High-speed transverse and axial optical force measurements using amplitude filter masks.

Direct optical force measurement is a versatile method used in optical tweezers experiments, providing accurate measurements of forces for a wide range of particles and trapping beams. It is based on the detection of the change of the momentum of light scattered by a trapped object. A digital micromirror device can be used to selectively reflect light in different directions using an appropriately defined mask. We have developed position-sensitive masked detection (PSMD) for measuring transverse (radial) and axial forces. The method is comparable in performance to the fastest split detectors, while maintaining the linearity and customizability similar to duo-lateral position-sensitive detectors (PSD) and cameras. We show an order of magnitude increase in the bandwidth compared to a conventional PSD for radial forces. We measure axial force and verify the measurement using the Stokes drag for the particle. Combining both detectors (PSMD and PSD), we can perform full 3-D optical force measurements in real time.

Optical-trapping of particles in air using parabolic reflectors and a hollow laser beam.

We present an advanced optical-trapping method that is capable of trapping arbitrary shapes of transparent and absorbing particles in air. Two parabolic reflectors were used to reflect the inner and outer parts of a single hollow laser beam, respectively, to form two counter-propagating conical beams and bring them into a focal point for trapping. This novel design demonstrated high trapping efficiency and strong trapping robustness with a simple optical configuration. Instead of using expensive microscope objectives, the parabolic reflectors can not only achieved large numerical aperture (N.A.) focusing, but were also able to focus the beam far away from optical surfaces to minimize optics contamination. This design also offered a large free space for flexible integration with other measuring techniques, such as optical-trapping Raman spectroscopy, for on-line single particle characterization.

Quantitative Acoustic Models for Superfluid Circuits.

We experimentally realize a highly tunable superfluid oscillator circuit in a quantum gas of ultracold atoms and develop and verify a simple lumped-element description of this circuit. At low oscillator currents, we demonstrate that the circuit is accurately described as a Helmholtz resonator, a fundamental element of acoustic circuits. At larger currents, the breakdown of the Helmholtz regime is heralded by a turbulent shedding of vortices and density waves. Although a simple phase-slip model offers qualitative insights into the circuit's resistive behavior, our results indicate deviations from the phase-slip model. A full understanding of the dissipation in superfluid circuits will thus require the development of empirical models of the turbulent dynamics in this system, as have been developed for classical acoustic systems.

Modelling of Cavity Optomechanical Magnetometers.

Cavity optomechanical magnetic field sensors, constructed by coupling a magnetostrictive material to a micro-toroidal optical cavity, act as ultra-sensitive room temperature magnetometers with tens of micrometre size and broad bandwidth, combined with a simple operating scheme. Here, we develop a general recipe for predicting the field sensitivity of these devices. Several geometries are analysed, with a highest predicted sensitivity of 180 p T / Hz at 28 µ m resolution limited by thermal noise in good agreement with previous experimental observations. Furthermore, by adjusting the composition of the magnetostrictive material and its annealing process, a sensitivity as good as 20 p T / Hz may be possible at the same resolution. This method paves a way for future design of magnetostrictive material based optomechanical magnetometers, possibly allowing both scalar and vectorial magnetometers.

Rotational control of computer generated holograms.

We develop a basis for three-dimensional rotation of arbitrary light fields created by computer generated holograms. By adding an extra phase function into the kinoform, any light field or holographic image can be tilted in the focal plane with minimized distortion. We present two different approaches to rotate an arbitrary hologram: the Scheimpflug method and a novel coordinate transformation method. Experimental results are presented to demonstrate the validity of both proposed methods.

Nondestructive Profilometry of Optical Nanofibers.

Single-mode optical nanofibers are a central component of a broad range of applications and emerging technologies. Their fabrication has been extensively studied over the past decade, but imaging of the final submicrometer products has been restricted to destructive or low-precision techniques. Here, we demonstrate an optical scattering-based scanning method that uses a probe nanofiber to locally scatter the evanescent field of a sample nanofibre. The method does not damage the sample nanofiber and is easily implemented by only using the same equipment as in a standard fiber-puller setup. We demonstrate the subnanometer radial resolution at video rates (0.7 nm in 10 ms) on single mode nanofibers, allowing for a complete high-precision profile to be obtained within minutes of fabrication. The method thus enables nondestructive, fast, and precise characterization of optical nanofibers, with applications ranging from optical sensors and cold atom traps to nonlinear optics.

