Correlations in primary spectral standards

Correlations in spectral standards between values at different wavelengths should be considered when estimating uncertainties of spectral integrals. Simple correlations are introduced through fixing an absolute value to a relative distribution over wavelengths, or through systematic errors. Such correlations are easily treated when calculating effects that depend only on the relative distribution. A much more complex situation arises when a fitting process is used as part of the primary derivation. Two examples are given: that of spectral responsivity when the quantum defect of silicon photodiodes is fitted to measured data, and that of spectral irradiance where filter radiometers are used to calibrate a lamp directly and a fitted function is used for interpolation. In both cases, correlations between spectral points are significant and varied, and while these are diluted in the transfer from the primary scales, the effects may be significant in calculating correction factors in subsequent measurement where values at different wavelengths are combined.