  Optical tweezers (OT) have become an essential technique in several fields of
physics, chemistry, and biology as precise micromanipulation tools and
microscopic force transducers. Quantitative measurements require the accurate
calibration of the trap stiffness of the optical trap and the diffusion
constant of the optically trapped particle. This is typically done by
statistical estimators constructed from the position signal of the particle,
which is recorded by a digital camera or a quadrant photodiode. The finite
integration time and sampling frequency of the detector need to be properly
taken into account. Here, we present a general approach based on the joint
probability density function of the sampled trajectory that corrects exactly
the biases due to the detector's finite integration time and limited sampling
frequency, providing theoretical formulas for the most widely employed
calibration methods: equipartition, mean squared displacement, autocorrelation,
power spectral density, and force reconstruction via
maximum-likelihood-estimator analysis (FORMA). Our results, tested with
experiments and Monte Carlo simulations, will permit users of OT to confidently
estimate the trap stiffness and diffusion constant, extending their use to a
broader set of experimental conditions.
