uncertainty of 8MHz. The uncertainty of the AC-Stark-shift extrapolation is 30 MHz. Other sources of uncertainty, such as line-fitting, I$_2$ calibration, etalon calibration, DC-Stark shift and residual Doppler shift, make much smaller contributions and can be ignored. The overall uncertainty ($1\sigma$) of the two-photon resonant frequencies of $^{13}$C$^{16}$O is then conservatively estimated to be 0.002 [cm$^{-1}$]{}.

The transition frequencies of six [$^{13}$C$^{16}$O]{} lines were measured, calibrated, and corrected for chirp and AC-Stark effects, with final values listed in Table \[AXlasertransition\].

[l@r]{}\
Line & Frequency\
\
S(0) & 64760.185\
S(1) & 64765.528\
R(1) & 64756.560\
Q(1) & 64750.481\
Q(2) & 64749.157\
P(2) & 64743.144\

VUV-FT synchrotron experiments
------------------------------

The [A$^1\Pi-$X$^1\Sigma^+$]{} $(0,0)$ single-photon absorption band of $^{13}$C$^{16}$O was measured using the VUV Fourier-transform spectrometer at the SOLEIL synchrotron. The operation of this device and its use for molecular spectroscopy have been well described [@Deoliveira2011; @Niu2016]. All measurements were performed under steady-state gas conditions, whereby gas is continuously introduced to the interaction region and flows out of a windowless cell. Recordings were made with the cell cooled to nearly liquid-nitrogen temperature (yielding an effective gas temperature of 90K), at room temperature (295K), and in a specially-designed high-temperature cell (900K) [@Niu2015a]. The VUV-FT measurements 