# Splitting light into colors, mathematical expression (fourier transforms)

I am trying to solve a problem that includes a function of the light hitting a certain area. My question is, how would I change a function $G(x)$ of photons hitting a certain area to include just photons of a certain wavelength, say red light. I feel like this could be accomplished using a Fourier transform and de Broglie's law, but I'm not sure. Can someone please help, just for a general Gaussian function $G(x)$?

More information: Basically, given a function that gives the number of photons hitting a certain area, I want a mathematical way to determine how many of those photons are of a specific frequency (such as red light).

G(x) is defined as the integral in a gaussian slit experiment (that is, a double slit experiment with the path integral of a gaussian probability) such as in Feynmann's Path Integrals and Quantum Mechanics or in arxiv.org/pdf/1110.2346.

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Can you give more detail on your problem? As it stands I can't figure out what you're trying to do. –  user2963 Dec 5 '12 at 3:09
If you know the frequency of the light you want, just use a band pass filter en.wikipedia.org/wiki/Band-pass_filter on the original dataset. –  tpg2114 Dec 5 '12 at 4:27
It doesn't sound like filtering or fourier transforms are at all relevant here. Just multiply (total number of photons) * (fraction of photons that are red) = (number of red photons). [The filtering or fourier transforms would be used if you only knew the electric field as a function of time, but it doesn't sound like that's the case. It sounds like you know the rate of photons as a function of position.] Don't make a simple thing complicated! –  Steve B Dec 5 '12 at 14:05
@tpg2114 Thanks for the response. This is what I want to do, but I want to know a way to do it mathematically, not with a device –  James Yu-tai Dec 5 '12 at 22:51
@Steve B Thanks for the response. How do you determine mathematically the "fraction of photons that are red?" Also, what do you mean by the "electric field as a function of time?" –  James Yu-tai Dec 5 '12 at 22:53