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A novel Radio-Frequency Frequency-Modulated (RF-FM) signal generation method is introduced and a prototype circuit developed to evaluate its functionality and performance. The RF-FM signal generator uses a modulated, voltage-controlled time delay to correspondingly modulate the phase of a 10 MHz sinusoidal reference signal. This modulated reference signal is, in turn, used to clock a Direct Digital Synthesizer (DDS) circuit resulting in an FM signal at its output. The modulating signal that is input to the voltage-controlled time delay circuit is generated by another DDS that is synchronously clocked by the same 10 MHz sine wave signal before modulation. As a consequence, all of the digital components are timed from a single sine wave oscillator that forms the basis of all timing. The resultant output signal comprises a center, or carrier, frequency plus a series of phase-synchronized sidebands having exact integer harmonic frequency separation. In this study, carrier frequencies ranging from 10 MHz to 70 MHz are generated with modulation frequencies ranging from 10 kHz to 300 kHz. The captured spectra show that the FM signal characteristics, amplitude and phase, of the sidebands and the modulation depth are consistent with the Jacobi-Anger expansion for modulated harmonic signals.

This paper presents two models for predicting the frequency response of micro-scale oscillatory probes. These probes are manufactured by attaching a thin fiber to the free end of one tine of a quartz tuning fork oscillator. In these studies, the attached fibers were either 75 μm diameter tungsten or 7 μm diameter carbon with lengths ranging from around 1 to 15 mm. The oscillators used in these studies were commercial 32.7 kHz quartz tuning forks. The first theoretical model considers lateral vibration of two beams serially connected and provides a characteristic equation from which the roots (eigenvalues) are extracted to determine the natural frequencies of the probe. A second, lumped model approximation is used to derive an approximate frequency response function for prediction of tine displacements as a function of a modal force excitation corresponding to the first mode of the tine in the absence of a fiber. These models are used to evaluate the effect of changes in both length and diameter of the attached fibers. Theoretical values of the natural frequencies of different modes show an asymptotic relationship with the length and a linear relationship with the diameter of the attached fiber. Similar results are observed from experiment, one with a tungsten probe having an initial fiber length of 14.11 mm incrementally etched down to 0.83 mm, and another tungsten probe of length 8.16 mm incrementally etched in diameter, in both cases using chronocoulometry to determine incremental volumetric material removal. The lumped model is used to provide a frequency response again reveals poles and zeros that are consistent with experimental measurements. Finite element analysis shows mode shapes similar to experimental microscope observations of the resonating carbon probes. This model provides a means of interpreting measured responses in terms of the relative motion of the tine and attached fibers. Of particular relevance is that, when a "zero" is observed in the response of the tine, one mode of the fiber is matched to the tine frequency and is acting as an absorber. This represents an optimal condition for contact sensing and for transferring energy to the fiber for fluid mixing, touch sensing, and surface modification applications.

The encoded Particle Tracking Velocimetry (ePTV) is introduce in this paper as a specific approach of Particle Tracking Velocimetry (PTV). This method is applied to track particles obtained from flow images that contain significant background noise and relatively low particle density. Encoding is achieved by illuminating the flow with a series of light pulses within individual image exposures. Dependent upon the velocity, each particle will be illuminated multiple times in each image frame with spacing determined by both the pulse train timing and the particle velocity. A search algorithm is used that identifies each particle and seeks the encoded pattern with other particles in the image, repeating this until all encoded particles are found. Based on probability analysis and finite image size an analytic model is developed to determine the ratio of true particles, false particles and those that are ‘lost’ by exiting the image frame. This ePTV technique has been experimentally implemented to track spherical particles suspended in stationary vortices. By using a suspension of micro-particles, subsequent imaging with encoded pulse trains provided snap-shots of the complex flow patterns. Typically, even after filtering, the images show around 100 to 200 particles from which encoded trajectories have been extracted and typically account for about 30% of the objects identified in the image.