shows that the primary cause of bead rejection is asymmetric in-plane motion. Experimentally, beads with multiple tethers can be minimized by reducing the concentration of DNA.

Acquisition Time
----------------

The drift-corrected $(x,y)$ trajectories are noisy due to the stochastic Brownian motion of the particle, and are thus filtered using over a particular time window $t$ (usually four seconds). Although analysis methods exist that make no use of this windowing step [@Beausang2007; @beau2007], nevertheless many experiments do use it, and so we investigated its effect on reported bead excursion. Too short a window will increase the noise, leading to broad peaks in the distribution of $\Jrmst$ that make signals from differently sized tethers too difficult to distinguish. Moreover, for short $t$ the bead will not adequately explore its full range of accessible configurations, leading to an underestimate of $\Jrmst$, as we document below. At the other extreme, however, too long a window will result in a loss of temporal resolution.

To determine the optimum TPM window size, we recorded data for 200$\,\sunit$, for several bead sizes and a wide range of tether lengths, then found the mean (${\langle \Jrmst\rangle}$) and standard deviation ($\mathrm{std}_t = \sqrt{\langle
\Jrmst^2 \rangle- \langle \Jrmst \rangle ^2}$) 