Type of Publication:  Journal article 
URI (citable link):  http://nbnresolving.de/urn:nbn:de:bsz:352opus106461 
Author:  Diederichs, Kay; Junk, Michael 
Year of publication:  2008 
Published in:  Journal of Applied Crystallography ; 42 (2008), 1.  pp. 4857.  ISSN 00218898.  eISSN 16005767 
DOI (citable link):  https://dx.doi.org/10.1107/S0021889808036716 
Summary: 
In a macromolecular Xray experiment, many sets of intensity measurements are collected, with each measurement corresponding to the intensity of a unique reflection at a different Xray 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 userdefined 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.

Subject (DDC):  510 Mathematics 
Keywords:  favourable dose values, postprocessing, intensity measurements, correction of radiation damage 
Link to License:  Terms of use 
Bibliography of Konstanz:  Yes 
DIEDERICHS, Kay, Michael JUNK, 2008. Postprocessing intensity measurements at favourable dose values. In: Journal of Applied Crystallography. 42(1), pp. 4857. ISSN 00218898. eISSN 16005767. Available under: doi: 10.1107/S0021889808036716
@article{Diederichs2008Postp762, title={Postprocessing intensity measurements at favourable dose values}, year={2008}, doi={10.1107/S0021889808036716}, number={1}, volume={42}, issn={00218898}, journal={Journal of Applied Crystallography}, pages={4857}, author={Diederichs, Kay and Junk, Michael} }
<rdf:RDF xmlns:dcterms="http://purl.org/dc/terms/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:rdf="http://www.w3.org/1999/02/22rdfsyntaxns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dspace="http://digitalrepositories.org/ontologies/dspace/0.1.0#" xmlns:foaf="http://xmlns.com/foaf/0.1/" xmlns:void="http://rdfs.org/ns/void#" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.unikonstanz.de/rdf/resource/123456789/762"> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dcterms:rights rdf:resource="https://kops.unikonstanz.de/page/termsofuse"/> <dcterms:bibliographicCitation>Publ. in: Applied Crystallography 42 (2009), 1, pp. 4857</dcterms:bibliographicCitation> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">20110322T17:48:46Z</dcterms:available> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dc:rights>termsofuse</dc:rights> <dc:creator>Junk, Michael</dc:creator> <dc:contributor>Diederichs, Kay</dc:contributor> <dc:creator>Diederichs, Kay</dc:creator> <bibo:uri rdf:resource="http://kops.unikonstanz.de/handle/123456789/762"/> <dcterms:title>Postprocessing intensity measurements at favourable dose values</dcterms:title> <dcterms:isPartOf rdf:resource="https://kops.unikonstanz.de/rdf/resource/123456789/28"/> <dc:contributor>Junk, Michael</dc:contributor> <dc:language>eng</dc:language> <dcterms:abstract xml:lang="eng">In a macromolecular Xray experiment, many sets of intensity measurements are collected, with each measurement corresponding to the intensity of a unique reflection at a different Xray 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 userdefined 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.</dcterms:abstract> <dspace:isPartOfCollection rdf:resource="https://kops.unikonstanz.de/rdf/resource/123456789/28"/> <dcterms:hasPart rdf:resource="https://kops.unikonstanz.de/bitstream/123456789/762/1/Diederichs_106461.pdf"/> <dcterms:issued>2008</dcterms:issued> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">20110322T17:48:46Z</dc:date> <dspace:hasBitstream rdf:resource="https://kops.unikonstanz.de/bitstream/123456789/762/1/Diederichs_106461.pdf"/> </rdf:Description> </rdf:RDF>
Diederichs_106461.pdf  196 