In underwater acoustic imaging (UAI), the combination of a two-dimensional (2-D) array and replicate correlation can produce 3-D images, typically of objects at a range of 2 m. A system already developed achieves the high data acquisition rate needed through one-bit sampling (sensing only the sign of the received signal). Noise added before the one-bit sampling avoids the production of 'ghosts' in the image. By simulation and mathematical analysis, the effects of one-bit and added noise are studied for a chirp signal, with a restriction so far to 1-D images (image amplitude versus range). Conditions are given for the avoidance of ghosts and the minimisation of 'image noise' - noise in the image due to one-bit and added noise. A model of image noise is proposed, which is corroborated by the tests carried out to date. A general formula for the root-mean-square image noise is obtained. It has previously been suggested that filtering the singal after sampling would improve the image. However, it is shown that filtering is unnecessary and indeed makes the image worse. It is shown that a strong target can suppress evidence of a weak target because, when the strength of the return signal is raised, essentially the amplitude of the added noise must be raised to avoid 'ghosts'. A general formula, giving the ratio of target strengths such that the weak target has a 50% probability of detection, is obtained
