Post-processing intensity measurements at favourable dose values

In a macromolecular X-ray experiment, many sets of intensity measurements are collected, with each measurement corresponding to the intensity of a unique reflection at a different X-ray dose. The computational correction of radiation damage, which occurs as a function of dose during the experiment, is a concept suggesting the approximation of each set of measured intensities with a smooth function. The value of the approximating function at a user-defined point common to all unique reflections is then used as an interpolated snapshot of the true intensities at this specific dose. It is shown here that, under realistic assumptions, interpolation with a linear function has the smallest amount of error at or near two well defined points in the dose interval. This result is a special case from a mathematical analysis of polynomial approximations which proves that the points of minimum error in the approximation of a polynomial of order n by a polynomial of order n - 1 are independent of the function values. Conditions are formulated under which better intensities are obtained from linear interpolation than from the usual averaging of observations.