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James L Gardner1

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Summary
This summary is machine-generated.

This study introduces methods for propagating uncertainties in interpolated spectral data, crucial for accurate integration. The findings show that uncertainties in integrals using interpolated data can be reliably estimated from the original data.

Keywords:
interpolationphotometryradiometryuncertainty

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Area of Science:

  • Scientific computing
  • Numerical analysis
  • Photometry

Background:

  • Interpolation is frequently employed to enhance the precision of integrals involving spectral data convolved with response functions or power distributions.
  • Accurate uncertainty propagation is essential when dealing with interpolated data, especially for integration tasks.

Purpose of the Study:

  • To develop formulae for propagating uncertainties through interpolation processes.
  • To analyze the impact of correlations in interpolated data on integral accuracy.
  • To provide practical examples using spectral integrals in photometry.

Main Methods:

  • Development of formulae for uncertainty propagation in Lagrangian interpolation (factors of 5 and 2) and cubic-spline interpolation.
  • Derivation of correlation coefficients for Lagrangian interpolation with uncorrelated input data.
  • Application of methods to a common spectral integral in photometry.

Main Results:

  • Interpolated data exhibit correlations that must be accounted for during integration.
  • Formulae for uncertainty propagation are established for specific interpolation techniques.
  • Demonstration that practical uncertainty estimation for integrals can rely on original data.

Conclusions:

  • The developed methods provide a reliable way to estimate uncertainties in integrals computed from interpolated spectral data.
  • Considering correlations in interpolated data is vital for accurate uncertainty assessment.
  • Original data can be effectively used for practical uncertainty estimation in integrated spectral analysis.