Fig. 2.

Measured and predicted SNR for two tethered, 860-nm microspheres in traps of equal stiffness as a function of the DNA stiffness. The data and predictions are scaled by the square-root of the bandwidth divided by the step size and thus correspond to the SNR for a 1-nm step on a 1-Hz bandwidth. The SNR measured in the optimal coordinate (red squares) (also the difference coordinate) increases linearly with DNA stiffness, whereas the SNR measured in the single-trap coordinate (green diamonds) saturates. To reflect the uncertainty in the experimental parameters, the predicted SNR (Eqs. 3 and 8) are plotted as shaded, 1-σ confidence intervals. The observed spread in the data is dominated not by measurement error but by the inherent stochasticity in finite measurements of spatial resolution. Disagreement between measured and predicted SNR at high DNA stiffness results from systematic errors due to nonlinearities in the traps at high force. Data from six DNA–microsphere dumbbells are plotted, with one of three data points displayed.