Experimental Verification of a Theory of1fNoise in a Model System

Abstract

$\frac{1}{f}$ noise has been predicted for simple physical systems that exhibit certain singularities in the fluctuation weighting function. We have produced a "quasi" singularity in the light-intensity pattern by focusing a laser beam with a cylindrical lens. The spectral density of the light scattered off polystyrene microspheres flowing through this region followed a $\frac{1}{f}$ dependence, as predicted. Other beam patterns gave the predicted noise spectra, including a $\frac{sin{\left(\pi f\tau \right)}^2}{{\left(\pi f\tau \right)}^2}$ spectral shape for flow past a slit.