Ultrasonic dispersion (delta V/V) determined from mechanical resonance frequency shifts

With standing wave ultrasonic techniques, small changes in phase velocity which result from changes in some external parameter (e.g., temperature or magnetic field) have traditionally been determined by observing shifts in the mechanical resonance frequency of a composite resonator. Some previous investigators have assumed that the fractional change in velocity is equal to the fractional change in frequency. Substantially improved formulas for determining the dispersion are presented and one of these is shown to be much more accurate than all previous approximations. The results of simulated and actual experiments over wide ranges of dispersion, transducer loading parameter, and frequency are analyzed in order to compare the errors inherent in the various approximations

Robust Hypothesis Tests for Detecting Statistical Evidence of 2D and 3D Interactions in Single-Molecule Measurements

A variety of experimental techniques have improved the 2D and 3D spatial resolution that can be extracted from \emph{in vivo} single-molecule measurements. This enables researchers to quantitatively infer the magnitude and directionality of forces experienced by biomolecules in their native cellular environments. Situations where such forces are biologically relevant range from mitosis to directed transport of protein cargo along cytoskeletal structures. Models commonly applied to quantify single-molecule dynamics assume that effective forces and velocity in the $x,y$ (or $x,y,z$) directions are statistically independent, but this assumption is physically unrealistic in many situations. We present a hypothesis testing approach capable of determining if there is evidence of statistical dependence between positional coordinates in experimentally measured trajectories; if the hypothesis of independence between spatial coordinates is rejected, then a new model accounting for 2D (3D) interactions should be considered to more faithfully represent the underlying experimental kinetics. The technique is robust in the sense that 2D (3D) interactions can be detected via statistical hypothesis testing even if there is substantial inconsistency between the physical particle's actual noise sources and the simplified model's assumed noise structure. For example, 2D (3D) interactions can be reliably detected even if the researcher assumes normal diffusion, but the experimental data experiences "anomalous diffusion" and/or is subjected to a measurement noise characterized by a distribution differing from that assumed by the fitted model. The approach is demonstrated on control simulations and on experimental data (IFT88 directed transport in the primary cilium).Comment: 7 pages, 6 figure

Interferometry of a Single Nanoparticle Using the Gouy Phase of a Focused Laser Beam

We provide a quantitative explanation of the mechanism of the far-field intensity modulation induced by a nanoparticle in a focused Gaussian laser beam, as was demonstrated in several recent direct detection studies. Most approaches take advantage of interference between the incident light and the scattered light from a nanoparticle to facilitate a linear dependence of the signal on the nanoparticle volume. The phase relation between the incoming field and the scattered field by the nanoparticle is elucidated by the concept of Gouy phase. This phase relation is used to analyze the far-field signal-to-noise ratio as a function of exact nanoparticle position with respect to the beam focus. The calculation suggests that a purely dispersive nanoparticle should be displaced from the Gaussian beam focus to generate a far-field intensity change

Two transducer formula for more precise determination of ultrasonic phase velocity from standing wave measurements

A two transducer correction formula valid for both solid and liquid specimens is presented. Using computer simulations of velocity measurements, the accuracy and range of validity of the results are discussed and are compared with previous approximations

Detection of Single Molecules Illuminated by a Light-Emitting Diode

Optical detection and spectroscopy of single molecules has become an indispensable tool in biological imaging and sensing. Its success is based on fluorescence of organic dye molecules under carefully engineered laser illumination. In this paper we demonstrate optical detection of single molecules on a wide-field microscope with an illumination based on a commercially available, green light-emitting diode. The results are directly compared with laser illumination in the same experimental configuration. The setup and the limiting factors, such as light transfer to the sample, spectral filtering and the resulting signal-to-noise ratio are discussed. A theoretical and an experimental approach to estimate these parameters are presented. The results can be adapted to other single emitter and illumination schemes.Comment: 7 pages, 5 figure

Interferometric scattering enables fluorescence-free electrokinetic trapping of single nanoparticles in free solution

Anti-Brownian traps confine single particles in free solution by closed-loop feedback forces that directly counteract Brownian motion. The extended-duration measurement of trapped objects allows detailed characterization of photophysical and transport properties, as well as observation of infrequent or rare dynamics. However, this approach has been generally limited to particles that can be tracked by fluorescent emission. Here we present the Interferometric Scattering Anti-Brownian ELectrokinetic trap (ISABEL trap), which uses interferometric scattering rather than fluorescence to monitor particle position. By decoupling the ability to track (and therefore trap) a particle from collection of its spectroscopic data, the ISABEL trap enables confinement and extended study of single particles that do not fluoresce, that only weakly fluoresce, or which exhibit intermittent fluorescence or photobleaching. This new technique significantly expands the range of nanoscale objects that may be investigated at the single-particle level in free solution.Comment: Manuscript and SI; videos available upon reques

Control and coherence of the optical transition of single defect centers in diamond

We demonstrate coherent control of the optical transition of single Nitrogen-Vacancy defect centers in diamond. On applying short resonant laser pulses, we observe optical Rabi oscillations with a half-period as short as 1 nanosecond, an order of magnitude shorter than the spontaneous emission time. By studying the decay of Rabi oscillations, we find that the decoherence is dominated by laser-induced spectral jumps. By using a low-power probe pulse as a detuning sensor and applying post-selection, we demonstrate that spectral diffusion can be overcome in this system to generate coherent photons.Comment: 5 pages,4 figure

Addressing systematic errors in axial distance measurements in single-emitter localization microscopy

Nanoscale localization of point emitters is critical to several methods in optical fluorescence microscopy, including single-molecule super-resolution imaging and tracking. While the precision of the localization procedure has been the topic of extensive study, localization accuracy has been less emphasized, in part due to the challenge of producing an experimental sample containing unperturbed point emitters at known three-dimensional positions in a relevant geometry. We report a new experimental system which reproduces a widely-adopted geometry in high-numerical aperture localization microscopy, in which molecules are situated in an aqueous medium above a glass coverslip imaged with an oil-immersion objective. We demonstrate a calibration procedure that enables measurement of the depth-dependent point spread function (PSF) for open aperture imaging as well as imaging with engineered PSFs with index mismatch. We reveal the complicated, depth-varying behavior of the focal plane position in this system and discuss the axial localization biases incurred by common approximations of this behavior. We compare our results to theoretical calculations.Comment: 16 pages, 10 figure