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Proceedings Paper

Accurate extraction of thermal expansion coefficients and their uncertainties from high precision interferometric length measurements
Author(s): R. Schoedel
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Paper Abstract

The evaluation of the coefficient of thermal expansion (CTE) from the observed temperature induced length changes becomes the more difficult the lower the final uncertainty of the CTE is desired. On a scale of nanometers the length as a function of the sample temperature clearly deviates from the linear approximation so that higher polynomials are used as fit functions to the measured data. From such polynomials of a certain degree the CTE can easily be evaluated according to its definition. In this paper it is demonstrated in which way the corresponding uncertainty of the CTE can be calculated in accordance with the GUM what is done on the basis of symbolic computation by means of MATHEMATICA. On the other hand, the arbitrariness of the choice of the polynomial order causes an additional uncertainty contribution as discussed in this paper. Examples are given to illustrate the mentioned problems.

Paper Details

Date Published: 24 August 2005
PDF: 11 pages
Proc. SPIE 5879, Recent Developments in Traceable Dimensional Measurements III, 587901 (24 August 2005); doi: 10.1117/12.616923
Show Author Affiliations
R. Schoedel, Physikalisch-Technische Bundesanstalt (Germany)

Published in SPIE Proceedings Vol. 5879:
Recent Developments in Traceable Dimensional Measurements III
Jennifer E. Decker; Gwo-Sheng Peng, Editor(s)

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