bend, independently of its neighbors. Thus the same Monte Carlo generation just described continues to be valid, except that some sterically forbidden chains must be discarded. Thus our computer code generated many simulated DNA chains and bead orientations in a Boltzmann distribution, applied the steric constraints [@sega06a], and tabulated the resulting values of the distance from the projected bead center to the attachment point. The necessary calculations were coded in *Mathematica* and ran conveniently on a laptop computer.

We chose to compare to experimental data with “safe” values of the window time $t$, so we simply had the code evaluate the RMS value of this distance. (For a procedure valid for any $t$, see the Supplement to [@Towles2008].) We also applied a correction to this theoretical result, to account for the bead’s motion during the rather long shutter time (see the following subsection). shows that an *a priori* calculation of the expected motion matches the data fairly well, with a value of persistence length consistent with others’ experiments; there were no other fitting parameters.

Blurring Effect
---------------

![\[fig:exposure\][RMS bead excursion as a function of camera shutter time in milliseconds. *Dots:* Experimental data. Each dot represents about $20$ different observed beads, 