激光功率对光镊光阱刚度标定的影响

光阱刚度是描述光镊对粒子进行操控的重要力学指标,实际使用过程中会受到激光功率的影响。采用均方位移法及玻尔兹曼统计法对搭建的光镊系统进行光阱刚度的标定,利用图像采集方法进行微粒位移的测量,并对两种方法的测量结果进行了比较。为了提高光阱刚度的标定结果的准确性,分析了光路放大倍数、温度变化对最后标定结果的精度影响。结果表明,两种方法进行标定的结果基本相同;光阱刚度在低激光功率（1 mW ~20 mW）范围时随功率近似线性增加,在高功率情况下（25 mW~60 mW）随功率增加不再线性增加,而是趋于一个饱和值。此外,光路放大倍数标定的精确性对标定的精度影响较大,10%的相对误差时,标定结果产生23%的变化,温度对标定的精度影响较小,0.1 ℃的温度变化导致标定结果0.034%的变化。     

球模型生物细胞在光镊势阱中的动力学分析

用动力学方法求出了球模型生物细胞在光阱中的横向位移均方差与时间的关系.结果表明：小球在光阱中服从Boltzman分布,两种方法可用于直接对细胞光阱力标定;细胞位移幅度典型值为纳米量级,定标系统的空间分辨率为纳米量级.结论和已有实验结果相符.     

用漂移和扩散概念求解光阱中细胞的热驱动分布

用漂移和扩散的概念对热驱动下光阱中的细胞进行动力学分析,得到细胞随空间位置的概率密度分布为玻尔兹曼分布,该分布可用于一般形状的、光学性质各向异性的生物细胞光阱力的标定.     

热驱动法测量光阱刚度的蒙特卡罗模拟

在应用光镊测量微米粒子或生物大分子之间力学特性之前,必须对光镊的光阱刚度进行精确标定,选择精确的标定方法对测量的准确性起着决定作用。采用Monte-Carlo方法,模拟了光阱中的一个粒子在5s时间内其位移随时间变化的信号序列,模拟采样频率为105Hz。基于不同程度噪声和光阱偏移量条件下的模拟实验数据,用三种热驱动力分析法对光阱刚度进行标定。结果表明,三种方法的理想误差均小于2.5%;将粒子位移序列的坐标减去其平均值后得到新的位移序列,然后进行刚度标定,可以消除光阱偏移引入的误差;均方位移法比功率谱法和玻尔兹曼分布法具有更好的抗噪声干扰能力。     

时间飞行法测量光阱刚度的实验研究

传统的测量光阱刚度的方法如功率谱法是基于微粒的布朗运动,适用于直径范围几百纳米到几微米的微球,在几微米以上并不具有明显优势．本文发展一种时间飞行的方法测量光阱对微球的刚度．该方法是基于跟踪微粒的运动轨迹获得光阱刚度．通过比较不同功率下,不同大小以及不同材料的微球的光阱刚度和误差,结果表明时间飞行法适用于直径范围5—10μm的微球;论文中用功率谱法和均方位移法测量了5μm标准聚苯乙烯小球的光阱刚度与时间飞行法测得的结果作为对比,由于受相机采集速率的影响,所测刚度值比理想值偏高,比较而言,时间飞行法的测量结果更加接近于真实值,对于光阱刚度的快速标定有着重要意义．该方法可以应用在特殊光场分布的激光阱中测量微球的光阱刚度;在实现细胞层次的力学特性测量中它可避免使用微球作为探针,为更深层次研究细胞上的复杂单分子过程提供了一个研究手段．     

两种单光纤光镊捕获效果的数值仿真与实验研究

采用一种基于时域有限差分(FDTD)的数值算法,仿真计算了抛物线形和大锥角形两种新型单光纤光镊的出射光场,并在稳态场下通过对麦克斯韦应力张量积分求得介质球在两种光场中受到的光阱力,得到大锥角型光纤端产生的光阱力较大的结论;讨论了不同介质球大小、折射率,光纤探针形状对光阱力的影响.在实验中这两种光纤探针都实现了对水中酵母菌细胞的捕获,且采用流体力学法对抛物线形和大锥角形二种新型单光纤光镊产生的光阱力进行了标定.结果表明:基于FDTD数值仿真方法计算受力与实验结果一致,并且这种计算光纤光镊产生的光阱力的方法简单.适用;且抛物线形和大锥角形光纤探头都具备构成单光纤光镊的条件.     

