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## Wavefront analysis using imperfect data

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Some of the problems that arise in the analysis of imperfect WFA data will now be briefly discussed. When the input data to a computer program are contaminated by noise and measurement errors it is no longer reasonable to expect a unique and correct answer from a minimum number of frames. Other potential sources of error include departures of the behaviour of the real wave-field from the assumed model, and differences between the real and computed patterns of the array; clearly, a measuring instrument of known properties is required if accurate measurements are to be made. Techniques for the statistical analysis of samples of imperfect data can, of course, be tested against simulated problems to which known amounts of noise, measurement errors, angle fluctuations etc. are added in a series of controlled numerical experiments. The ability of an array to resolve a given wave-field must eventually break down when the signal/noise ratio becomes sufficiently unfavourable. In a problem involving (say) two strong rays and one weak ray, it is likely to be the weak ray that is the first to be lost from the solution as the noise level increases. In these circumstances, a partially-correct solution might be obtained.

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