We report on our successful real-time measurement of the dynamic frequency-shift of light by particles in Brownian motion through self-mixing laser spectroscopy with extreme optical sensitivity. We show that the changes over time in the non-stationary random walks of small particles suspended in water result in different averaged dynamics when the field of vision for particles seen by the laser beam (scale of the observation) is changed. At a small focal volume of the laser beam, in which the relevant diffusion broadening is observed, the averaged motion which can be represented by the motion of a "virtual" single particle, whose velocity possesses a Gaussian-white property, constitutes stationary fluctuations, featuring random sequences of the Lorentz-type spectrum and double-peaked probability distribution function for displacements.
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