Calibration of optical tweezers based on an autoregressive model

The power spectrum density (PSD) has long been explored for calibrating optical tweezers stiffness. Fast Fourier Transform (FFT) based spectral estimator is typically used. This approach requires a relatively longer data acquisition time to achieve adequate spectral resolution. In this paper, an autoregressive (AR) model is proposed to obtain the Spectrum Density using a limited number of samples. According to our method, the arithmetic model has been established with burg arithmetic, and the final prediction error criterion has been used to select the most appropriate order of the AR model, the power spectrum density has been estimated based the AR model. Then, the optical tweezers stiffness has been determined with the simple calculation from the power spectrum. Since only a small number of samples are used, the data acquisition time is significantly reduced and real-time stiffness calibration becomes feasible. To test this calibration method, we study the variation of the trap stiffness as a function of the parameters of the data length and the trapping depth. Both of the simulation and experiment results have showed that the presented method returns precise results and outperforms the conventional FFT method when using a limited number of samples.