Joseph L. Garbini

Measurement of fluid turbulence based on pulsed ultrasound techniques. Part 1. Analysis

The pulsed ultrasonic Doppler velocimeter has been used extensively in transcutaneous measurement of the velocity of blood in the human body. It would be useful to evaluate turbulent flow with this device in both medical and non-medical applications. However, the complex behaviour and limitations of the pulsed Doppler velocimeter when applied to random flow have not yet been fully investigated. In this study a three-dimensional stochastic model of the pulsed ultrasonic Doppler velocimeter for the case of a highly focused and damped transducer and isotropic turbulence is presented. The analysis predicts the correlation and spectral functions of the Doppler signal and the detected velocity signal. The analysis addresses specifically the considerations and limitations of measuring turbulent intensities and one-dimensional velocity spectra. Results show that the turbulent intensity can be deduced from the broadening of the spectrum of the Doppler signal and a mathematical description of the effective sample-volume directivity. In the measurement of one-dimensional velocity spectra at least two major complicacations are identified and quantified. First, the presence of a time-varying, broad-band random process (the Doppler ambiguity process) obscures the spectrum of the random velocity. This phenomenon is similar to that occurring in laser anemometry, but the ratio of the level of the ambiguity spectrum to the largest detected velocity spectral component can be typically two to three orders of magnitude greater for ultrasonic technique owing to the much greater wavelength. Secondly, the spatial averaging of the velocity field in the sample volume causes attenuation in the measured velocity spectrum. For the ultrasonic velocimeter, this effect is very significant. The influence of the Doppler ambiguity process can be reduced by the use of two sample volumes on the same acoustic beam. The signals from the two sample volumes are cross-correlated, removing the Doppler ambiguity process, while retaining the random velocity. The effects of this technique on the detected velocity spectrum are quantified explicitly in the analysis for the case of a three-dimensional Gaussianshaped sample-volume directivity.

The theory of oscillator-coupled magnetic resonance with potential applications to molecular imaging

This article describes systems in which the precession of a single particle spin is magnetically coupled to the excitation of an oscillator. The behavior of such systems resembles that of a ‘‘folded’’ Stern–Gerlach experiment, in which the linear spatial trajectory of the original Stern–Gerlach experiment is folded into the cyclic trajectory of an oscillator. Both quantum and semiclassical solutions to the equations of motion are derived. The results encompass any kind of oscillator which couples to a magnetic field. Examples include mechanical cantilevers with a magnetic source affixed to them, as well as inductor‐capacitor resonant circuits. One potential application of oscillator‐coupled magnetic resonance is the imaging of biological molecules. Some design issues relevant to molecular imaging are discussed.

OPTIMAL CONTROL OF FORCE MICROSCOPE CANTILEVERS. II. MAGNETIC COUPLING IMPLEMENTATION

We describe the implementation of optimal controllers for damping the motion of cantilevers used in magnetic resonance force microscopy. We demonstrate that optimal control is achievable and that torsional magnetic coupling provides an effective actuation method. Cantilever Brownian vibrational amplitude was reduced from 2 to 0.16 A and resonant quality was reduced from 2000 to 5. Applied control fields were sufficiently small that they would not affect magnetic resonance phenomena.

Force-detected magnetic resonance in a field gradient of 250 000 Tesla per meter

We report the detection of slice-selective electron spin resonance with an external magnetic field gradient comparable to local interatomic gradients, using the techniques of magnetic resonance force microscopy. An applied microwave field modulated the spin-gradient force between a paramagnetic DPPH sample and a micrometer-scale ferromagnetic tip on a force microscope cantilever. A sensitivity equivalent to 184 polarized electron moments in a one-Hertz detection bandwidth was attained. We mapped the tip magnetic field with a resonant slice thickness of order one nanometer, thereby demonstrating magnetic resonance on length scales comparable to molecular dimensions.

