Mapping the restoring force of an optical trap in three dimensions using a two laser dual-trap approach

A two laser optical tweezers set-up is developed and used to measure deflections of a microsphere trapped in a calibrated spatial light modulator steered probe trap as it is stepped through a three dimensional grid about a fixed test trap. These measurements are used to map the restoring force of the test trap on the microsphere in three dimensions. Results are validated over a common range by comparison to drag force measurements for both silica and polystyrene microspheres.     

Simplified description of optical forces acting on a nanoparticle in the Gaussian standing wave

We study the axial force acting on dielectric spherical particles smaller than the trapping wavelength that are placed in the Gaussian standing wave. We derive analytical formulas for immersed particles with relative refractive indices close to unity and compare them with the numerical results obtained by generalized Lorenz-Mie theory (GLMT). We show that the axial optical force depends periodically on the particle size and that the equilibrium position of the particle alternates between the standing-wave antinodes and nodes. For certain particle sizes, gradient forces from the neighboring antinodes cancel each other and disable particle confinement. Using the GLMT we compare maximum axial trapping forces provided by the Gaussian standing-wave trap (SWT) and single-beam trap (SBT) as a function of particle size, refractive index, and beam waist size. We show that the SWT produces axial forces at least ten times stronger and permits particle confinement in a wider range of refractive indices and beam waists compared with those of the SBT.     

Three-dimensional Coherent Transfer Function in Reflection-mode Confocal Microscopy Using Annular Lenses

Abstract

The three-dimensional (3D) coherent transfer function (CTF) in a reflection-mode confocal scanning microscope using two equal annular lenses has been derived analytically under the paraxial approximation. This analytic 3D CTF is then generalized to a confocal system using optical fibres as an illumination source and a signal collector. Various 3D- and two-dimensional (2D) numerical plots are presented to reveal the dependence of the 3D CTF on the size of the central obstruction and on the fibre spot size. As expected, using annular lenses may result in improved transverse resolution but poorer axial resolution compared with those for circular lenses, and using optical fibres of finite cross-section may result in degraded resolution in both axial and transverse directions. The relationship of the 3D CTF to the 2D in-focus CTF is discussed.     

Investigation of transverse oscillation method

Conventional ultrasound scanners can display only the axial component of the blood velocity vector, which is a significant limitation when vessels nearly parallel to the skin surface are scanned. The transverse oscillation (TO) method overcomes this limitation by introducing a TO and an axial oscillation in the pulse echo field. The theory behind the creation of the double oscillation pulse echo field is explained as well as the theory behind the estimation of the vector velocity. A parameter study of the method is performed, using the ultrasound simulation program Field II. A virtual linear-array transducer with center frequency 7 MHz and 128 active elements is created, and a virtual blood vessel of radius 6.4 mm is simulated. The performance of the TO method is found around an initial point in the parameter space. The parameters varied are: flow angle, transmit focus depth, receive apodization, pulse length, transverse wave length, number of emissions, signal-to-noise ratio (SNR), and type of echo-canceling filter used. Using an experimental scanner, the performance of the TO method is evaluated. An experimental flowrig is used to create laminar parabolic flow in a blood mimicking fluid, and the fluid is scanned under different flow-to-beam angles. The relative standard deviation on the transverse velocity estimate is found to be less than 10% for all angles between 50 degrees and 90 degrees. Furthermore, the TO method is evaluated in the flowrig using pulsatile flow, which resembles the flow in the femoral artery. The estimated volume flow as a function of time is compared to the volume flow derived from a conventional axial method at a flow-to-beam angle of 60 degrees. It is found that the method is highly sensitive to the angle between the flow and the beam direction. Also, the choice of echo canceling filter affects the performance significantly.     

