Video microscopy-based accurate optical force measurement by exploring a frequency-changing sinusoidal stimulus

Tan Xu, Shangquan Wu, Zhaoxiang Jiang, Xiaoping Wu, and Qingchuan Zhang

Optical tweezers are constantly evolving micromanipulation tools that can provide piconewton force measurement accuracy and greatly promote the development of bioscience at the single-molecule scale. Consequently, there is an urgent need to characterize the force field generated by optical tweezers in an accurate, cost-effective, and rapid manner. Thus, in this study, we conducted a deep survey of optically trapped particle dynamics and found that merely quantifying the response amplitude and phase delay of particle displacement under a sine input stimulus can yield sufficiently accurate force measurements. In addition, Nyquist–Shannon sampling theorem suggests that the entire recovery of the accessible particle sinusoidal response is possible, provided that the sampling theorem is satisfied, thereby eliminating the requirement for high-bandwidth (typically greater than 10 kHz) detectors. Based on this principle, we designed optical trapping experiments by loading a sinusoidal signal into the optical tweezers system and recording the trapped particle responses with 45 frames per second (fps) charge-coupled device (CCD) and 163 fps complementary metal–oxide–semiconductor (CMOS) cameras for video microscopy imaging. The experimental results demonstrate that the use of low-bandwidth detectors is suitable for highly accurate force quantification, thereby greatly reducing the complexity of constructing optical tweezers. The trap stiffness increases significantly as the frequency increases, and the experimental results demonstrate that the trapped particles shifting along the optical axis boost the transversal optical force.

DOI