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Post-processing intensity measurements in X-ray crystallography
Collaborator: K. Diederichs
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Key words: least squares fit, points of least fitting error, stochastic simulations
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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 to approximate 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 interpolated snapshot of the true intensities at this
specific dose. In this project, we show 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 minimal error in the approximation of a
polynomial of order n by a polynomial of order n-1 are independent of the
function values. Conditions under which better intensities are obtained from linear
interpolation than from the usual averaging of observations are formulated.
Post-processing intensity measurements at favourable dose values.
Applied Crystallography, 42, 48-57, 2009
with K. Diederichs
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