Infrared interferometry of supergiant and Mira stars has recently been reinterpreted as revealing the presence of deep molecular layers .
Empirical models for a photosphere surrounded by a simple molecular layer or envelope have led to a consistent interpretation of previously inconsistent data .
The stellar photospheres are found to be smaller than previously understood , and the molecular layer is much higher and denser than predicted by hydrostatic equilibrium .
However , the analysis was based on spatial observations with medium-band optical filters , which mixed the visibilities of different spatial structures .
This paper reports spatial interferometry with narrow spectral bands , isolating near-continuum and strong molecular features , obtained for the supergiant \mu  Cep .
The measurements confirm strong variation of apparent diameter across the K-band .
A layer model shows that a stellar photosphere of angular diameter 14.11 \pm 0.60  mas is surrounded by a molecular layer of diameter 18.56 \pm 0.26  mas , with an optical thickness varying from nearly zero at 2.15 \mu m to > 1 at 2.39 \mu m. Although \mu  Cep and \alpha  Ori have a similar spectral type , interferometry shows that they differ in their radiative properties .
Comparison with previous broad-band measurements shows the importance of narrow spectral bands .
The molecular layer or envelope appears to be a common feature of cool supergiants .