Influence of experimental parameters on the laser heating of an optical trap.

In optical tweezers, heating of the sample due to absorption of the laser light is a major concern as temperature plays an important role at microscopic scale. A popular rule of thumb is to consider that, at the typical wavelength of 1064 nm, the focused laser induces a heating rate of B = 1 °C/100 mW. We analysed this effect under different routine experimental conditions and found a remarkable variability in the temperature increase. Importantly, we determined that temperature can easily rise by as much as 4 °C at a relatively low power of 100 mW, for dielectric, non-absorbing particles with certain sets of specific, but common, parameters. Heating was determined from measurements of light momentum changes under drag forces at different powers, which proved to provide precise and robust results in watery buffers. We contrasted the experiments with computer simulations and obtained good agreement. These results suggest that this remarkable heating could be responsible for changes in the sample under study and could lead to serious damage of live specimens. It is therefore advisable to determine the temperature increase in each specific experiment and avoid the use of a universal rule that could inadvertently lead to critical changes in the sample.

Extending calibration-free force measurements to optically-trapped rod-shaped samples.

Optical trapping has become an optimal choice for biological research at the microscale due to its non-invasive performance and accessibility for quantitative studies, especially on the forces involved in biological processes. However, reliable force measurements depend on the calibration of the optical traps, which is different for each experiment and hence requires high control of the local variables, especially of the trapped object geometry. Many biological samples have an elongated, rod-like shape, such as chromosomes, intracellular organelles (e.g., peroxisomes), membrane tubules, certain microalgae, and a wide variety of bacteria and parasites. This type of samples often requires several optical traps to stabilize and orient them in the correct spatial direction, making it more difficult to determine the total force applied. Here, we manipulate glass microcylinders with holographic optical tweezers and show the accurate measurement of drag forces by calibration-free direct detection of beam momentum. The agreement between our results and slender-body hydrodynamic theoretical calculations indicates potential for this force-sensing method in studying protracted, rod-shaped specimens.

Beyond the Hookean Spring Model: Direct Measurement of Optical Forces Through Light Momentum Changes.

The ability to measure forces in the range of 0.1-100 pN is a key feature of optical tweezers used for biophysical and cell biological studies. Analysis of the interactions between biomolecules and the forces that biomolecular motors generate at the single-molecule level has provided valuable insights in the molecular mechanisms that govern key cellular functions such as gene expression and the long-distance transport of organelles. Methods for determining the minute forces that biomolecular motors generate exhibit notable constraints that limit their application for studies other than the well-controlled in vitro experiments (although recent advances have been made that permit more quantitative optical tweezers studies insight living cells). One constraint comes from the linear approximation of the distance vs. force relationship used to extract the force from the position of the bead in the trap. This commonly employed "indirect" approach, although usually sufficiently precise, restricts the use of optical tweezers to a limited range of displacements (typically up to ±150 nm for small beads). Measurements based on the detection of the light-momentum changes, on the other hand, offer a "direct" and precise way to determine forces even when the generated displacements reach the escape point, thus covering the complete force range developed by the trap. In this chapter, we detail the requirements for the design of a force-sensor instrument based on light-momentum changes using a high-numerical-aperture objective lens and provide insights into its construction. We further discuss the calibration of the system and the main steps for its routine operation.

Holographic optical tweezers combined with back-focal-plane displacement detection.

A major problem with holographic optical tweezers (HOTs) is their incompatibility with laser-based position detection methods, such as back-focal-plane interferometry (BFPI). The alternatives generally used with HOTs, like high-speed video tracking, do not offer the same spatial and temporal bandwidths. This has limited the use of this technique in precise quantitative experiments. In this paper, we present an optical trap design that combines digital holography and back-focal-plane displacement detection. We show that, with a particularly simple setup, it is possible to generate a set of multiple holographic traps and an additional static non-holographic trap with orthogonal polarizations and that they can be, therefore, easily separated for measuring positions and forces with the high positional and temporal resolutions of laser-based detection. We prove that measurements from both polarizations contain less than 1% crosstalk and that traps in our setup are harmonic within the typical range. We further tested the instrument in a DNA stretching experiment and we discuss an interesting property of this configuration: the small drift of the differential signal between traps.

Optimized back-focal-plane interferometry directly measures forces of optically trapped particles.

Back-focal-plane interferometry is used to measure displacements of optically trapped samples with very high spatial and temporal resolution. However, the technique is closely related to a method that measures the rate of change in light momentum. It has long been known that displacements of the interference pattern at the back focal plane may be used to track the optical force directly, provided that a considerable fraction of the light is effectively monitored. Nonetheless, the practical application of this idea has been limited to counter-propagating, low-aperture beams where the accurate momentum measurements are possible. Here, we experimentally show that the connection can be extended to single-beam optical traps. In particular, we show that, in a gradient trap, the calibration product κ · ß (where κ is the trap stiffness and 1/ß is the position sensitivity) corresponds to the factor that converts detector signals into momentum changes; this factor is uniquely determined by three construction features of the detection instrument and does not depend, therefore, on the specific conditions of the experiment. Then, we find that force measurements obtained from back-focal-plane displacements are in practice not restricted to a linear relationship with position and hence they can be extended outside that regime. Finally, and more importantly, we show that these properties are still recognizable even when the system is not fully optimized for light collection. These results should enable a more general use of back-focal-plane interferometry whenever the ultimate goal is the measurement of the forces exerted by an optical trap.

Positional stability of holographic optical traps.

The potential of digital holography for complex manipulation of micron-sized particles with optical tweezers has been clearly demonstrated. By contrast, its use in quantitative experiments has been rather limited, partly due to fluctuations introduced by the spatial light modulator (SLM) that displays the kinoforms. This is an important issue when high temporal or spatial stability is a concern. We have investigated the performance of both an analog-addressed and a digitally-addressed SLM, measuring the phase fluctuations of the modulated beam and evaluating the resulting positional stability of a holographic trap. We show that, despite imparting a more unstable modulation to the wavefront, our digitally-addressed SLM generates optical traps in the sample plane stable enough for most applications. We further show that traps produced by the analog-addressed SLM exhibit a superior pointing stability, better than 1 nm, which is comparable to that of non-holographic tweezers. These results suggest a means to implement precision force measurement experiments with holographic optical tweezers (HOTs).

A force detection technique for single-beam optical traps based on direct measurement of light momentum changes.

Despite the tremendous success of force-measuring optical traps in recent years, the calibration methods most commonly used in the field have been plagued with difficulties and limitations. Force sensing based on direct measurement of light momentum changes stands out among these as an exception. Especially significant is this method's potential for working within living cells, with non-spherical particles or with non-Gaussian beams. However, so far, the technique has only been implemented in counter-propagating dual-beam traps, which are difficult to align and integrate with other microscopy techniques. Here, we show the feasibility of a single-beam gradient-trap system working with a force detection technique based on this same principle.

Stretching single DNA molecules to demonstrate high-force capabilities of holographic optical tweezers.

The well calibrated force-extension behaviour of single double-stranded DNA molecules was used as a standard to investigate the performance of phase-only holographic optical tweezers at high forces. Specifically, the characteristic overstretch transition at 65 pN was found to appear where expected, demonstrating (1) that holographic optical trap calibration using thermal fluctuation methods is valid to high forces; (2) that the holographic optical traps are harmonic out to >250 nm of 2.1 mum particle displacement; and (3) that temporal modulations in traps induced by the spatial light modulator (SLM) do not affect the ability of optical traps to hold and steer particles against high forces. These studies demonstrate a new high-force capability for holographic optical traps achievable by SLM technologies.