Resolution improvement in acoustic holography using aperture expansion techniques
One of the main reasons for the restricted application of holography in acoustic imaging is the limited resolution due to the relatively small numerical aperture for a given physical aperture. There is also a lack of suitable acoustic area detectors which provide adequate sensitivity and spatial resolution and which can be extended over large areas. The number of points at which the hologram can be sampled is limited by time or cost considerations. A requirement therefore exists for investigating signal processing techniques for resolution improvement in acoustic holography. Fortunately, the availability of linear detectors in acoustics and the relatively small amount of available data make such techniques easier to implement, especially with the increased availability of fast, efficient, and cheap computers and signal processing devices. This thesis treats the limited resolution in holography as one facet of the basic problem of diffraction and wavelength limitations on the resolu tion of imaging systems. Although a number of techniques have been reported in the literature for resolving beyond the diffraction limit both in optics and microwaves, these suffer from sensitivity to noise, the requirement for a priori information on the object or the need for long computation times. The thesis proposes a new method for resolution improvement by aperture expansion using the principle of analytic continuation. This method has the advantages of computation simplicity, versatility, and robustness against noise. In the proposed technique, the hologram function is modelled using the data at the available limited aperture and the model is used to predict new points outside this aperture. A number of predictive models are discussed together with a method for correcting the predicted data. The effect of disturbing noise is then considered. Simulation results are presented for both noise-free and noisy data when imaging single and multiple point objects and the extension of the technique to the imaging of continuous objects is discussed. Examples for doubling the size of an aperture in the presence of 30% relative noise are given. An experimental holographic imaging system is described which has been designed and implemented to allow verification of the proposed aperture expansion algorithm on realistic measured holograms.