= Motion blur
<Motion blur> arises when a detector averages changing image positions during a finite exposure rather than recording an instantaneous position. For a stationary harmonic optical trap with position variance $k_BT/k$ and relaxation time $\tau$, rectangular exposure of duration $W$ reduces that variance by the factor $2[\alpha-1+e^{-\alpha}]/\alpha^2$, where $\alpha=W/\tau$. Integrating the exponential position covariance over both exposure times proves this formula. Ignoring the reduction makes a naive equipartition stiffness estimate too large.<The effect of integration time on fluctuation measurements: calibrating an optical trap in the presence of motion blur by Wesley P. Wong and others>[§II, equations (12)–(15): exposure-averaged variance]{ref}
Back to article page
