Theoretical Design and Performance Assessment of a BSO-Based Optical Correlator

The main objective of the research, presented in this thesis, was the design of an updatable optical correlator. This was based on the use of a crystal of Bismuth Silicon Oxide (BSO) placed in the Fourier plane. The system performance was prescribed to meet specific targets: the correlation of images comprising 512x612 pixels; at 40 milliseconds per image. To undertake the design work, the predictions of the Band Transport Model were used to describe the performance of the BSO crystal. In addition to this, coupled wave theory was used to model the effects of a 'thick' hologram in the correlator. Several, previously unreported, aspects of the system were considered in the design. These included the effects of the positions of the input images, with respect to the transforming lenses. It was shown theoretically, that spatial filtering effects occur if the images are not in the front focal planes of the lenses. Specification of the lens combinations to be used in the correlator wcis carried out using stcindard ray-tracing software with manufacturer's lens data. Digital simulation was also used to predict intensities in both the Fourier and the correlation pleine of the optical system. An important effect, not hitherto reported, was that of the hologram's grating vector becoming tilted with respect to the electric field which is applied to the BSO. The drop in diffraction efficiency thus caused can be comparable with that due to the Bragg de-tuning of the beam reading out the hologram. It was shown that the correlator could be designed to meet the imposed specifications. The main problems encountered were the angular selectivity of the BSO hologram, and low writing-beam intensities in the Fourier plane. In order to predict the maximum sizes of the images that could be processed, the equations governing system performance were expressed in terms of a reduced parameter set. Limits on the number of pixels, in the images on the read and write sides of the correlator, were then determined. It was predicted that it would be difficult to correlate two images of more than about 2000 pixels across. This limit was imposed by the angular selectivity effects. It was also predicted that a system would be feasible, which could correlate an image of 6000x6000 pixels with a small reference template. In both cases, optical path lengths of several meters would be needed; as well as large-aperture, thin BSO crystals. From the results it was concluded that BSO was not going to compete with other, recently developed, materials and devices: such as switchable photo-chromic materials and phase modulating spatial light modulators (SLMs). Severe problems with the acquisition of suitable SLMs, meant that the designed correlator could not be constructed. Effort was therefore diverted to extend the digital simulation work to cover these devices. Models were developed which represented the distortions typically found in optically addressed SLMs. The results produced highlighted some shortcomings of published work in this field. Finally, an experimental method was chosen, which allowed combinations of different distortions to be applied to pairs of images. This method, and the computer models developed, can be used to assess fully the effects of SLM distortions on any optical processing task. An example is presented in which correlations were performed in the presence of a grey-level non-uniformity and two types of phase distortion. The effects of the distortions on peak-height, signal-to-noise ratio, shift-invariance and the accuracy of peak location were computed