Due to its capabilities of three-dimensional (3D) non-contact manipulation and measurement with sub-picoNewton force resolution, optical trapping is a modern technique that has been particularly important for studying biological systems under physiological conditions. An optical trapping system, composed of an FPGA-based digital controller, 3D high-speed laser measurement, and 3D rapid laser steering, is developed. The 3D steering actuators consist of a deformable mirror enabling axial actuation and a two-axis acousto-optic deflector for lateral steering. The actuation range is designed and calibrated to be over 20μm along the two lateral axes and over 10μm along the axial direction. The actuation bandwidth along lateral axes is over 50 kHz and the associated resolution is 0.016nm (1σ). The axial resolution is 0.16nm, while the bandwidth is enhanced to over 3 kHz by model cancellation method.
To enhance the manipulation resolution of the developed system, Brownian motion control is theoretically and experimentally investigated. A 1st-order ARMAX model describing the Brownian motion of an optically trapped probe is derived for controller design and analysis. The derived model is experimentally validated by proportional control results. An optimal controller based on minimum variance control theory is then designed and implemented. The theoretical analysis is validated by both experiment and simulation to illustrate the performance envelope of active control. Moreover, adaptive minimum variance control is implemented and experimentally verified to be capable of maintaining the optimal control performance in a time-varying environment.
Adaptive estimation is developed to enhance the system’s dynamic force probing capability. An adaptive observer is designed using the augmented system model that includes the dynamics of the external interaction and trapping system variation. It recursively estimates the external force and the system parameter from the noisy motion of the probe. Due to the principle of control-estimation separation, its performance of dynamic force sensing is unaffected by the manipulation and control of the system. The force probing is also corrected automatically according to the parameter estimation of the trapping dynamics. From inferring the cause of the variation, additional information of the process under investigation can be gained. Kalman filter algorithm is employed to minimize the estimation error of the designed estimator, achieving best linear unbiased and maximum likelihood estimation when the process and measurement noises satisfy the white Gaussian condition.
The potential of the developed optically trapped probing system for biological researches is demonstrated by experiments with living cells. Intracellular trapping of an organelle is accomplished in a living CHO cell, and extracellular experiments of single-point cell pushing and cell tapping are performed to measure the mechanical property and/or the topography of living cells. The sample interference to the system’s actuation and measurement is eliminated by the modification of the sample holder and the employment of a different measurement optical path. After the non-specific binding of the probe to the cell is prevented, a topography map is obtained on a living MCF-7 cancer cell from multi-location cell tapping. The cell’s normal stiffness is also measured simultaneously, which is comparable to that of the trapping system.