Optimal Absorbance for Transmission or Reflection Spectra Measured under Conditions of Constant Detector Noise in the Presence of Stray Radiation

Abstract

The signal-to-noise ratio (S/N) for absorption spectrometers can be expressed as absorbance/absorbance noise (A_m/S_Am), where A_m is the measured absorbance and S_mm is the standard deviation in A_m, or as concentration/concentration noise (c/s_c) calculated from Beer's law. For measurements made under ideal conditions, A_m/S_Am. However, when stray radiation, or an analogous phenomenon, such as detector nonlinearity in FT-IR measurements or surface reflection in diffuse reflection spectrometry, contributes to the spectrum, C/S_c ≠ A_m/S_Am. It is known that the optimum value of A_m/S_Am in the absence of stray light is found at an absorbance of 0.4816 when noise from the reference spectrum is taken into account and 0.4343 when noise from the reference spectrum is excluded from the calculations. In the present paper we discuss the effect of stray light on the absorbance and concentration S/N. The maximum value of c/s_c is found at lower absorbance than is the case if stray light is absent. While this effect is negligibly small for the typical levels of stray light found with most contemporary monochromators, it can be significant when, for example, the response of a detector used in Fourier transform spectrometry is nonlinear or when the front-surface reflection in diffuse reflection measurements is large. For effective stray light levels of 10%, the maximum value of c/s_c is found at an absorbance that is 22% lower than when no source of stray light is present.