The effect of integration time on fluctuation measurements: calibrating an optical trap in the presence of motion blur

Dynamical instrument limitations, such as finite detection bandwidth, do not simply add statistical errors to fluctuation measurements, but can create significant systematic biases that affect the measurement of steady-state properties. Such effects must be considered when calibrating ultra-sensitive force probes by analyzing the observed Brownian fluctuations. In this article, we present a novel method for extracting the true spring constant and diffusion coefficient of a harmonically confined Brownian particle that extends the standard equipartition and power spectrum techniques to account for video-image motion blur. These results are confirmed both numerically with a Brownian dynamics simulation, and experimentally with laser optical tweezers.