Of the two solar lines, K I $D_1$ and $D_2$, almost all attention so far has been devoted to the $D_1$ line, as $D_2$ is severely affected by an O$_2$ atmospheric band. This, however, makes the latter appealing for balloon and space observations from above (most of) the Earths atmosphere. We estimate the residual effect of the O$_2$ band on the K I $D_2$ line at altitudes typical for stratospheric balloons. Our aim is to study the feasibility of observing the 770 nm window. Specifically, this paper serves as a preparation for the third flight of the Sunrise balloon-borne observatory. The results indicate that the absorption by O$_2$ is still present, albeit much weaker, at the expected balloon altitude. We applied the obtained O$_2$ transmittance to K I $D_2$ synthetic polarimetric spectra and found that in the absence of line-of-sight motions, the residual O$_2$ has a negligible effect on the K I $D_2$ line. On the other hand, for Doppler-shifted K I $D_2$ data, the residual O$_2$ might alter the shape of the Stokes profiles. However, the residual O$_2$ absorption is sufficiently weak at stratospheric levels that it can be divided out if appropriate measurements are made, something that is impossible at ground level. Therefore, for the first time with Sunrise III, we will be able to perform polarimetric observations of the K I $D_2$ line and, consequently, we will have improved access to the thermodynamics and magnetic properties of the upper photosphere from observations of the K I lines.
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