A new method for estimation of velocity vectors

The paper describes a new method for determining the velocity vector of a remotely sensed object using either sound or electromagnetic radiation. The movement of the object is determined from a field with spatial oscillations in both the axial direction of the transducer and in one or two directions transverse to the axial direction. By using a number of pulse emissions, the inter-pulse movement can be estimated and the velocity found from the estimated movement and the time between pulses. The method is based on the principle of using transverse spatial modulation for making the received signal influenced by transverse motion. Such a transverse modulation can be generated by using apodization on individual transducer array elements together with a special focusing scheme. A method for making such a field is presented along with a suitable two-dimensional velocity estimator. An implementation usable in medical ultrasound is described, and simulated results are presented. Simulation results for a flow of 1 m/s in a tube rotated in the image plane at specific angles (0, 15, 35, 55, 75, and 90 degrees) are made and characterized by the estimated mean value, estimated angle, and the standard deviation in the lateral and longitudinal direction. The average performance of the estimates for all angles is: mean velocity 0.99 m/s, longitudinal S.D. 0.015 m/s, and lateral S.D. 0.196 m/s. For flow parallel to the transducer the results are: mean velocity 0.95 m/s, angle 0.10, longitudinal S.D. 0.020 m/s, and lateral S.D. 0.172 m/s.     

Elastoplastic model of cylindrical projectile-plate interaction

Elastoplastic models of the transverse impact of a cylindrical solid projectile on an isotropic elastic Uflyand-Mindlin plate have been studied using numerical simulation methods. Displacements of the plate points outside the contact region are caused by a transverse shear wave propagating at a finite velocity. This wave is formed at the moment of impact and represents a surface of strong discontinuity. Behind the transverse wave front, the unknown dynamic quantities are represented in the form of single-term ray expansions. The local crumpling of the target material proceeds in a quasi-static manner and its dependence on the contact force is described using an elastoplastic model. The dependence of the contact force on the elastoplastic properties of a target plate at the site of impact and on the contact disk inertia has been considered.     

Optical levitation measurements with intensity-modulated light beams

Illumination of an optically levitated particle with an intensity-modulated transverse beam induces a transverse vibration of a particle in an optical trap. Based on this, the trapping force of a trap can be measured. Using an intensity-modulated longitudinal levitating beam causes a particle to move vertically, allowing for the determination of some aerodynamic parameters of a particle in air. The principles and the experimental phenomena are described and the initial results are given.     

Application of an ultrasonic technique to creep cavitation in silicon nitride

A non-destructive method based on measurements of ultrasonic wave velocities and Young's modulus is proposed for quantification of creep cavitation in silicon nitride. Tensile creep tests of silicon nitride were conducted at 1400°C in air and the tests were periodically interrupted to measure the longitudinal and transverse ultrasonic wave velocities and Young's modulus. The velocities and Young's modulus decreased linearly with tensile creep strain. The volume fraction of cavities was estimated from the values of the ultrasonic wave velocities and Young's modulus, and compared with the cavity volume predicted from tensile creep strain. The dependence of Young's modulus on volume fraction of cavities is discussed.     

A fast 3D shape measurement method based on sinusoidal and triangular fringe projection

Existing methods to measure 3D shape of complex object involve processing more than six captured images to obtain the absolute phase, which limit the measurement speed. This paper presents two sinusoidal fringes and two triangular wave fringes which is used to measure 3D shape of complex object. The two-step phase-shifting sinusoidal fringes and two-step phase-shifting triangular wave fringes are calculated to obtain the wrapped phase, and then the two-step phase-shifting triangular wave fringes are used to determine the fringe order. Due to decrease the number of projection fringes, the speed of measurement increases. The triangular wave fringe carries more information of the object than linear increasing/decreasing ramp fringe in the actual measurement, more noise in the base phase to be overcome, thus improving the measurement accuracy. The benefits can be widely applied in high-speed, real-time 3D measurement of complex shape. Experimental results have demonstrated that the proposed method is simple, but effective.     

