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Double-aperture Young interferometry is widely used in accelerators to provide a one-dimensional beam measurement. We improve this technique by combining and further developing techniques of non-redundant, two-dimensional, aperture masking and self-calibration from astronomy. Using visible synchrotron radiation, tests at the ALBA synchrotron show that this method provides an accurate two-dimensional beam transverse characterisation, even from a single 1 ms interferogram. The non-redundancy of the aperture mask in the technique enables it to be resistant to spatial phase fluctuations that might be introduced by vibration of optical components, or in the laboratory atmosphere.

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