A javafx stage with a transparent background and d

Question

I'd like to create a simple protactor in javafx. To that aim, I need to create a stage with a transparent backgrount but WITH decorations. I mean : I still want to be able to move my window or close it when finished. I tried to use those properties :

stage.initStyle(StageStyle.TRANSPARENT);

But all the window disappear : the background AND the decoration. I also tried to use :

stage.setOpacity(0.9);

In that case, all the window, background and decoration is partially translucent and that's not what I want to get. I would like a stage with a full opaque decoration and a fully transparent background on which I'll can draw a protractor partially opaque, like if I was using the real object on my screen.

Does someone could give me a tip to do that ?

Thank you for your help.