功率谱密度法标定光镊的三维光阱刚度

采用四象限探测器和功率谱密度法,搭建了一套快速标定光镊三维光阱刚度的测量系统.实验中,用四象限探测器记录微粒做受限布朗运动时的位置信息,用功率谱密度法标定光阱刚度,测得了直径0.97μm SiO2小球和直径1μm PMMA小球的光阱刚度与激光功率的关系.结果表明:对于SiO2小球,当激光功率为50~120mW时,光阱刚度与激光功率成正比;对于PMMA小球,当激光功率为80~130mW时,光阱刚度与激光功率成正比.该光镊系统可用于生物、物理等微观领域研究的高准确度测力系统.     

基于自回归模型的光阱中粒子运动模拟

通过分析光阱中颗粒位移信号特性, 建立描述粒子受限布朗运动过程的自回归模型, 进而提出了一种基于自回归模型的光阱中颗粒运动信号模拟的新方法. 对半径为1 μm的粒子处于光阱刚度分别为10, 20, 50 pN/μm 光阱时的位移信号进行了模拟, 得到的模拟位移信号的自相关函数与理论值相一致. 为了进一步阐明自回归模型的有效性, 在相同光阱参数下, 分别采用自回归模型与蒙特卡罗方法模拟光阱中微粒的位移信号, 采用功率谱法分别对两种模拟方法所得的微粒位移标定光阱刚度, 结果表明自回归模型方法能够取得和蒙特卡洛法相同的精度. 因此, 本文为分析光阱中粒子的随机运动提出了一种新的模拟方法, 可以用来对光阱中的噪声及特性进行分析. 关键词： 光阱 布朗运动 信号模拟 自回归模型     

细胞光阱刚度与折射率关系理论计算

为了探讨用光镊技术进行细胞折射率的测量方法,用几何光线理论对可作为米氏粒子模型的生物细胞(半径a=10μm,折射率n=1.35~1.70),在单光束梯度力光阱[激光波长λ=780 nm,功率P=6 mW,焦斑半径w(0)=0.6μm、0.8μm和1.0μm]中的轴向光阱刚度与细胞折射率关系进行了数值计算。结果表明,光阱刚度随折射率的变化关系与三次多项式曲线拟合得较好;用测量光阱刚度计算细胞的折射率时,需要用折射率已知的四种标准粒子对三次多项式曲线进行标定。     

液晶空间光调制器产生可调三光学势阱

提出了产生三光学势阱的新方案, 在该方案中用液晶空间光调制器制作相位型闪耀光栅, 单色相干光照明, 产生按等边三角形分布的三个光学势阱, 三个光阱光强大小分布相同, 调节空间光调制器的相位分布, 可以改变光阱的相对位置, 实现三光阱到单个光阱、两光阱合并为一个光阱等演变及其反向演变, 调节过程简单、方便. 根据现有空间光调制器性能和尺寸, 模拟设计光栅, 计算三光阱的光强分布和调控过程中光强的变化, 结果表明: 用一般功率的激光照明, 能够得到具有较大峰值光强和较高光强梯度的可调三光阱, 在原子和分子光学实验研究中有多种重要的应用. 关键词： 原子和分子光学 可调三光学势阱 空间光调制器     

Methods of calibration to optical trapping force upon non-spherical cells

The dynamical equation of a trapping cell is solved to find calibration methods for the trapping force, and two methods are compared by synthetic experiment data. Results indicate that: Boltzmann distribution method (BDM) is available for the force calibration of non-spherical or anisotropic cells in arbitrary trap potential; the mean square displacement method (MSDM) is available only for a symmetric harmonic optical trap. The spatial resolution requirement of the calibration system is about a nanometer. The results agree with the reported experiments.     

