Twenty-Five-Fold Reduction in Measurement Uncertainty for a Molecular Line Intensity

To accurately attribute sources and sinks of molecules like ${\mathrm{CO}}_2$, remote sensing missions require line intensities ($S$) with relative uncertainties $u_r(S)<0.1\%$. However, discrepancies in $S$ of $\approx 1\%$ are common when comparing different experiments, thus limiting their potential impact. Here we report a cavity ring-down spectroscopy multi-instrument comparison which revealed that the hardware used to digitize analog ring-down signals caused variability in spectral integrals which yield $S$. Our refined approach improved measurement accuracy 25-fold, resulting in $u_r(S)=0.06\%$.

Figure 1

General illustration of a cavity ring-down spectrometer. From the top left, a continuous-wave laser (blue lines) was injected into an optical cavity (yellow curved mirrors) containing a flowing gas sample of ${\mathrm{CO}}_2$ in air (gray, carbon; red, oxygen; blue, nitrogen). Upon reaching a predefined transmission threshold, an optical switch shuttered the laser and passive cavity decays were observed incident on a photoreceiver (PR). The electrical output of the PR (black dashed arrow) was coupled to an analog-to-digital converter (or digitizer), and the resulting digitized decay signals were fitted in real time using homebuilt acquisition software and a personal computer (PC).

Figure 2

A portion of representative unbiased (red squares) and apparent (blue circles) spectra of the $R$ $16e$ ${\mathrm{CO}}_2$ transition with ${\tilde{\nu }}_0=6359.967{\mathrm{cm}}^{-1}$ are shown in the top panel. Fitted spectra spanned a frequency detuning range of 0–28 GHz, the sample pressure was 8.88 kPa, and the sample ${\mathrm{CO}}_2$ mole fraction was ${\chi }_{{\mathrm{CO}}_2}=(387.98\pm 0.05)\mu \mathrm{mol}/\mathrm{mol}$. The apparent spectrum was recorded by the digitizer-spectrometer combination $D4–S2$, and ${\tau }_A$ were corrected to yield $\tau$ using the coefficients in the Supplemental Material [42]. A fitted model of the unbiased absorption coefficient ($\alpha =1/c\tau$) is also shown as a red line and fitted residuals are plotted as another red line in the middle panel. In the bottom panel, the relative difference $\tau /{\tau }_A-1$ (equal to ${\alpha }_A/\alpha -1$, where ${\alpha }_A$ is the apparent absorption coefficient) is plotted as black dots.

Figure 3

Unbiased ($S$, blue circles) and apparent ($S_A$, orange squares) values of the $R$ $16e$ ${\mathrm{CO}}_2$ line intensity at $T=296\mathrm{K}$ ($30012─00001$ band). Error bars show $\pm 1\sigma$ standard uncertainties. The gray shaded region comprising $D1–S1$ and $D1–S3$ (far left) highlights values of $S$ measured by the metrology-grade reference digitizer. For values of $S$ with corresponding values of $S_A$, light orange boxes indicate the magnitude of each digitizer correction. The light blue dashed lines bound the standard deviation of the weighted mean value of $S$ (solid blue line).