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Assume we want to measure how stable an interferometer is. We send two ultrashort pulses (left figure), delayed by the fixed time $\Delta t=T$ relative to each other, into a spectrometer to observe an interference pattern (middle figure). The distance between the chosen two peaks in this interferometric pattern is $2\pi/T$. Now we want to measure how stable this pattern is over a long-term period (many hours), i.e. how much it moves around (left or right) in the frequency domain over time. In other words, we want to obtain a graph similar to what is schematically shown in the right figure. How should this properly done?

I assume that one should choose a peak in the spectrum (e.g. red dot in the middle figure), and plot its shifts over time. I also reckon though that the shifts will have different sensitivity depending on the time delay between pulses (due to the reciprocal dependence indicted in the middle figure). Then, how should it be properly taken into account? Any other nuances that should be taken into account?

enter image description here

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This is really an engineering problem, not a physics problem. Nevertheless there are probably half a dozen if not more ways to skin the cat.

The way I would do it is capture the initial spectrum as a baseline. Then at regular intervals, seconds, minutes hours (you should decide based on the expected spectrum of your interferometer disturbance source) capture another spectrum and calculate the cross correlation. This would provide you with an overall measure of spectral stability relative to your baseline.

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  • $\begingroup$ Thanks! In this cas, how would I extract how much radians the fringes shifted by? $\endgroup$ Feb 27, 2020 at 6:33
  • $\begingroup$ Your cross correlation should be with respect to radian frequency, but it's a function of frequency shift. The maximum of the the cross correlation would be a good metric. $\endgroup$
    – docscience
    Feb 27, 2020 at 19:48
  • $\begingroup$ So then I just convert the frequency shift into the number of waves expressed in the units of the carrier wavelength multiplied by $2\pi$, right? So, for the sake of an example, if the frequency shift will correspond to the wavelength shift equal to the central wavelength of the spectrum, then the y-axis value would be $2\pi$? $\endgroup$ Feb 28, 2020 at 13:08
  • $\begingroup$ ... yes if that's what you're after. $\endgroup$
    – docscience
    Feb 28, 2020 at 17:26

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