Optical tweezers: Characterization and systems approach to high bandwidth force estimation

In recent times, the hard boundaries between classical fields of sciences have almost disappeared. There is a cross-pollination of ideas between sciences, engineering and mathematics. This work investigates a modern tool of micro-manipulation of microscopic particles that is used primarily by bio-physicists and bio-chemists for single cell, single molecule studies. This tool called the Optical Tweezers can trap microscopic dielectric particles using radiation pressure of light. Optical tweezers is increasingly being used in bio-assays as it provides a means to observe bio-molecules non invasively and offers a spatial resolution in nanometers and force resolution in femto-Newtons at millisecond timescales.In this work, physics governing the operating principle behind optical tweezers is presented, followed by a step by step procedure to build an optical tweezers system having measurement and actuation capability along with a controller logic for feedback implementation. The working of optical tweezers system is presented using a spring mass damper model and the traditional methods of optical tweezers characterization are discussed. A comprehensive view of Optical tweezers is then presented from a system theoretic perspective, underlying the limitations of traditional methods of tweezers characterization that are based on the first principle. The role of feedback in Optical tweezers is presented along with the fundamental limitations that the plant model imposes on optical tweezers performance to be used as a force sensor for fast dynamics input force. The purpose of optical tweezers as a pico-newton force probe is emphasized and a classical controls based method to improve the bandwidth of force estimation using an ad-hoc approach of system inversion is presented. The efficacy of system inversion based method in improving the force probe capability of feedback enhanced optical tweezers is validated by experimental results. It is shown experimentally that the system inversion method results in an order of magnitude improvement in the bandwidth of external force estimation. Finally, a robust control strategy is presented, where the problem of estimation of high bandwidth force is casted as an H-infinity optimization problem along with other performance objectives. This strategy is then compared with the traditional method using PI-controllers and experimental results presented. The robust control strategy is found to further improve the ability of optical tweezers as a force sensor for fast changing force profile by approximately three times over the system inversion approach.