Figure 1

Experimental Gaussian full width at half-maximum (FWHM) and theoretical Doppler widths (dashed horizontal lines) in megahertz for the ${}^{17}\mathrm{O}$-containing isotopologues with fit uncertainties. Each experimental Gaussian width was determined by a Levenberg-Marquardt least-squares fit using a single Voigt line shape with the pressure-broadening parameter constrained to the previously determined ${}^{16}\mathrm{O}$${}_2$ value [12]. Note that collisional narrowing is negligible (i.e., $<$1 MHz) at the pressure utilized in this study, although it can be very important at higher pressures [16, 17]. Also shown are calculated (solid black lines) broadenings for ${}^{16}\mathrm{O}$${}^{17}\mathrm{O}$ and ${}^{17}\mathrm{O}$${}^{18}\mathrm{O}$ based upon the model described in the text. (a) $\mathit{RR}$-branch transitions which exhibit minimal broadening (except for very-low-$N^{″}$ transitions). (b) $\mathit{RQ}$-branch transitions exhibit significant broadening due to the large hyperfine splitting (note the different $y$-axis scales between the two figures). The hyperfine splitting of the ${}^{17}\mathrm{O}$${}_2$ transitions exhibit a dependence on the parity of $N^{″}$ due to symmetry constraints. For both branches, the model performs well for transitions with $N^{″}>1$.Reuse & Permissions

Figure 2

Upper panel: Measured absorption given by (c$\tau$)${}^{-1}$ where $c$ is the speed of light and $\tau$ is the measured ring-down decay time (symbols) and fitted spectrum (solid black line) for the $R$3$Q$4 ${}^{16}\mathrm{O}$${}^{17}\mathrm{O}$ transition, at 236 Pa (1.77 Torr) and 299.5 K. The sum of six Voigt profiles corresponding to the hyperfine structure were fit to the measurements (solid black line) using a Levenberg-Marquardt least-squares fitting algorithm. Each of these Voigt profiles [shown in solid colored (gray) lines with larger values of $F^{″}$ corresponding to higher intensity hyperfine components] had its relative position and intensity fixed to values calculated using the model described in the text. Each Voigt profile’s Gaussian width was constrained to the theoretical Doppler width, and the pressure-broadening parameter was set equal to the measured ${}^{16}\mathrm{O}$${}_2$ value [12]. Thus, only the position of the spectral center of mass and the total integrated area of the composite spectrum were floated. Also shown is a single Voigt profile whose Doppler width was constrained to the theoretical ${}^{16}\mathrm{O}$${}^{17}\mathrm{O}$ value (dashed gray line). Lower panel: Fit residual for the sum of hyperfine structure. Based upon the peak height and the root-mean-square fit residual, the signal-to-noise ratio of this spectrum is $~$825:1.Reuse & Permissions