Direct optical observations of surface thermal motions at sub-shot noise levels

We measure spectral properties of surface thermal fluctuations of liquids, solids, complex fluids and biological matter using light scattering methods. The random thermal fluctuations are delineated from random noise at sub-shot noise levels. The principle behind this extraction, which is quite general and is not limited to surface measurements, is explained. An optical lever is used to measure the spectrum of fluctuations in the inclinations of surfaces down to $\sim 10^{-17}\rm rad^2/Hz$ at $1\sim10 \mu$W optical intensity, corresponding to $\sim 10^{-29} \rm m^2/\rm Hz$ in the vertical displacement, in the frequency range $1{\rm}\rm kHz\sim10 MHz$. The dynamical evolution of the surface properties is also investigated. The measurement requires only a short amount of time and is essentially passive, so that it can be applied to a wide variety of surfaces.