Accuracy assessment of a least-squares estimator for scanning X-ray interferometry

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Abstract
A least-squares estimate of the interference signals from a scanning X-ray interferometer was checked. The redundancy inherent in the double interference, one in the transmitted and the other in the diffracted beam, was used to assess the estimator performance. As a rule, the uncertainty resulting from the conventional least-squares calculation is too small and has to be scaled up by the noise correlation. To avoid underestimation, noise characterization was carried out, which proved the noise to be exponentially correlated. An asymptotic formula expressing the estimate uncertainty was then written and, in the specific case investigated, was verified experimentally. Uncertainties of 0.001 of a period in fringe division (which corresponds to 0.2 pm when the diffracting planes are the silicon (220) planes) and of 1% in mean count-rate and visibility were obtained.
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