covered by a background H region. Assuming that the H region has a diameter of 6 arcsec (e.g., @2009ApJ...689..1422) and a radiation temperature of 6000 K (e.g., ), we obtain for T$_{non-H\uppercase\expandafter{\romannumeral2}-region(H_2CO)}$/T$_{H\uppercase\expandafter{\romannumeral2}-region(H_2CO)}$ values of about 0.01 and 0.1 for a 1.3 arcmin beam and 4 arcmin beam, respectively. The result indicates that in this case the tiny spot in front of the H region dominates the H$_2$CO absorption budget and the difference in beam sizes can be neglected. If the respective clouds are not filling the entire 4 arcmin beam, the comparatively small area covered by the continuum emission becomes even more dominant and the difference in beam size can also be neglected.

Photon Trapping Corrections  {#subsec:correct}
----------------------------

Photon trapping in the millimeter H$_2$CO rotation lines, connecting the J = 1 and 2 K-doublets (i.e. the 2$_{11}$ - 1$_{10}$ and 2$_{12}$ - 1$_{11}$ transitions), has also to be considered. In case the two millimeter lines (2$_{11}$ - 1$_{10}$ and 2$_{12}$ - 1$_{11}$) are not entirely optically thin, their excitation temperature values rise and are higher than in the optically thin case, represented by H$_2$$^{13}$CO. Thus, more population ends up in the H$_2$CO J = 2 doublet than in the entirely 