Nanometer-scale magnetic resonance imaging

Magnetic resonance force microscopy (MRFM) images the three-dimensional spatial distribution of resonant spins by mechanical force detection. Image reconstruction in MRFM is challenging because the resonance occurs in a strongly curved shell that extends beyond the scan range. In contrast with conventional magnetic resonance imaging, where Fourier techniques work well, the curved-shell resonant geometry inherent to MRFM requires novel reconstruction methods. Here, we show the application of iterative reconstruction in an electron spin resonance imaging experiment with 80 nm voxels. The reconstructed image has a total scan volume of 0.5 cubic micrometers, and was generated by a magnetic resonant shell with a curvature radius of 2.3 μm. The imaged object was a paramagnetically doped solid with an obliquely tilted surface. The reconstructed image correctly identified the location and orientation of the surface, and mapped the spin distribution within the solid. Applications of MRFM include three-dimensional nanometer-scale mapping of dopant distributions in semiconductors, studies of magnetism of thin films, and spin diffusion physics. An ultimate goal of MRFM is the direct observation of molecular structure at the atomic scale.

Optimal control of force microscope cantilevers. I. Controller design

In magnetic resonance force microscopy (MRFM) experiments, magnetic forces couple to the motion of microscale cantilever beams. Extension of MRFM to the detection of single electrons will require both unprecedented force sensitivity and motional stability of the cantilever. We describe the principles and performance of optimal cantilever motion control. The method accounts for inherent noise processes and practical application of control forces. We show that active feedback control improves cantilever motional stability, enabling instrument designs of much higher sensitivity and faster imaging than passive designs. Experimental results of implemented cantilever control systems are presented in Part II.

Anharmonic modulation for noise reduction in magnetic resonance force microscopy

This article presents a new modulation technique for noise reduction in magnetic resonance force microscopy. Applied fields are modulated at frequencies that are not rational fractions of the cantilever resonant frequency, thus avoiding overtones that contribute to the noise level. An on‐resonance signal is obtained because the nonlinear sample magnetization acts as a frequency mixer of the two modulation frequencies, producing a net force modulation at the cantilever resonant frequency. These techniques are experimentally demonstrated using electron spin resonance in a <15 ng sample of diphenylpicrylhydrazil.

Optimal control of ultrasoft cantilevers for force microscopy

The goals of optimal control in force microscopy are: (1) to obtain favorable cantilever dynamic properties and (2) to control the cantilever to a desired amplitude, while (3) exerting as little control force as possible, and (4) preserving the force signal-to-noise ratio of the uncontrolled cantilever. This article describes the experimental implementation of an optimal controller that achieves these goals. The application of this controller to an ultrasoft cantilever with spring constant of 110 μN/m at 10 K reduced the resonant quality from 15 000 to 220, reduced the Brownian amplitude from 11.2 A to 1.4 A, used less than 7×10−17 N of control effort, left the force sensitivity unaltered at 9.8×10−18 N/ Hz, and demonstrated feedback control can force cantilever motion to track a reference input.

Thermal tuning of a fiber-optic interferometer for maximum sensitivity

We describe a fiber-optic interferometer that employs wavelength changes to achieve maximum sensitivity. Wavelength changes are induced by adjusting the operating temperature of the laser, eliminating the need for an actuator to vary the spacing between the sensing fiber and the object to be monitored. The instrument and techniques described are suitable for cryogenic, high vacuum applications such as magnetic resonance force microscopy, where space is limited and micromanipulation can be challenging. The noise floor of 1.6×10−3 nm/Hz is adequate for monitoring subangstrom displacement of force microscope cantilevers.

Measurement of fluid turbulence based on pulsed ultrasound techniques. Part 2. Experimental investigation

An extensive experimental programme in both laminar and turbulent flow was undertaken to examine the validity of all of the major implications of the model of the pulsed ultrasonic Doppler velocimeter for turbulent flow developed in part 1 of this investigation. The turbulence measurements were made in fully developed flow at the centre of a 6·28 cm diameter pipe. The Reynolds number of the flow ranged from 6000 to 40000. The carrier frequency of the ultrasonic velocimeter was 4·7 MHz. Measurements of the turbulence intensity and of the one-dimensional velocity spectra made with the ultrasonic velocimeter are compared with the analysis and with the actual quantities as measured by a hot-film anemometer. The experimental results are in agreement with theoretical predictions. Measurements of one-dimensional turbulence spectra with reduced ambiguity spectra made by the two sample volume methods described in part 1 are presented. The results verify the analysis and indicate that an improvement in the useful dynamic range of the velocity power spectrum of nearly three orders of magnitude can realistically be achieved.