Closed-form solutions for the frequency shift of V-shaped probes scanning an inclined surface

The analytical method to determine the frequency shift of an AFM V-shaped probe scanning the relative inclined surface in non-contact mode is proposed. If the tip is not perpendicular to the surface plane, the lateral force to the tip will occurs. Consequently, there exists a moment to the end of probe. The closed-form solution of the partial differential equation with a nonlinear boundary condition is derived. The error of transforming the distributed-masses system into lumped-masses one in the force gradient method or the perturbation method is eliminated. The dimensionless parameters are introduced for reducing the numerical transaction error. The limiting case such as a uniform or tapered beam can be obtained easily from the general system. The assessments of the force gradient method, the perturbation method and the propose method determining the frequency shift of a V-shaped probe are made. It is discovered that increasing the absolute inclined angle θ decreases the frequency shift especially for a small tip-surface distance.     

Theoretical evaluation of the frequency shift and dissipated power in noncontact atomic force microscopy

An exact analytical formula of the frequency shift and dissipated power in noncontact atomic force microscopy (nc-AFM) is obtained, in the case of a tip-surface interaction force with an inverse power law. The frequency shift for various tip shapes is evaluated. It is confirmed that the tip-height dependence of the analytical frequency shift shows very good agreement with that of the experimental one. The tip-height dependence of the dissipated power derived from a Langevin equation approach is also evaluated.     

Calculation of the frequency shift in dynamic force microscopy

A theoretical study of the quality and the range of validity of different numerical and analytical methods to calculate the frequency shift in dynamic force microscopy is presented. By comparison with exact results obtained by the numerical solution of the equation of motion, it is demonstrated that the commonly used interpretation of the frequency shift as a measure for the force gradient of the tip–sample interaction force is only valid for very small oscillation amplitudes and leads to misinterpretations in most practical cases. Perturbation theory, however, allows the derivation of useful analytic approximations.     

An analysis of the distortion effects of Coulomb damping on the vector plots of lightly damped systems

An analysis of the vector plot responses of lightly damped single degree-of-freedom systems with Coulomb damping has been made. The vector plots, as derived by using both an exact and an approximate method (the method of harmonic balance) are compared and it is shown that the distortion of the normally circular vector locus is due to the Coulomb damping. Although the vector plots of such systems are distorted it is also shown that the frequency gradient criterion is still applicable for location of a natural frequency even when the frictional force levels approach the excitation force levels. To permit estimation of the modal damping of these systems a criterion by means of which the limits of the useful frequency range can be specified is suggested. The criterion, which is based upon the quadrature input power necessary to excite the mode of vibration, is found to be equivalent to that obtained from the half power point theory when applied to linear systems.     

The sensitivity of monitoring by measuring the frequency shifts of the sound field interference pattern

The sensitivity of the remote method of reconstructing the frequency spectrum of a water medium perturbation from the measured frequency shifts of the sound field interference peaks is investigated. On the basis of the Rayleigh criterion, an expression is derived for estimating the minimal frequency shift that allows the resolution of two neighboring peaks. The detection sensitivity for the sound velocity fluctuations caused by the time variability of the medium along the track is estimated. Results of computations for a perturbation in the form of background internal waves are presented.     

全光纤M-Z干涉仪的高灵敏度与大动态范围多普勒激光雷达风场探测技术

多普勒测风激光雷达是大气风场探测的重要手段之一。通过检测风速导致的大气后向散射谱的多普勒频移从而实现风速的探测。由于受鉴频器本身特性的影响,高灵敏度与大动态范围的探测一直是大气风场探测的难点。提出采用双光纤Mach-Zehnder干涉仪(FMZI)作为多普勒激光雷达的鉴频器件,设计两路不同动态范围及风速探测灵敏度的FMZI鉴频器同时对大气回波信号进行鉴频。采用小光程差(13.7 cm)、大动态范围(±100 m·s-1)鉴频光路FMZI-2对风速区间进行定位,大光程差(74.8 cm)、高探测灵敏度(2.62%/(m·s-1))的鉴频光路FMZI-1进行风速精细探测,从而实现大动态范围高灵敏度的风场探测。利用标准大气模型对不同参数条件下的系统灵敏度、系统探测的信噪比及风速误差进行仿真分析。结果表明,该系统可以实现±100 m·s-1大动态范围内风速误差小于1 m·s-1的大气风场探测,为大动态范围高灵敏度测风激光雷达的发展进行了有益的探索。     

Internal tissue displacement measurement based on ultrasonic wave Doppler signal digital detection and its application to fetal movement monitoring

We have developed a fetal movement monitoring system based on small displacement measurement of internal tissues. When ultrasonic pulses are transmitted to the fetus, the reflected ultrasonic waves which have a Doppler frequency shift due to the fetal movements are detected by using an ultrasonic pulsed Doppler technique. In this paper, we propose a displacement measurement method for internal tissues which is based on the Doppler signal digital detection technique. In the method, the received ultrasonic RF signals are sampled with a sampling frequency of four times higher than the centre frequency of the ultrasonic waves; the Doppler frequency shift signals are derived using digital signal processing. From the detected signals, the internal displacements are estimated using the arc-tangent method. The basic algorithm of the detection method has already been used in the area of blood flow sensing, however, we apply the algorithm to the displacement measurement of internal tissues. The comparison between the proposed method and the conventional method is presented. The fetal movement quantitative monitoring system based on the method which has been constructed is shown.     

