the width of the central maxima? At first, I thought that maybe taking the reciprocal of the width of the central max. of the MATLAB result would yield the same width as I saw experimentally. But then again, I'm not taking into account the wavelength of the light in the code. How could I modify my code to give an accurate comparison?

2. May 25, 2010

### bcjochim07

I guess I'm technically not taking the Discrete Fourier transform but just plotting what I know the Fourier transform should be based on F.T. pairs.

3. May 26, 2010

### bcjochim07

Any suggestions?