and analyzed in the benchmark study of Field *et al.* [@Field-thesis; @Field1972a] and studied many times thereafter in its dominant isotopologue $^{12}$C$^{16}$O and minor variants (e.g., [@Haridass1994; @Eikema1994; @Jolly1997; @Kepa2011]). Recently the spectrum of [A$^1\Pi-$X$^1\Sigma^+$]{} in $^{12}$C$^{16}$O was reinvestigated by Doppler-free laser methods [@Niu2015] and vacuum-ultraviolet Fourier-transform (VUV-FT) spectroscopy [@Niu2013; @Niu2016], both at high resolution. The [A$^1\Pi-$X$^1\Sigma^+$]{} system of the $^{13}$C$^{16}$O isotopologue was investigated in detail by Haridass and Huber [@Haridass1994], after the observation of unresolved band heads by Tilford and Simmons [@Tilford1972]. Recently, a high-resolution study of the [A$^1\Pi-$X$^1\Sigma^+$]{} ($v'$,0) bands for $v'=0-9$ was reported, based on measurements with the VUV-FT instrument at the SOLEIL synchrotron [@Gavilan2013]. Further observations of [A$^1\Pi$]{}$(v)$ levels for this isotopologue were made in visible emission via the [B$^1\Sigma^+-$A$^1\Pi$]{} Ångström bands by the Rzeszów group [@Kepa2003; @Kepa2011; @Hakalla2012], while the [B$^1\Sigma^+-$X$^1\Sigma^+$]{} system was investigated by two groups with improved accuracy [@Tilford1968; @Eidelsberg1987]. Higher lying states for the $^{13}$C$^{16}$O isotopologue have also been investigated [@Eidelsberg1992; @Cacciani1995], while the level structure of the [X$^1\Sigma^+$]{} ground state is known to great precision [@George1994].

The present study aims to re-investigate the spectroscopic structure of the [$v=0$]{} vibrational level of the [A$^1\Pi$]{} state for the $^{13}$C$^{16}$O isotopologue with the highest-possible 