Finding trap stiffness of optical tweezers using digital filters

Obtaining trap stiffness and calibration of the position detection system is the basis of a force measurement using optical tweezers. Both calibration quantities can be calculated using several experimental methods available in the literature. In most cases, stiffness determination and detection system calibration are performed separately, often requiring procedures in very different conditions, and thus confidence of calibration methods is not assured due to possible changes in the environment. In this work, a new method to simultaneously obtain both the detection system calibration and trap stiffness is presented. The method is based on the calculation of the power spectral density of positions through digital filters to obtain the harmonic contributions of the position signal. This method has the advantage of calculating both trap stiffness and photodetector calibration factor from the same dataset in situ. It also provides a direct method to avoid unwanted frequencies that could greatly affect calibration procedure, such as electric noise, for example.