What are the relevant regulations regarding use of HUD displays in non-military aviation?
The specific application in mind would involve providing information to pilots of turboprop survey aircraft flying VFR at about 100m altitude so it's of benefit to have the pilots' focus on what's going on out the window.
You can read about some guidance from the FAA about HUD design in these two Advisory Circulars:
General electronic displays
Enhanced Flight Vision Systems
This handbook is a bit dated but covers certification.
It really depends on what exactly the HUD is supposed to do. Any pilot can bring a handheld GPS along, with the understanding that it is not an "official" navigation instrument. A HUD could be used in a similar way. There are a couple things to keep in mind:
If the HUD is to be used for real navigation or pilot reference, then certification will be an issue. The handbook above talks about this. The HUD would need to be certified just like any other instruments in the cockpit for that use. If a HUD is used for special situations, like low visibility landing, it must be certified in order to be used in those situations. Otherwise you are not allowed to do anything you could not do without the HUD.
Even if the HUD is not to be used for critical flight data, the HUD needs to comply with the FAR 25 sections 25.773 and 25.775, which talk about the windows in the cockpit. The HUD can't interfere with the normal visibility the pilot should have.