Forces due to pulsed beams in optical tweezers: linear effects.

We present a method for the precise calculation of optical forces due to a tightly-focused pulsed laser beam using generalized Lorenz-Mie theory or the T-matrix method. This method can be used to obtain the fields as a function of position and time, allowing the approximate calculation of weak non-linear effects, and provides a reference calculation for validation of calculations including non-linear effects. We calculate forces for femtosecond pulses of various widths, and compare with forces due to a continuous wave (CW) beam. The forces are similar enough so that the continuous beam case provides a useful approximation for the pulsed case, with trap parameters such as the radial spring constant usually differing by less than 1% for pulses of 100 fs or longer. For large high-index (e.g., polystyrene, with n = 1.59) particles, the difference can be as large as 3% for 100 fs pulses, and up to 8% for 25 fs pulses. A weighted average of CW forces for individual spectral components of the pulsed beam provides a simple improved approximation, which we use to illustrate the physical principles responsible for the differences between pulsed and CW beams.

Escape forces and trajectories in optical tweezers and their effect on calibration.

Whether or not an external force can make a trapped particle escape from optical tweezers can be used to measure optical forces. Combined with the linear dependence of optical forces on trapping power, a quantitative measurement of the force can be obtained. For this measurement, the particle is at the edge of the trap, away from the region near the equilbrium position where the trap can be described as a linear spring. This method provides the ability to measure higher forces for the same beam power, compared with using the linear region of the trap, with lower risk of optical damage to trapped specimens. Calibration is typically performed by using an increasing fluid flow to exert an increasing force on a trapped particle until it escapes. In this calibration technique, the particle is usually assumed to escape along a straight line in the direction of fluid-flow. Here, we show that the particle instead follows a curved trajectory, which depends on the rate of application of the force (i.e., the acceleration of the fluid flow). In the limit of very low acceleration, the particle follows the surface of zero axial optical force during the escape. The force required to produce escape depends on the trajectory, and hence the acceleration. This can result in variations in the escape force of a factor of two. This can have a major impact on calibration to determine the escape force efficiency. Even when calibration measurements are all performed in the low acceleration regime, variations in the escape force efficiency of 20% or more can still occur. We present computational simulations using generalized Lorenz-Mie theory and experimental measurements to show how the escape force efficiency depends on rate of increase of force and trapping power, and discuss the impact on calibration.

Driving corrugated donut rotors with Laguerre-Gauss beams.

Tightly-focused laser beams that carry angular momentum have been used to trap and rotate microrotors. In particular, a Laguerre-Gauss mode laser beam can be used to transfer its orbital angular momentum to drive microrotors. We increase the torque efficiency by a factor of about 2 by designing the rotor such that its geometry is compatible with the driving beam, when driving the rotation with the optimum beam, rather than beams of higher or lower orbital angular momentum. Based on Floquet's theorem, the order of discrete rotational symmetry of the rotor can be made to couple with the azimuthal mode of the Laguerre-Gauss beam. We design corrugated donut rotors, that have a flat disc-like profile, with the help of the discrete dipole approximation and the T-matrix methods in parallel with experimental demonstrations of stable trapping and torque measurement. We produce and test such a rotor using two-photon photopolymerization. With a rotor that has 8-fold discrete rotational symmetry, an outer radius of 1.85 µm and a hollow core radius of 0.5 µm, we were able to transfer approximately 0.3 h̄ per photon of the orbital angular momentum from an LG04 beam.

Comparison of T-matrix calculation methods for scattering by cylinders in optical tweezers.

