Well, I'm not exactly sure what sort of cloth that is supposed to be, if you could be more detailed on what kind of fine cloth (wool, silk, etc..) maybe people could give more specific input.
Sometimes an indicator of fineness would be a bit of translucency, or perhaps sheen. Also fineness could mean perhaps a thinner cloth, it looks just a bit bulky as it curves over the headband. But it all depends on what you were going for.