Statistical Error Calibration in UV-Visible Spectrophotometry

Abstract

A procedure for spectrophotometric statistical error calibration is described, in which estimates of the variance (σ _A ²) in the absorbance A are derived as a function of A and the wavelength λ, directly from recorded spectra. Spectra are obtained over the desired wavelength range for a number of neutral-density filters, and are then least-squares fitted piecemeal to low-order polynomials. The variances from these fits constitute the estimates of the instrumental variance σ _A ² for the λ and A of the respective fitted segments. These values are in turn expressed as functions of λ and A, by means of a small number of parameters. In the present case a representation in terms of A and I₀, the “effective” source intensity, is even more compact, requiring only five parameters to cover the 200–850 nm region for absorbances up to and exceeding 2. For the instrument studied here, the high-A precision is limited by digitization error, the error being independent of λ and I₀.