S/N of the HDO detection in the spectrum of a directly imaged gas planet as a function of the planetary T_equ. The HDO/H₂O ratio was 4 × 10⁻⁵. Here we assumed S/N_{*, at 3.7μm} = 3317 per spectrum, a stellar flux 1000 times smaller at the position of the planet, considering 100 spectral observations. Orange boxes: detection S/N when correlating the contaminant removed observation (data set B) with a pure HDO isotopologue template. Black boxes: detection S/N when correlating with the noiseless, telluric-free model B spectrum. The box height corresponds to the measured 16 and 84 percentiles of the measured S/Ns, when running the simulation multiple times. The black dotted line denotes the S/N scaling expected purely from the increasing planet–star contrast as the planet becomes hotter. This assumes that the ratio of the HDO and H₂O opacities isnot temperature dependent. The black dashed line shows the prediction of the S/N signal following Eq. (5), indicating good agreement.