Optical Force Sensing with Cylindrical Microcontainers

Quantitative force sensing reveals essential information for the study of biological systems. Forces on molecules, cells, and tissues uncover functioning conditions and pathways. To analyze such forces, spherical particles are trapped and controlled inside an optical tweezers (OT) trap. Although these spherical particles are well‐established sensors in biophysics, elongated probes are envisioned for remote force sensing reducing heat damage caused by OT. There is thus a growing demand for force metrology with OT using complexly shaped objects, e.g., sac‐like organelles or rod‐like bacteria. Here, the employment of Zeolite‐L crystals as cylindrical force sensing probes inside a single optical trap is investigated. It is shown that cylindrical objects can be used as force probes since existing calibration assays can be performed with suitable corrections. Forces of active driving assays are compared with passive calibration methods. Finally, the investigations are extended to direct force measurements based on momentum calibration, in which the influence of rotation due to torque in a single optical trap is unveiled. Simulations reveal the relation between torque and the position of equilibrium in the trap. The results highlight the functionality of Zeolite‐L crystals as probes for force sensing, while opening perspectives for enhanced, accurate force metrology in biophotonics.     

Measuring the complete force field of an optical trap

The use of optical traps to measure or apply forces on the molecular level requires a precise knowledge of the trapping force field. Close to the trap center, this field is typically approximated as linear in the displacement of the trapped microsphere. However, applications demanding high forces at low laser intensities can probe the light-microsphere interaction beyond the linear regime. Here, we measured the full nonlinear force and displacement response of an optical trap in two dimensions using a dual-beam optical trap setup with back-focal-plane photodetection. We observed a substantial stiffening of the trap beyond the linear regime that depends on microsphere size, in agreement with Mie theory calculations. Surprisingly, we found that the linear detection range for forces exceeds the one for displacement by far. Our approach allows for a complete calibration of an optical trap.     

New calibration method for position detector for simultaneous measurements of force constants and local viscosity in optical tweezers

We present a new method to calibrate a quadrant photodiode used as position detector to monitor latex beads trapped in optical tweezers. The method combines the dragging Stoke’s force with the thermal noise analysis (power spectral density (PSD)) of the Brownian motion of the trapped bead. Position detector calibrations used in other similar methods normally utilise a bead attached to the coverslip: the voltage-position calibration factor is found by translating the bead across the waist of a laser beam. The so determined calibration factor is then assumed to be the same when beads are investigated in the optical trap. This procedure presents some drawbacks since attached beads can be affected by proximity effects due to the coverslip glass surface which alter the position sensor response itself. On the contrary, our method is able to provide, simultaneously, the calibration factor, the trap stiffness, and the local viscosity of the medium making use of a single trapped bead.     

Monte-Carlo simulation of optical trap stiffness measurement

The high precision calibration of optical trap stiffness is the foundation of the weak force measurement in an optical tweezers system. And the accuracy of the trap stiffness measurement is limited by the bandwidth of the acquisition system. In this article, such an influence is analyzed and discussed. The stiffness measuring process using an acquisition system with a finite acquisition time is numerically simulated by using Monte-Carlo method. Then the simulated results are analyzed by thermal motion analysis method to deduce the trap stiffness for different trapping system and for measuring systems with different acquisition time. As a comparison the power spectrum analysis method is used to study the thermal motion of the bead and to compute the trap stiffness for the same acquisition system, from which it is concluded that the bandwidth of the acquisition system is determined by its acquisition time, not the sampling frequency. The influence of the finite acquisition time or the limited bandwidth on the trap stiffness measurement is discussed. The numerical simulation shows that the measured position, which is here the average position within the acquisition time, shifts to the trap center due to the trapping force, which gives an alternative interpretation for the deviation of the measured stiffness from the true trap stiffness.     

