Accurate extraction of thermal expansion coefficients and their uncertainties from high precision interferometric length measurements

摘要

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.