# White light interferometer

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

• could you provide a reference for the article? Commented Apr 19, 2021 at 10:36
• 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 Commented Apr 20, 2021 at 16:35

## 1 Answer

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 $$2x$$!

• 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. Commented Apr 20, 2021 at 17:07
• @VytautasSirautas nice work! Commented Apr 23, 2021 at 4:48