(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

a light source a(x) is defined by

a(x) = Acos(pi*x/a)[theta(x+(a/2)) -theta(x-(a/2))]

calculate the diffraction pattern I(X)

2. Relevant equations

I(X)=2pi|a^{~}((2pi/(LAMBDA*d))*X)|^{2}

this is the equation for a diffraction pattern on a screen at distance d from a 1D souce

of light with wavelength LAMBDA, where a^{~}(k) is the fourier transform of a(x)

3. The attempt at a solution

using the fourier transform

a^{~}(k) = A/sqrt(2pi)(integrate)[exp^(-ikx) * cos((pi*x)/a)]

(integrating over the range -a/2 to a/2)

i then use euler's method to change cosine term into exponential terms, then simplify to get

= A/2*sqrt(2pi)(integrate)[exp^((i*pi*x)/a)-(ikx)) +exp^(-(i*pi*x)/a)-(ikx))]

(integrating over the range -a/2)

the answer i get once i have simplified wont simplify down to trig terms and so makes no sense when i put the value of a^{~}(k) into the equation for I(X). how can this integral be performed elegantly to give a decent looking answer? any help would be great

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Fourier transform question (optics)

**Physics Forums | Science Articles, Homework Help, Discussion**