On spatial and temporal stability in three dimensional fluid flows

Summary A three-dimensional stability analysis is presented for an incompressible viscous non-parallel boundary layer flow over a rotating disk. The method of multiple scales is used to derive partial differential equations that describe the axial and cross-flow variations of the disturbance amplitude, phase and wave numbers. These equations are then employed to derive the expressions that relate the spatial and temporal stabilities. These equations are also used to obtain the expression that relates the spatial growth rate along a given direction to a spatial growth rate along any other direction. These relations are verified by numerical results, obtained for three-dimensional disturbances. The numerical results are presented in order to relate the spatial and temporal stability for different values of Reynolds number, wave number and frequency. It is shown that the predicted results are in excellent agreement with those of the present numerical calculations. Further, it is predicted for a quasiparallel flow that any spatial growth rate can be transformed into a temporal growth rate, while a temporal growth rate can be transformed into a spatial growth rate along any specified direction.     

轴向时变冲击载荷作用下直杆弹性动力屈曲研究

基于应力波理论,用半解析半数值方法对轴向时变冲击载荷作用下的直杆进行研究,给出了一种利用压应力波前附加约束条件求解轴向时变载荷作用下直杆弹性动力屈曲问题的方法。以三角脉冲载荷作用下的直杆为例,对其临界屈曲长度、初始屈曲模态和动力特征参数进行了求解,探讨了脉冲载荷峰值和载荷持续时间对临界屈曲长度和屈曲模态的影响。总结了三角脉冲载荷作用下直杆弹性动力屈曲的规律,并与阶跃载荷作用下的情况进行对比分析,结果与之前文献研究结果吻合良好。     

High trapping forces for high-refractive index particles trapped in dynamic arrays of counterpropagating optical tweezers

We demonstrate the simultaneous trapping of multiple high-refractive index (n > 2) particles in a dynamic array of counterpropagating optical tweezers in which the destabilizing scattering forces are canceled. These particles cannot be trapped in single-beam optical tweezers. The combined use of two opposing high-numerical aperture objectives and micrometer-sized high-index titania particles yields an at least threefold increase in both axial and radial trap stiffness compared to silica particles under the same conditions. The stiffness in the radial direction is obtained from measured power spectra; calculations are given for both the radial and the axial force components, taking spherical aberrations into account. A pair of acousto-optic deflectors allows for fast, computer-controlled manipulation of the individual trapping positions in a plane, while the method used to create the patterns ensures the possibility of arbitrarily chosen configurations. The manipulation of high-index particles finds its application in, e.g., creating defects in colloidal photonic crystals and in exerting high forces with low laser power in, for example, biophysical experiments.     

离子在矩形波四极场中的运动与四极场离子阱质谱的数字化操作

矩形波驱动的四极场同样可用于对离子进行质量分析和存储。本文推导了离子在矩形波四极场中的运动规律,并以常用于正弦波四极场的马绍方程参量a,q来表出离子的稳定性。运用赝势阱概念探讨了离子在这种四极场中的本征振动,推导了本征振动频率的近似公式。在理论研究的基础上,提出了数字化离子阱质谱的概念,并运用离子光学模拟,研究了实际离子阱几何结构下的共振出射以及数字化质量扫描的可行性。     

高层斜交网格结构体系的性能研究

为研究钢管混凝土柱的轴向恢复力模型,设计制作了8个钢管混凝土柱试件并对其进行轴向往复加载,分析其受力机理和恢复力特性。基于试验结果,选用退化三线型模型,建立了钢管混凝土柱无量纲骨架曲线模型,并提出其轴拉与轴压方向的峰值承载力和位移的计算方法。鉴于钢管混凝土试件在轴拉与轴压方向受力机理的差异,对滞回曲线的正负向选用不同的滞回规则,建立了相应的卸载刚度函数。据此提出了钢管混凝土柱的轴向恢复力模型,并与试验滞回曲线进行对比,验证了恢复力模型的合理性,所建立的恢复力模型可为斜交网格结构体系的弹塑性分析提供依据。     

