There has gradually emerged a class of linear, acousto-optic filtering systems that offer gigahertz bandwidth capability, filter Q's exceeding 1000, and real-time programmability of the frequency response in either the time or frequency domain. This class of linear systems is referred to as LAHF (linear, acousto-optic, heterodyne, frequency-plane) filtering and is expected to provide new levels of real-time performance for wideband radar, communications, and signal-processing systems. One important application involves the automatic rejection of narrowband interference from broadband signals.;This dissertation describes the basic principles, characteristics and limitations of the LAHF filter. The related area of phase distortion introduced by the acousto-optic interaction is also examined.;One area of research is concerned with the LAHF filter response. A general LAHF filter response is derived. A specific LAHF filter response form useful for narrowband frequency rejection is studied with computer simulation and verified experimentally. Tradeoffs among window apodization, frequency rejection notch width, and filter time delay are discussed.;Another research area examines the properties of heterodyne detection with a large-area photodetector in relation to the LAHF filter. The results show that some filter configurations are sensitive to the spatial and temporal coherence of the optical source, while other configurations are not. Also, some filter configurations are sensitive to mechanical vibrations that phase-modulate the output RF signal, while other configurations avoid this vibration sensitivity. This potential phase modulation does not affect the filter group delay.;The three key elements of LAHF filter are: (1) acousto-optic modulation to convert the electrical RF input to an optical amplitude signal, (2) optical heterodyne detection with a large-area photodetector for linear filtering and conversion to an electrical RF output, and (3) a frequency-plane spatial light modulator for additional filter response control.;The dynamic range of the LAHF filter is calculated and optimized. The signal-to-noise ratio is seen to be inversely proportional to the filter time-bandwidth product. A numerical example shows that a shoebox size LAHF designed for narrowband frequency rejection using a time-bandwidth product of 500 and a 5 mW laser can achieve a 37-dB signal-to-noise ratio over a full 200 mHz of bandwidth.;Acousto-optic phase distortion is also studied and related to phase distortion in the LAHF filter response. One source of potential phase distortion is shown to be the planar, acousto-optic-medium-to-air boundary. The results show that the quadratic phase distortion resulting from this boundary can be eliminated in a plane parallel to the boundary, while the remaining higher-order phase distortions are typically small if the acousto-optic modulator width is designed near its theoretical minimum width.;Another source of acousto-optic phase distortion is shown to be the acousto-optic diffraction process. To demonstrate this, a new highly accurate model for weak acousto-optic diffraction in isotropic media is derived. This three-dimensional model accounts for acoustic diffraction and numerical results can be obtained using a simple computer integration program. The results show that quadratic phase distortion can be eliminated along a certain skew plane within the acousto-optic medium. The remaining higher-order, non-quadratic phase distortions typically become significant for bandwidths of 1 GHz or more. The acousto-optic diffraction model is also used to calculate magnitude and phase distortions that occur when the acoustic transducer and/or optical beam heights are too small.
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