Re: Dual camera convergence points

[bercov@xxxxxxxxxx (John Bercovitz)]

John Merritt writes:
 
> Maybe someone like John B can tell us if the keystoning created 
> by toeing-in the pair of cameras could be corrected by toeing-in 
> the pair of slide projectors (or video projectors, for video 
> cameras)
 
This is actually a very tricky question.  Yes, you can get rid of 
the keystoning by toeing in the projectors but that isn't the only 
constraint.  So let's back up a minute.  Suppose you take a 
picture of a rectangle whose proportions are 1:2 and the camera 
back is not parallel to the plane of the rectangle (the camera is 
toed in).  The image on the film will be a trapezoid as we all 
recognize.  Now when you project it, you can angle the optic axis 
of the projector to the screen and make the opposite sides of the 
rectangle parallel to each other and the adjacent sides 
perpendicular to each other but will the rectangle still have a 
1:2 aspect ratio?  When you get through all the math, the answer 
is no unless the projecting lens' focal length is equal* to the 
taking lens' focal length.  Coming up with a projection lens this 
short could be really tough.
 
> While toeing-in the projectors would make their two "lighted 
> rectangle" formats into equal-but-opposite trapezoids, so the 
> formats would not match, would the stereo space model then 
> become undistorted within their common overlap areas?
 
Yes, provided the above criteria are met.  You can get rid of the 
trapezoidal windows by blacking out the top and bottom of the 
screen just as some movie theaters (with high projectors) black 
off the sides of the screen because their projectors tilt down to 
the screen instead of using lens shift to center the image on the 
screen.
 
> Is keystoning with cameras a function of distance from the 
> objects in the scene, but with projectors the keystoning is 
> simply a function of distance from the screen, thus making an 
> over-correction for far scene objects and an undercorrection for 
> objects that were close to the cameras?
 
According to my way of looking at it, no, but if someone has a 
contrary argument I'd like to hear it.
 
There are a couple of other things we need to mention.  One is 
that if you have a lot of toe-in, you may not be able to get the 
image quite so sharp clear across the screen as you could by using 
the projector in the usual way.  You would have to swing the 
projection lens to correct this.  The other thing is that the 
lighting intensity will vary across the screen, more as the toe-in 
increases.  You'd have to have a graduated filter at the 
transparency plane to correct this.
 
* This statement assumes that when taking the picture, the 
distance from the camera to the objects >>> focal length of the 
lens and that during projection, the distance of the screen from 
the projector >>> than the distance from transparency to lens.
 
John B


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