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Uncertainties in Interpolated Spectral Data



J L. Gardner


Interpolation is often used to improve the accuracy of integrals over spectral data convolved with various response functions or power distributions. Formulae are developed for propagation of uncertainties through the interpolation process, specifically for Lagrangian interpolation increasing a regular data set by factors of 5 and 2, and for cubic-spline interpolation. The interpolated data are correlated; these correlations must be considered when combining the interpolated values, as in integration. Examples are given using a common spectral integral in photometry. Correlation coefficients are developed for Lagrangian interpolation where the input data are uncorrelated. It is demonstrated that in practical cases, uncertainties for the integral formed using interpolated data can be reliably estimated using the original data.
Journal of Research (NIST JRES) -
108 No. 1


interpolation, photometry, radiometry, uncertainty


Gardner, J. (2003), Uncertainties in Interpolated Spectral Data, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD (Accessed April 21, 2024)
Created February 1, 2003, Updated February 17, 2017