轴向往复荷载作用下圆钢管混凝土柱恢复力模型研究

为研究钢管混凝土柱的轴向恢复力模型,设计制作了8个钢管混凝土柱试件并对其进行轴向往复加载,分析其受力机理和恢复力特性。基于试验结果,选用退化三线型模型,建立了钢管混凝土柱无量纲骨架曲线模型,并提出其轴拉与轴压方向的峰值承载力和位移的计算方法。鉴于钢管混凝土试件在轴拉与轴压方向受力机理的差异,对滞回曲线的正负向选用不同的滞回规则,建立了相应的卸载刚度函数。据此提出了钢管混凝土柱的轴向恢复力模型,并与试验滞回曲线进行对比,验证了恢复力模型的合理性,所建立的恢复力模型可为斜交网格结构体系的弹塑性分析提供依据。     

轴向力作用下非对称支承Euler-Bernoulli梁在过屈曲前后的横向自由振动

基于轴线可伸长杆的几何非线性理论，建立了Euler-Bemoulli梁在轴向载荷作用下过屈曲横向自由振动的精确模型，并采用打靶法数值求解了一端可移简支一端固定的Euler-Bemoulli梁在过屈曲前后的小振幅自由振动，获得了线性振动的响应。结果表明，轴向力对过屈曲前后梁的各阶固有频率均有影响。     

Measurement of Relaxation Time Constants of Optically Pumped Stored Mercury Ions

A method is described which makes it possible to measure the relaxation time constants of mercury ions. They are confined in a radio-frequency trap and optically pumped in order to observe the hyperfine transition in their ground state. This method is based on the study of the fluorescence signal emitted by the ions in various steady- and transient-state experiments. The storage time, longitudinal and transverse relaxation times, and the optical pumping time are measured.     

地下管线在空间随机分布的地震作用下的反应

强震作用下地下管线地震反应计算以往多采用波动法求解。这种方法假定地震波为一行进波,沿管线的轴向或成某一角度传播,它只能求得地面运动的相位差引起的管线的变形和内力。有些文献将地震地面运动假定为空间变化的平稳随机过程,用随机振动理论求得管线的地震反应,但不能反映地面运动的非平稳性对管线地震反应的影响。而地面运动的非平稳性,特别是时域非平稳性很可能是产生地下管线变形和内力的最重要原因。根据地面运动的统计模型生成管线轴线上各点的地面运动时程,用级数解法求管道的地震反应。由于这种方法能较好地反映地面运动的时域非平稳性,所以得到的计算结果更真实。     

Three-dimensional optical-transfer-function analysis of fiber-optical two-photon fluorescence microscopy

The three-dimensional optical transfer function is derived for analyzing the imaging performance in fiber-optical two-photon fluorescence microscopy. Two types of fiber-optical geometry are considered: The first involves a single-mode fiber for delivering a laser beam for illumination, and the second is based on the use of a single-mode fiber coupler for both illumination delivery and signal collection. It is found that in the former case the transverse and axial cutoff spatial frequencies of the three-dimensional optical transfer function are the same as those in conventional two-photon fluorescence microscopy without the use of a pinhole.However, the transverse and axial cutoff spatial frequencies in the latter case are 1.7 times as large as those in the former case. Accordingly, this feature leads to an enhanced optical sectioning effect when a fiber coupler is used, which is consistent with our recent experimental observation.     

Influence of dislocations on magnon-phonon couplings: A phenomenological approach

On the basis of a nonlinear theory of finitely deformable elastoviscoplastic ferromagnetic crystals developed in a companion paper, the present work presents an attempt at a phenomenological study of the influence of dislocations and viscoplastic flow on the behavior of spin waves (the collective modes of oscillations typical of ferromagnetism). This is achieved by linearizing the above mentioned nonlinear theory about a fundamental ferromagnetic phase with a practically vanishing viscoplastic threshold. The main results obtained after a study of wave modes and asymptotic evaluations in terms of a piezomagnetic coupling parameter are the evidence of a magnetoacoustic resonance between spin waves and left circularly polarized transverse elastoviscoplastic disturbances, a slight shift towards higher wave numbers of the corresponding critical wave number as compared to the perfectly elastic-crystal case and the fact that spin waves suffer a damping which is directly proportional to the piezomagnetic coupling parameter and to the reciprocal primary relaxation time (the relaxation time associated with the viscosity processes inherent in viscoplasticity, in the absence of restoring effects.