In order to minimize scattered light from the inside of the dome, it needs to be painted a flat/matte black. In the instructions, a flat black spray paint or chalkboard paint is specified, but you will still get some scattered light from both of those. It hasn't been a problem until now, but I've been doing some RTI on shiny metal surfaces that are doing a great job of picking up scattered light from the dome surface, resulting in odd artifacts. So I've been poking around for a solution.
Vantablack would be an ideal solution, as it absorbs up to 99.965% of visible light. However, it's not really available in commercial form, and the only paint version of it is dedicated to exclusive use by one artist. That has pissed off a number of other artists, one of whom has created a quasi-clone of it called Black 2.0 that he is offering for sale. Not cheap (150 ml for about $30 including shipping from the UK). I've just ordered a bottle, and will check out whether it's worth the price..