Focal Length for an Effective Virtual Window?

[George Scharoun]

Ok, I think this is kind of a cool unique problem to solve, but maybe someone will have a quick answer! Or they'll tell me I'm an idiot, which is very possible.

I want to project a virtual window in an art gallery. The viewer will be positioned approximately 15' away from a 20' x 12' projection, and my hope is that by filming a static scene with the right focal length - adjusted for the viewing distance - that the effect will approximate the experience of looking out a big picture window.

I'm not very good at geometry so I'm looking for help. I've only gotten as far as thinking that if the human eye's focal length is about 22mm (controversial I know), then this would be narrower because of your physical distance from the "window". But how much narrower? There must be a way to calculate it.

Ok, I think I've over-explained at this point. Much appreciated if you could help me figure this out.

[Dom Jaeger]

I don’t think the focal length of human vision has anything to do with this.

I think as long as you film the window from the same distance as the expected viewing distance (15 ft) then it will match the perspective. 

The focal length should then be a choice based on the size of your projected image, and how magnified the window image within that projection needs to be to replicate the real window size. So if your projection is 12 ft high, but you want the window to be only 6 ft high within that, then choose a focal length that records the window height as half the frame height. Or if you want the window to fill the entire projection, choose a longer focal length where the window fills the frame. Your projection is a 1.66 frame, so use 1.66 frame lines in the camera to visualise it.

 

[George Scharoun]

Hi thanks for your reply, and I see your point about the focal length of human vision not mattering. I need to clarify what I'm trying to do though - it's not to film an actual window, it's to film a landscape and then by projecting it in the gallery space we'd be creating a kind of virtual window. The objects in the image should appear life-size though, and that's where I believe the focal length comes into play.

But based on your logic, we could just hold up a tape measure and say, 12' should just fill the frame vertically, when the camera is 15' away? Makes sense! Is it possible to figure this out before going on location though, so we book the right lenses?

 

[Satsuki Murashige]

I think you have two factors to consider here: 

1. Angle of view. Since your 20’x12’ screen is the ‘window,’ the landscape should extend beyond it in theory, only being cut-off by the edges of the screen. That would make me think that a wider focal length would work better. I would suggest shooting a few different focal lengths for safety and erring on the wider side, something like 14,18,21,24,27,32mm (on S35 format). A wide zoom lens may be more economical to rent at a certain point.

2. Degree of magnification. As you say, you want objects to appear proportionally natural. So then you should make sure that when you shoot, there are no objects within 15’ of the lens. Otherwise, they will appear foreshortened and like they should be closer than they appear to be. 

Camera format will also make a big difference. You should be able to test all of this before going out on location, shooting in an urban landscape would give you the same information. The only issue would be in projecting the image, although maybe you can preview it in pre-vis software.