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What do we know about optical signal processing based on Fourier transform?

I tried and searched around this subject, but I could not find any relative article about it. Please help me find a proper answer.

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You could take the Fourier transform of the interference pattern over time with a moving mirror in a Michaelson interferometer to get the wavelength of the light. Or taking the Fourier transform of other interference patterns to get various parameters. The Fourier transform is also used to get a THz spectrum from a probe beam. I'm sure there are other examples.

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