# Measuring translational, rotational, and vibrational dynamics with digital holographic microscopy

## Methodology

In this paper, the authors use in-line digital holographic micrscopy (DHM) to probe the dynamics of interacting micron sized colloidal particles. By using an exact model for multiple particle scattering, the authors are able to achieve nanometer resolution in 3 dimensions over both short (ms) and long (s) timescales.

*Imaging*

The authors use a DHM microscope which is shown below in Figure 1. A 685 nm laser is collected by a 10x collection lens, and collimated by a high NA condenser so that the unscattered light is collimated at the sample plane. They image the sample with a water immersion objective (to redeuce spherical abberation), followed bya tube lense and a monochrome camera. Their set-up is further equipped with an optical trap that is solely used for particle isolation and cluster forming.

*Experimental*

*Theory*

For an arbirarily shaped colloidal particle, diffusion can be fully described by a rotational (D_r) and translational diffusisivity (D_t) tensor. For an axisymettric body, Dt can be fully described by D|| and D_|_ for motional paralell and perpendicular to the axis of rotational symettry (respectively).

For particles that are in equillibrium with the fluid (ie densities are matched so there is no deterministic drift), the interaction potential U(r) of two particles can be easily obtained from the Boltzmann distribution, namely <math>P(r)\propto e^{-U(r)/k_bT}</math>

IN PROGRESS

Holograms of a single particle contain

## Keywords

Digital Holographic Microscopy, Brownian Motion, Optical Trap, Interaction Potential, Boltzmann Distribution