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I am building white-light Michaelson interferometer and I am registering interference in frequency domain via spectrometer. I read an article, where the same is done (just Mach-Zender interferometer) and it is said, that Fourier trasform gives direct access to absolute path-length difference:

But if we apply Fourier transform to spectra (x axis is frequency in Hz), Fourier transform will gives us something in seconds (1/Hz), not in meters. My question is, how it is done here? Is "seconds" axis multiplied by c (light speed), or something different is applied? What relation is used here?

Article reference: Attosecond beamline with actively stabilized and spatially separated beam paths M. Huppert, I. Jordan, and H. J. Wörner http://dx.doi.org/10.1063/1.4937623

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  • $\begingroup$ could you provide a reference for the article? $\endgroup$ Apr 19, 2021 at 10:36
  • $\begingroup$ Yes, I should have added reference to main question too. Attosecond beamline with actively stabilized and spatially separated beam paths M. Huppert, I. Jordan, and H. J. Wörner dx.doi.org/10.1063/1.4937623 $\endgroup$ Apr 20, 2021 at 16:35

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Yes, the fact that light travels at speed $c$ is implicit in the conversions between units here. What you’re actually measuring is an interferogram with $x$ (the mirror position) as the independent axis. Then to convert to frequency, you’ll need to include $c$ in your calculation. And don’t forget that in a Michelson interferometer, a change of mirror position $x$ corresponds to a change in light path length of $2x$!

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  • $\begingroup$ Thank you for your comment. Just day after my question I uploaded my modulated spectra to MatLAB and wrote simple FFT code. Changed wavelength axis to frequency by dividing c by wavelength, did FFT and I got FFT of spectra vs time. I multiplied time axis again by c and got distance in meters. And the center of modulation frequency peak gave me direct absolute path difference, which was, like you said, double mirror position. $\endgroup$ Apr 20, 2021 at 17:07
  • $\begingroup$ @VytautasSirautas nice work! $\endgroup$
    – Gilbert
    Apr 23, 2021 at 4:48

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