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[Yuzurihara, Yamamura]

Abstract

Assumption

This noise was caused by the scattered light.
This noise followed the model in the above paper (https://iopscience.iop.org/article/10.1088/0264-9381/27/19/194011).
The motion of the scatterer was a single vibration.

Then, the parameters of the motion were

Amplitude: 14 [um]
Frequency: 0.42 [Hz]

Details

By focusing on the 10 seconds from 3:30:00 (UTC), we focused on the structure of the finest oscillation.
The plot of Q-transform (Fig.1) was similar to Fig.4 in the paper, so we assumed the noise came from scattered light.
From eq.(3) in the paper, $f_{\mathrm{fringe}} = \left | \frac{2v}{\lambda}\right |$ , the frequency of the noise corresponds to the absolute value of the velocity of the scatterer, and the velocity calculated from data is shown in Fig.2.
This figure shows that the maximum velocity of the scatterer was about 37 [um/s] and the period was about 2.4 [s]. Thus, the frequency was 0.42 [Hz]

Lastly, we assumed that the motion of the scatterer was a single vibration. In this case, the displacement x(t) can be written as

$x(t) = A \, \cos \omega t$ .

Then, the velocity is

$v(t) = -A\omega \, \sin \omega t$ ,

which means the maximum velocity $v_{\mathrm{max}} = A\omega$ . Therefore,

$A = \frac{v_{\mathrm{max}}}{\omega} = 37\times \frac{2.4}{2\pi}\,\,\,\,[\mathrm{um/s}] \simeq 14 \,\,\,\, [\mathrm{um}].$