Dynamic analysis of a multi-span uniform beam carrying a number of various concentrated elements

This paper employs the numerical assembly method (NAM) to determine the “exact” frequency–response amplitudes of a multiple-span beam carrying a number of various concentrated elements and subjected to a harmonic force, and the exact natural frequencies and mode shapes of the beam for the case of zero harmonic force. First, the coefficient matrices for the intermediate concentrated elements, pinned support, applied force, left-end support and right-end support of a beam are derived. Next, the overall coefficient matrix for the whole vibrating system is obtained using the numerical assembly technique of the conventional finite element method (FEM). Finally, the exact dynamic response amplitude of the forced vibrating system corresponding to each specified exciting frequency of the harmonic force is determined by solving the simultaneous equations associated with the last overall coefficient matrix. The graph of dynamic response amplitudes versus various exciting frequencies gives the frequency–response curve for any point of a multiple-span beam carrying a number of various concentrated elements. For the case of zero harmonic force, the above-mentioned simultaneous equations reduce to an eigenvalue problem so that natural frequencies and mode shapes of the beam can also be obtained.     

Characteristics of the distributed Bragg reflector fiber laser sensor for lateral force measurement

Characteristics of the distributed Bragg reflector fiber laser sensor for lateral force measurement are investigated. The distributed Bragg reflector fiber laser operates in dual-polarization modes and converts the lateral force into a corresponding shift in the beat frequency generated by the fiber laser. The sensitivity dependence on the angle between the force direction and the polarization axis orientation of the fiber is investigated theoretically and experimentally. The impact of the force action location and force length on the sensor response is also discussed. Good agreement between the theoretical data and the experimental results was obtained. A maximal sensitivity magnitude of ∼10 GHz/(N/mm) is recorded.     

An optimization of frame structures with exact dynamic constraints based on Timoshenko beam theory

Sensitivity analyses of eigensolutions and eigenfunctions of 3-D frame structures using the exact frequency equation from the transfer dynamic stiffness matrix that was derived on Timoshenko beam theory were developed in this paper. Based on the sensitivity data of frame structures, the minimum weight design with an exact frequency constraint can be carried out efficiently. Three examples that demonstrated the results obtained by the proposed method, are in good agreement with those computed by ANSYS.     

A noncontact atomic force microscope in air using a quartz resonator and the FM detection method

Noncontact imaging was successfully performed with the quartz resonator in air by using the FM detection method. A constant frequency shift mode was used. The frequency shift was about -30 mHz, which was induced by the attractive force gradient. A noncontact image of the Si(111) atomic step was obtained with vertical and lateral resolutions of 0.8 Å and 60 Å.     

应变梯度对布里渊光时域反射计测量精度的影响

基于脉冲抽运的布里渊光时域反射计技术具有米数量级的空间分辩力。为了分析在其空间分辨力范围内的应变梯度增加对布里渊谱测量的影响,建立了后向布里渊散射谱与应变梯度的函数关系。数值分析结果表明应变梯度增大,不仅使布里渊频移随之线性增大,也会使后向布里渊散射谱峰值非线性降低,谱峰变得平坦。空间分辨力10m的100με／m应变梯度相对于零应变梯度,引起的布里渊频移测量误差增加2．04倍。传感光纤固定于悬臂梁上以模拟不同应变梯度,采用对频宽小于1MHz的激光脉冲调制和基于相干平衡检测的布里渊光时域反射计系统,实验测得了沿传感光纤的后向布里渊散射谱数据和应变分布。布里渊谱数据经最小二乘法拟合后,得到的不同应亦梯度的谱曲线变化与理论分析相吻合。     

Vibration-based damage detection and evaluation of sheet materials using a remote acoustic excitation

A simple method of damage severity assessment on sheet materials is suggested and proved by theory and experiment. The investigated defect types are in forms of added mass and crack. The method is based on the frequency shift measurement of a material vibrating as a membrane subjected to static tension and irradiated by an acoustic wave. It is shown both theoretically and experimentally that the natural frequency of the damaged membrane is shifted relative to its position in the ideal material. A local increase in thickness (or addition of mass) shifts the natural frequency down, while a crack shifts the frequency up. The method can be considered as acoustic weighting through the frequency shift. The sensitivity of this method can be high because frequency measurement is one of the most accurate measurements in physics and metrology. Published in Russian in Akusticheskiĭ Zhurnal, 2008, Vol. 54, No. 1, pp. 147–155. The text was submitted by the authors in English.     