The T-matrix method, or the T-matrix formulation of scattering, is a framework for mathematically describing the scattering properties of an object as a linear relationship between expansion coefficients of the incident and scattering fields in a basis of vector spherical wave functions (VSWFs). A variety of methods can be used to calculate the T-matrix. We explore the applicability of the extended boundary condition method (EBCM) and point matching (PM) method to calculate the T-matrix for scattering by cylinders in optical tweezers and hence the optical force acting on them. We compare both methods with the discrete-dipole approximation (DDA) to measure their accuracy for different sizes and aspect ratios (ARs) for Rayleigh and wavelength-size cylinders. We determine range of sizes and ARs giving errors below 1% and 10%. These results can help researchers choose the most efficient method to calculate the T-matrix for nonspherical particles with acceptable accuracy.

Tired and stressed: direct holographic quasi-static stretching of aging echinocytes and discocytes in plasma using optical tweezers [Invited].

Red blood cells (RBCs) undergo a progressive morphological transformation from smooth biconcave discocytes into rounder echinocytes with spicules on their surface during cold storage. The echinocytic morphology impacts RBCs' ability to flow through narrow sections of the circulation and therefore transfusion of RBC units with a high echinocytic content are thought to have a reduced efficiency. We use an optical tweezers-based technique where we directly trap and measure linear stiffness of RBCs under stress without the use of attached spherical probe particles or microfluidic flow to induce shear. We study RBC deformability with over 50 days of storage performing multiple stretches in blood plasma (serum with cold agglutinins removed to eliminate clotting). In particular, we find that discocytes and echinocytes do not show significant changes in linear stiffness in the small strain limit (∼20% change in length) up to day 30 of the storage period, but do find differences between repeated stretches. By day 50 the linear stiffness of discocytes had increased to approximately that measured for echinocytes throughout the entire period of measurements. These changes in stiffness corresponded to recorded morphological changes in the discocytes as they underwent storage lesion. We believe our holographic trapping and direct measurement technique has applications to directly control and quantify forces that stretch other types of cells without the use of attached probes.

Shining Light in Mechanobiology: Optical Tweezers, Scissors, and Beyond.

Mechanobiology helps us to decipher cell and tissue functions by looking at changes in their mechanical properties that contribute to development, cell differentiation, physiology, and disease. Mechanobiology sits at the interface of biology, physics and engineering. One of the key technologies that enables characterization of properties of cells and tissue is microscopy. Combining microscopy with other quantitative measurement techniques such as optical tweezers and scissors, gives a very powerful tool for unraveling the intricacies of mechanobiology enabling measurement of forces, torques and displacements at play. We review the field of some light based studies of mechanobiology and optical detection of signal transduction ranging from optical micromanipulation-optical tweezers and scissors, advanced fluorescence techniques and optogenentics. In the current perspective paper, we concentrate our efforts on elucidating interesting measurements of forces, torques, positions, viscoelastic properties, and optogenetics inside and outside a cell attained when using structured light in combination with optical tweezers and scissors. We give perspective on the field concentrating on the use of structured light in imaging in combination with tweezers and scissors pointing out how novel developments in quantum imaging in combination with tweezers and scissors can bring to this fast growing field.

Calibration of nonspherical particles in optical tweezers using only position measurement.

Nonspherical probe particles are an attractive choice for optically-trapped scanning probe microscopy. We show that it is possible to calibrate a trap with a nonspherical particle using only position measurements, without requiring measurement of orientation, using a pseudopotential based on the position occupation probability. It is not necessary to assume the force is linear with displacement.

Roadmap on Deep Learning for Microscopy.

Through digital imaging, microscopy has evolved from primarily being a means for visual observation of life at the micro- and nano-scale, to a quantitative tool with ever-increasing resolution and throughput. Artificial intelligence, deep neural networks, and machine learning are all niche terms describing computational methods that have gained a pivotal role in microscopy-based research over the past decade. This Roadmap is written collectively by prominent researchers and encompasses selected aspects of how machine learning is applied to microscopy image data, with the aim of gaining scientific knowledge by improved image quality, automated detection, segmentation, classification and tracking of objects, and efficient merging of information from multiple imaging modalities. We aim to give the reader an overview of the key developments and an understanding of possibilities and limitations of machine learning for microscopy. It will be of interest to a wide cross-disciplinary audience in the physical sciences and life sciences.

