Detecting the motion of an object involves the measurement of its position or velocity. In this thesis, we consider optical detection of motion for two different cases: the monitoring of particle displacement in optical tweezers and the detection of surface displacements due to ultrasonic vibrations.In the first part of the thesis, we consider the resolution limit of particle sensing in optical tweezers. Optical tweezers are formed by tightly focusing light. The resulting optical gradient then gives rise to a restoring force which can be used to trap a particle. Displacement measurements can then be carried out by monitoring the scattered light from the trapped particle. Optimal displacement measurements can be performed by measuring the position of every photon, for example, by using an idealised detector array consisting of infinitesimally small pixels. In practice, quadrant photodiodes are typically used; however, these have previously been shown to be non-optimal for measurements of small beam displacements. Here we developed a model of an optical tweezers system and similarly show that quadrant photodiodes are non-optimal for particle displacement measurements in optical tweezers. We propose an alternative detection scheme based on spatial homodyne detection, where the local oscillator beam is spatially tailored in order to optimally detect the particle displacement. We show that spatial homodyne detection is optimal and outperforms quadrant photodiodes for all cases at the shot noise limit. Measurements below this limit can be performed by using quantum resources such as quadrature squeezed light.In the second part of the thesis, we investigate the optical detection of surface displacements due to ultrasonic vibrations. Ultrasound is commonly used in industrial and biological imaging applications due to its non-destructive nature. By using optical means, detection capability can be extended to include remote sensing capabilities, as well as selective detection of materials using their optical absorption spectrum. Light reflecting off a vibrating surface becomes phase modulated, resulting in upper and lower sidebands in the optical spectrum which are shifted by the ultrasound frequency. To detect the modulated light,interferometers are typically used. However, they have found limited practical use when optically rough surfaces are encountered due to a low light collection efficiency, or étendue, arising from mode-matching requirements. In contrast, a filter engraved in a rare earth doped crystal (Tm:YAG) to bandpass one sideband has recently been demonstrated to allow much greater étendue. However, to obtain high sensitivity, narrow yet deep engraved features are required, which are difficult to obtain due to the transient nature of the Tm3+ ion. Here we demonstrate detection using dispersive filters to shift the phase of the unmodulated light with respect to the sidebands. This induces an amplitude modulation, which can then be detected using a photodiode. We show that sensitive detection is possible even with modest material properties. A drawback of using these crystals is the requirement of an expensive and bulky cryogenic cooler. To address this, we also demonstrate the detection of ultrasound using dispersive filters formed using two-photon Raman processes in rubidium vapour at near room temperature.
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