FPGA-Based Real-Time Feedback Control of Optical Tweezers

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"The NI R Series multifunction RIO met our requirements, and we plan to develop future variations on the new real-time nanoscale control concept."

- Anders E. Wallin, University of Helsinki

The Challenge:
Reducing optical damage and associated heating when using optical tweezers, or traps, based on an emerging micromanipulation technique using focused and intense laser light to trap dielectric particles.

The Solution:
Using a field-programmable gate array (FPGA)-based real-time controller to connect back-focal-plane interferometric detection of trapped particles with fast trap steering using acousto-optic deflectors, and employing a simple proportional control algorithm to achieve a four-fold increase in effective trap stiffness without increasing laser power, thus significantly reducing optical damage to biological specimen.

Author(s):
Anders E. Wallin - University of Helsinki
Heikki Ojala - University of Helsinki

In optical tweezers, optical damage and associated heating restricts sensitive single-molecule experiments. By connecting position detection and trap steering using a real-time controller, we built a closed-loop instrument. A proportional gain position-clamp algorithm provides approximately four-fold increased effective trap stiffness without increased laser power, which enables the execution of a broader range of experiments.

Optical tweezers trap micron-sized dielectric particles using focused and intense light. Laser light creates a harmonic trap with approximately 0.1 pN/nm stiffness that we can use to exert or measure one to 100 pN forces. Nanoscale sensing and actuation in this force range facilitates experiments with single biomolecules, where a molecule is bound to a trapped latex or silica microsphere (1 μm in diameter). With back-focal-plane interferometry, we can measure the position of a trapped sphere with millisecond temporal and subnanometer spatial resolution.

These experiments that elucidate the molecular architecture of life usually determine the microsphere position while a controlled force is exerted on the bead or as the biomolecule is chemically modified. However, nanoscale measurements are impeded by thermal noise. A trapped particle experiences frequent collisions with solvent molecules (water) that, due to the minuscule particle mass, randomly kick the particle around in the trap. This thermal motion of the microsphere degrades the position resolution of the instrument. We can reduce thermal noise by employing a stiffer trap, which requires higher laser intensity. But for biological specimen, any increase in laser intensity causes adverse effects due to heating and optical damage, or “opticution.”

Therefore, to increase the effective trap stiffness and reduce the thermal noise, we combined high-resolution position detection with rapid trap steering to create a feedback-controlled optical tweezers instrument. For control, we used a real-time reprogrammable FPGA-based R Series multifunction RIO board.

Instrument Description

Our single-beam optical tweezers are built around an inverted microscope with a 100 times, 1.3 NA objective. A high-power infrared continuous wave laser (4 W, 1,064 nm) produces a beam that is collimated and isolated before passing through acousto-optic deflectors (AODs), which provide +/-16 mrad deflection in both the x- and y-axis. After beam expansion by three times, we can translate the laser focus by +/-11 µm in the specimen plane. We operate the AODs using digital direct synthesizers (DDSs) that accept a digital 30-bit control word. The least-significant bit of the 30-bit DDS control word corresponds to 0.02 pm of movement, much below the current detection level. A separate HeNe (633 nm, 6 mW) laser provides back-focal-plane interferometric detection, and a duo-lateral photodiode produces +/-10 V analog position detection signals.

Our controller requirements were a minimum of 60-bit digital I/O to control two DDSs; three or more analog-to-digital converter (ADC) inputs to collect analog position data; and rapid signal processing to implement real-time feedback algorithms. Based on these requirements, we chose the NI R Series multifunction RIO board because it had the required inputs and outputs, and we could program with the NI LabVIEW FPGA Module, which we use daily. The analog-to-digital conversion (4 μs) and the acoustic time of flight in the AOD (4.5 μs) are the major contributors to the 8.5 μs loop delay. Thus, the instrument response is significantly faster than most biological processes of interest.

Results

We implemented, calibrated, and tested the NI LabVIEW host and FPGA target VIs for open-loop control. The instrument operator can steer the trap position using on-screen controls or mechanical handwheels that output quadrature signals to the FPGA. This manual control mode is useful at the initial stages of an experiment when we have to find and trap a suitable microsphere.

Next, we implemented a proportional gain feedback loop. For example, any bead motion to the left is counteracted by trap movement to the right. This algorithm is termed as a position clamp because it strives to immobilize the bead at the setpoint position. Then we measured the position fluctuations while varying the loop gain and found that the effective trap stiffness can be increased by up to a factor of approximately four. By using moderate negative feedback, we could also decrease the effective trap stiffness.

In addition, we can use the force signal as an input to the feedback loop instead of the position signal from the trapped bead. This creates a force clamp that maintains constant tension in the biomolecule under study. A constant tension is required in stepping assays where the biomolecule length changes. To measure only structure-related length changes, we have to avoid unwanted length changes in the biomolecule due to stretching by maintaining constant tension in the assay.

Using real-time feedback control, we can increase the effective stiffness of optical tweezers by approximately four fold without an increase in laser power, meaning we can use a quarter of the laser power necessary without feedback control. The R Series multifunction RIO board met our requirements, and we plan to develop future variations on the new real-time nanoscale control concept. Furthermore, the NI Finland branch was very professional and cooperative while helping us with the project.

Author Information:
AndersE. Wallin
University of Helsinki
Gustaf Hallstrominkatu 2
000114
Finland
Tel: +358408240925
Fax: +358919150694
anders.wallin@helsinki.fi

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