How to scale an object in near eye optics and have it appear at correct height at a distance?

Question

I'm trying to draw an object in my near eye display and have it appear at the correct size at a distance. I can accomplish this if I'm looking at a wall in my office but not when I step outside. I'm an electrical engineer with only a cursory understanding of optics.

For reference my setup looks something like this. A tiny display above a birdbath optics setup projects the image back to the eye.

So I learned that if I want to draw an object, say a flat tree picture on a wall 10ft away then it is a simple ratio. Based on the eye relief (15mm in my case), and the size of the display and of the pixels. So if I draw my tree on my display and look at a wall 10ft away, everything is pretty close to the right size. As I back away it gets larger, and as I get closer it gets smaller. That makes sense.

Now if I step outside and look down the road my tree looks huge. How do I learn to draw objects appropriately so they appear the correct size here? Is there some maximum virtual screen size defined by my eye and the optics at infinity? I don't quite understand the concept or math I'd have to do for the scaling.

Answer 1

The perceived size of objects is calculated by your brain based on two major items:

• The angular size presented to your optic system
• The perceived distance to the object

Two objects with the same angular size will be perceived to be of different sizes if the perceived distance is different. Something that is "far away" must be larger to give the same angular size.

However, there's no single cue to present depth. In your office, by seeing the wall, you are assuming objects to be in front of it. Outside, objects might be much further away and your brain assigns a different distance to the same image. This is an artefact of the visual processing system.

Unfortunately, this may mean that there is no simple way to present an image such that it always has the same perceived size. At least not without a much greater understanding of what the user is seeing as cues.

http://psylux.psych.tu-dresden.de/i1/kaw/diverses%20Material/www.illusionworks.com/html/ames_room.html has some descriptions of an Ames room, which exploits this ambiguity to intentionally fool your visual processing system.