Here we pick up from where we left off. Figure 1a shows what happens to the noise level, for the same condition of constant
"sample transmittance" as a function of signal-to-noise ratio (S/N), for different values of sample transmittance. In the
"low noise" regime, the noise has the behavior we have derived for it. However, the effect of the exaggeration of the random
variations very quickly takes over, and in the "high noise" regime there is virtually no difference in the noise behavior
at different values of transmittance because that is now dominated by the divergence of the integrals involved.
Howard Mark
A verification of the effects seen in Figure 1 is presented in Figure 2, in which we present a graph showing the transmittance
noise as a function of the sample transmittance (Es/Er). Except for the occasional spike, when S/N is 5 and even when it is only 4.5, the transmittance noise varies essentially,
as we saw in working out the exact solution for transmittance noise in the low-noise case. Naturally, the underlying transmittance
noise value is higher when the reference S/N is lower. When S/N decreases to 4, "spikes" happen frequently enough that it
becomes almost impossible to tell where the "underlying" transmittance noise level is, because the computed values are again
dominated by the divergent integrals.
Absorbance Noise in the "High Noise" Regime
Just as equation 5, which led to equation 76a, was the starting point for investigating the behavior of transmittance noise
in the high noise regime, so too is equation 24 the starting point for investigating the behavior of absorbance noise in the
high noise regime. While we presented equation 24 previously, in the original analysis, we did not follow through to investigate
its behavior, because we went directly to the analysis of the behavior of Var (ΔA/A), instead. Therefore, we present equation 24 again and take this opportunity to investigate it:
Figure 1: (a) Transmittance noise as a function of reference S/N, at various values of sample transmittance. (b) Expansion
of Figure 1a.
Again we see that the variance of the absorbance equals (n - 1)/n times the mean value of the summand of equation 80a, and also that we can ignore the premultiplier term (n - 1)/n for large values of n.