Equilibrium orientations and positions of non-spherical particles in optical traps.

Dynamic simulation is a powerful tool to observe the behavior of arbitrary shaped particles trapped in a focused laser beam. Here we develop a method to find equilibrium positions and orientations using dynamic simulation. This general method is applied to micro- and nano-cylinders as a demonstration of its predictive power. Orientation landscapes for particles trapped with beams of differing polarisation are presented. The torque efficiency of micro-cylinders at equilibrium in a plane is also calculated as a function of tilt angle. This systematic investigation elucidates in both the function and properties of micro- and nano-cylinders trapped in optical tweezers.

Picoliter rheology of gaseous media using a rotating optically trapped birefringent microparticle.

An optically trapped birefringent microparticle is rotated by a circularly polarized beam in a confined gaseous medium. By recording the terminal rotation velocity and the change in polarization of the incident trapping beam, we determine the viscosity by probing a picoliter volume of air, carbon dioxide, and argon in the vicinity of the microparticle. We also characterize the optical force acting on a trapped particle in air using the generalized Lorenz-Mie theory taking into account the aberrations present. This opens up a new potential application of optical tweezers for the accurate measurement of gas viscosity in confined geometries.

Measurement of viscosity of lyotropic liquid crystals by means of rotating laser-trapped microparticles.

We describe a simple microrheology method to measure the viscosity coefficients of lyotropic liquid crystals. This approach is based on the use of a rotating laser-trapped optically anisotropic microsphere. In aligned liquid crystals that have negligible effect on trapping beam's polarization, the optical torque is transferred from circularly polarized laser trapping beam to the optically anisotropic microparticle and creates the shear flow in the liquid crystalline fluid. The balance of optical and viscous torques yields the local effective viscosity coefficients of the studied lyotropic systems in cholesteric and lamellar phases. This simple yet powerful method is capable of probing viscosity of complex anisotropic fluids for small amounts of sample and even in the presence of defects that obstruct the use of conventional rheology techniques.

Enhanced Signal-to-Noise and Fast Calibration of Optical Tweezers Using Single Trapping Events.

The trap stiffness us the key property in using optical tweezers as a force transducer. Force reconstruction via maximum-likelihood-estimator analysis (FORMA) determines the optical trap stiffness based on estimation of the particle velocity from statistical trajectories. Using a modification of this technique, we determine the trap stiffness for a two micron particle within 2 ms to a precision of ∼10% using camera measurements at 10 kfps with the contribution of pixel noise to the signal being larger the level Brownian motion. This is done by observing a particle fall into an optical trap once at a high stiffness. This type of calibration is attractive, as it avoids the use of a nanopositioning stage, which makes it ideal for systems of large numbers of particles, e.g., micro-fluidics or active matter systems.

A method for achieving super-resolved widefield CARS microscopy.

We propose a scheme for achieving widefield coherent anti-Stokes Raman scattering (CARS) microscopy images with sub-diffraction-limited resolution. This approach adds structured illumination to the widefield CARS configuration [Applied Physics Letters 84, 816 (2004)]. By capturing a number of images at different phases of the standing wave pattern, an image with up to three times the resolution of the original can be constructed. We develop a theoretical treatment of this system and perform numerical simulations for a typical CARS system, which indicate that resolutions around 120 nm are obtainable with the present scheme. As an imaging system, this method combines the advantages of sub-diffraction-limited resolution, endogenous contrast generation, and a wide field of view.

Anomalous power laws of spectral diffusion in quantum dots: a connection to luminescence intermittency.

We show that the wandering of transition frequencies in colloidal quantum dots does not follow the statistics expected for ordinary diffusive processes. The trajectory of this anomalous spectral diffusion is characterized by a sqrt[t] dependence of the squared deviation. The behavior is reproduced when the electronic states of quantum dots are assumed to interact with environments such as, for example, an ensemble of two-level systems, where the correlation times are distributed according to a power law similar to the one generally attributed to the dot's luminescence intermittency.