Precise force measurement method by a Y-shaped cavity dual-frequency laser

A novel precise force measurement based on a Y-shaped cavity dual-frequency laser is proposed.The principle of force measurement with this method is analyzed,and the analytic relation expression between the input force and the change in the output beat frequency is derived.Experiments using a 632.8-nm Y-shaped cavity He-Ne dual-frequency laser are then performed;they demonstrate that the force measurement is proportional to a high degree over almost five decades of input signal range.The maximum scale factor is observed as 5.02×109 Hz/N,with beat frequency instability equivalent resolution of 10-5 N.By optimizing the optical and geometrical parameters of the laser sensor,a force measurement resolution of 10-6 N could be expected.     

A simplified but intuitive analytical model for intermittent-contact-mode force microscopy based on Hertzian mechanics

The forces acting on the substrate in intermittent-contact-mode (IC mode, tapping mode) atomic force microscopy are not accessible to a direct measurement. For an estimation of these forces, a simple analytical model is developed by considering only the shift of the cantilever resonance frequency caused by Hertzian (contact) forces. Based on the relationship between frequency shift and tip–sample force for large-amplitude frequency-modulation atomic force microscopy, amplitude and phase versus distance curves are calculated for the intermittent contact mode, and the forces on the substrate are calculated. The results show a qualitative agreement with numerical calculations, yielding typical maximal forces of 50–150 nN. When working above the unperturbed resonance, forces are found to be significantly larger than below the resonance.     

Complex calibration of a pressure gradient receiver using the reciprocity method procedure

Absolute complex free-field calibration of a pressure gradient receiver is considered. The calibration is carried out in a reflecting water tank using the reciprocity method procedure during radiation of continuous signals with linear free-field frequency modulation. To obtain the free-field frequency dependences, complex moving weighted averaging is used. It is shown that this method, developed for calibration of sound pressure receivers, allows effective recovery and measurement of the vector component of a direct acoustic wave in the presence of reflections. The method makes it possible to measure the modulus and phase angle of the complex sensitivity and reveal the insufficiencies of an experimental pressure gradient receiver.     

An NMR technique for measurement of magnetic field gradient waveforms

Almost all NMR imaging and localized spectroscopic methods fundamentally rely on the use of magnetic field gradients. It follows that precise information on gradient waveform shape and rise-times is often most useful in experimental MRI. We present a very simple and robust method for measuring the time evolution of a magnetic field gradient. The method is based on the analysis of the NMR signal in the time domain, and requires no specialized field measurement probes for its implementation. The technique makes use of the principal that for small flip angles the excitation profile is a good approximation to the Fourier transform of the radio frequency pulse shape. Creation of the NMR signal can be considered as an inverse Fourier transform and thus variation of the gradient strength during the excitation pulse influences the shape of the NMR signal. Although originally designed for measurement of the rise time only, we have now extended the technique to measure the exact time course of the gradient. The theory is confirmed by experimental results for gradient waveform field measurements in a high-field vertical bore system.     

Single-spin measurements for quantum computation using magnetic resonance force microscopy

The quantum theory of a single-spin measurement using magnetic resonance force microscopy is presented. We use an oscillating cantilever-driven adiabatic reversal technique. The frequency shift of the cantilever vibrations is estimated. We show that the frequency shift causes the formation of a Schrödinger cat state for the cantilever. The interaction between the cantilever and the environment quickly destroys the coherence between the two cantilever trajectories. It is shown that using partial adiabatic reversals one can obtain a significant increase in the frequency shift. We discuss the possibility of sub-magneton spin density detection in molecules using magnetic resonance force microscopy.     

Detection of moving objects and flows in liquids by ultrasonic phase conjugation

The possibility for the application of the method of parametric phase conjugation of ultrasonic waves in measuring the velocity of moving objects and flows is investigated. Results of experimental measurements of the Doppler frequency shift are presented for a low-frequency wave (1 MHz) generated by phase-conjugate waves (10 MHz and 11 MHz) propagating in opposite directions in the presence of a moving scatterer. The super high sensitivity of the phase of the low-frequency wave to variations in the spatial position of the scatterer is used to measure the velocity of the object. The presence of flows in the region of propagation of phase-conjugate waves returned leads to an uncompensated Doppler shift of the phase of the phase-conjugate wave at the primary radiation source. The implementation of this feature of ultrasonic phase conjugation for the detection and measurement of the flow velocities in a liquid is demonstrated experimentally.     

低β162.5 MHz taper型HWR腔的机械性能分析（英）

北京大学正在设计=0.09, 频率为162.5 MHz taper型的二分之一波长射频超导谐振腔（HWR腔）, 这种腔针对高流强质子束（约100 mA）和氘束（约50 mA）的加速而设计。对于这种超导腔而言机械性能分析是十分重要的, 可以通过机械性能分析来估计由于腔体的形变带来的频率偏移。用ANSYS分析了由于液氦压力不稳定造成的麦克风效应以及洛伦兹力造成的腔体失谐, 并且对沿腔体轴线方向的调谐进行了分析。模拟结果显示这只腔压力敏感系数为31.1 Hz/kPa, 洛伦兹力系数为－0.41 Hz/(MVm-1)2。 腔体的调谐范围达到177 kHz, 足够补偿腔体可能的频率偏移。腔体的机械性能满足腔体正常运行的要求。