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I am using a Michelson interferometer with the interferogram recorded on a CMOS sensor. I have taken a video of the fringes moving when a displacement of 50 $\mu m$ is imposed to one of the mirrors. The frame rate is 17.9980 and it is already the maximum I can have.

For a 50 $\mu m$ displacement I should see around 79 fringes passing on the sensor, as each fringe that passes corresponds to one full wavelength (632.8 nm). However, I cannot obtain clear "peaks" that allow me to identify if a fringe is moving.

In the picture you can see the frame with the fringes (top left) and the signal in the central pixel column (top right) for each frame. Then, I transformed the signals using FFT in Matlab, and I obtained the spatial frequency (always the same, so it should be correct) and the phase. Theoretically, I should be able to extract the displacement in two consecutive frames checking the phase difference, so that $$\Delta x = \frac{\lambda}{2} \frac{1}{2\pi}\Delta\phi$$ and the total displacement being the sum of the $\Delta x$ for each couple of frames. Alternatively, I thought that I could extract the displacements looking at the integral of the signal $$\Delta S_k = S_k - S_0 $$, which is the difference between the signal at the $k$-frame and the initial signal at frame $0$. When the two signals are in phase, the integral of the difference signal should be close to zero, while when the two signals are not in phase the integral increase to a maximum when the $\Delta \phi=\pi$ (bottom right)

enter image description here

In the following picture there is the wrapped phase (top), unwrapped phase (centre) at the main frequency, and the integral of the difference signal at each frame (bottom). Imposing a 50 $\mu m$ in the same direction, the sign of $Delta \phi$ should be always the same, but apparently it is not. As you can see, from the difference signal the peaks are not easy to determine, there are "double peaks" and small peaks. Theoretically, I should find 79 peaks but I got more. enter image description here

Is there an easier way to count fringes? I guess that the peaks would be easier to identify if I move the mirrors more slowly?

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  • $\begingroup$ The frequency of the fringes is always the same because if your movement is perfectly translational, then the interference pattern only moves, but the frequency is the same. I am very confused with all of this, it's hard to really understand the whole thing (too much information, in a small post). Why don't you first try to record a very slow movement and analyse the picture in an orthogonal direction to the fringes and not diagonally (about 30° from vertical in your picture), and first count the actual fringe movement (so, track a fringe across the sensor) and compare to single pixel signal. $\endgroup$
    – José Andrade
    Commented Mar 4, 2021 at 13:59
  • $\begingroup$ (and btw, 50µm of movement of your mirror, should be 158 fringes as the path is doubled: 50µm one direction + 50µm back direction=100µm total beam path change) $\endgroup$
    – José Andrade
    Commented Mar 4, 2021 at 14:13
  • $\begingroup$ I think you are working far too hard. Just take the raw intensity data and set a threshold which unambiguously defines a true peak vs. noise (or smooth the data via spline functions). Then just count the peaks. DFTs and all that are not needed. $\endgroup$
    – Carl Witthoft
    Commented Mar 4, 2021 at 14:57
  • $\begingroup$ @JoséAndrade you're abosolutely right about the double path, my mistake. I am using a translational mirror mount with a manual knob with 1 micron resolution, I reckon it's not easy to be accurate with manual devices. I am monitoring the differnece of intensity between signals, so for instance if I expect 158 fringe-transitions I should have 158 distinct peaks, does it make sense? $\endgroup$
    – Gianluca
    Commented Mar 4, 2021 at 15:19
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    $\begingroup$ analyse a single pixel data, not a row first. Plot a single pixel over your movie time, do analysis from there first. slowly build it up to a second dimension later and only after you got those mastered, go on to analyse the 3 dimensional set with displacement and tilt change. I might be wrong, but I guess you also have to 0 pad your data to increase resolution in frequency space. $\endgroup$
    – José Andrade
    Commented Mar 4, 2021 at 15:45

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