Optimizing active and passive calibration of optical tweezers

To obtain quantitative information from optical trapping experiments it is essential to perform a precise force calibration. Therefore, sources of noise should be pinpointed and eliminated. Fourier analysis is routinely used to calibrate optical trapping assays because it is excellent for pinpointing high frequency noise. In addition, Allan variance analysis is particularly useful for quantifying low frequency noise and for predicting the optimal measurement time. We show how to use Allan variance in combination with Fourier analysis for optimal calibration and noise reduction in optical trapping assays. The methods are applied to passive assays, utilizing the thermal motion of a trapped particle, and to active assays where the bead is harmonically driven. The active method must be applied in assays where, for example, the viscoelastic properties of the medium or the size or shape of the trapped object are unknown. For measurement times shorter than the optimal calibration time the noise is larger in active than in the passive assays. For times equal to or longer than the optimal measurement time, though, the noise on passive and active assays is identical. As an example, we show how to quantify the influence on measurement noise of bead size and chamber geometry in active and passive assays.