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Is mixed light the same as interfered light?

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Hey all!

I'm building a simple low cost Fourier Transform Infrared Spectroscope as a summer project. for those unaware, the process involves a Michelson-style interferometer which takes a coherent source and splits it. One ray is reflected directly back whereas the other ray has a path difference introduced by a mirror at a different distance. The mirror is moved by small amounts and the combined and interfered light is passed through the sample. on the other side the signal has an FFT algorithm applied to it and a plot of wavelength vs. absorbance can be recovered.

My question is about light. I was planning to use an RGB LED or a series of IR LEDs of different wavelengths and change their brightness like so:

http://www.youtube.com/watch?v=63dEOtYOpy8

Is mixing different wavelengths of light the same as interfering light? is there any chance that I could avoid this complex system of mirrors and go for LEDs instead?

Thanks!

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