Calculation and optical measurement of laser trapping forces on non-spherical particles

Optical trapping, where microscopic particles are trapped and manipulated by light is a powerful and widespread technique, with the single-beam gradient trap (also known as optical tweezers) in use for a large number of biological and other applications. The forces and torques acting on a trapped particle result from the transfer of momentum and angular momentum from the trapping beam to the particle. Despite the apparent simplicity of a laser trap, with a single particle in a single beam, exact calculation of the optical forces and torques acting on particles is difficult. Calculations can be performed using approximate methods, but are only applicable within their ranges of validity, such as for particles much larger than, or much smaller than, the trapping wavelength, and for spherical isotropic particles. This leaves unfortunate gaps, since wavelength-scale particles are of great practical interest because they are readily and strongly trapped and are used to probe interesting microscopic and macroscopic phenomena, and non-spherical or anisotropic particles, biological, crystalline, or other, due to their frequent occurance in nature, and the possibility of rotating such objects or controlling or sensing their orientation. The systematic application of electromagnetic scattering theory can provide a general theory of laser trapping, and render results missing from existing theory. We present here calculations of force and torque on a trapped particle obtained from this theory and discuss the possible applications, including the optical measurement of the force and torque.     

Tunable gradient force of hyperbolic-cosine–Gaussian beam with vortices

Gradient force plays an important role in optical tweezers technique. In this paper, the tunable gradient force in focal plane of the hyperbolic-cosine–Gaussian (ChG) beam is investigated numerically. The ChG beam contains one spiral vortex and one non-spiral vortex. Simulation results show that the gradient force distribution can be altered considerably by decentered parameters of ChG beam, topological number of the spiral vortex, and vortex parameter of the non-spiral vortex. Many novel gradient force patterns can occur, which means corresponding optical traps may come into being, including ring optical trap, multiple-point trap pattern, line optical trap, rectangle trap pattern, and rhombus trap pattern. In addition, force pattern evolution principle may also differ significantly.     

Investigations on the Behaviour of an Aerodynamic Particle Sizer and its applicability to calibrate an optical particle counter

The calibration of an optical particle counter (OPC) by means of the Aerodynamic Particle Sizer APS (TSI, Model 3310) was investigated. The pulse-height distribution and the aerodynamic size distribution were measured by parallel use of an OPC and the APS. A calibration curve was obtained by comparison of the two different cumulative distribution curves. First calibration results are presented for spherical particles (water droplets and glycerine droplets): A comparison of these results with Mie calculations and aerodynamic calibrations by means of sampling cyclones shows good agreement. Furthermore, measurements were carried out with non-spherical particles. Quartz dust was used for these measurements. In order to calibrate the OPC by means of the APS, the behaviour of both devices was investigated.     

Radiation torque and force on optically trapped linear nanostructures

We study the optical trapping of highly elongated linear nanostructures in the focal region of a high-numerical aperture lens (optical tweezers). The radiation torque and trapping force on these nanostructures that are modeled as chains of identical spherical scatterers are calculated by means of multipole field expansions in the framework of the transition matrix approach. We investigate both orientational and trapping stability and calculate force constants and trap parameters in order to clarify the role of the linear geometry in the optical trapping mechanism. Furthermore, we calculate optical trapping of nanowires of different materials and compare our theoretical findings with available experimental results.     

Gradient force evolution of Gaussian beam induced by a phase plate

The evolution of gradient force pattern induced by an annular phase distribution plate is numerically investigated in this paper. The phase plate, which may alter the wavefront phase of incident Gaussian beam with tunable topological charge, consists of two concentric portions, one center circle portion and one annular portion. Numerical simulations show that the proposed plate can induce the tunable gradient force on the particles in the focal region. By adjusting the geometrical parameters or changing the topological charge of the phase-shifting plate, some novel trap patterns may occur, such as triangle shape trap, quadrangle shape trap, pentagon shape trap, hexagon shape trap, and the shapes of optical traps change very considerably. Therefore, the phase plate may be very advantageous for constructing tunable optical traps. The method is more versatile in that it allows precise control of the parameters and has the possibility of generating specific patterns of optical vortices. The gradient force pattern focal of intensity distribution depends on both the annular width and the topological charge.