Dynamic light scattering from an optically trapped microsphere

Using a single microscope objective lens to optically trap, illuminate, and collect backscattered light of a dielectric microsphere, we measure the temporal-intensity-autocorrelation functions (ACFs), and intensity profiles to obtain the trap stiffness and friction coefficient of the bead. This is an interesting study of an harmonically bound Brownian particle, with nanometer resolution. We extend the work of Bar-Ziv et al. [Phys. Rev. Lett. 78, 154 (1997)] to more general situations allowing for the use of our simpler geometry in other applications. As examples, we present measurements of the parallel Stokes friction coefficient on the trapped bead as a function of its distance from a surface and the entropic force of a single $\lambda -\mathrm{DNA}$ molecule.