Why does tilt work?

[poco]

Heroique's current T vs B question prompts me to bring up something of my own that actually did keep me up last night thinking about:

I've heard it explained here that surprisingly large scratches on the front element of a lens have no effect on image quality because rays of light from all points in the scene enter through all parts of the front element before being focused onto specific points on the film. Fine, I guess, except if that's the case, then why does tilt work? Wouldn't rays of light from near points of the scene, entering the part of the lens tilted to focus far points, then be sent to the film as an unfocused near point? That's one hell of a tangled sentence, but I hope it makes sense.

So why does tilt work?

[Paul Metcalf]

Refraction, good stuff when combined with optics theory. google scheimpflug principle.

[aduncanson]

What, no takers? I actually derived the Scheimpflug principle for my self edification years ago when my facility with algebra was much more current. Or at least I thought that I had. I'm not going to do that again, so what follows is more hand waving than proof, hoping only to show you that your question is based on a misunderstanding.

I hope that you are familiar with the lens equation which states that 1/focal length = 1/object distance + 1/image distance. In this equation, object distance and image distance are the distances measured along the axis of lens, rather than the actual distance from the lens to the object or the image. Consider that as you tilt the lens back slightly, the objects that are above the optical axis get slightly further away in terms of object distance because more of their total distance from the lens lies along the optical axis. Similarly, objects below the lens get slightly closer because less of their total distance lies along the axis of the lens.

So by the lens equation as you tilt the lens upward, images of objects above the axis become closer to the lens and images of objects below the axis become further from the lens. In this way tilting the lens plane, induces a tilt in the image plane for a set of points which comprise a vertical plane in the object field.

I would love to say QED, except I am pretty sure that that is not going to answer the question.

[ic-racer]

You would be correct in assuming tilt does not work with a pinhole lens.

[Mark Barendt]

I'll take a stab at explaining this.

Tilt (and similarly swing) varies the distances of the top and the bottom of the lens from the film.

You are essentially adjusting the top of the lens to focus at one point and the bottom to focus at another.

With the lens "squared" and camera level the plane of sharp focus is vertical like a canvass hanging on the wall. Theoretically that plane, like the surface of the canvass, is the only place there is sharp focus.

When you tilt your lens, the plane of sharp focus tilts; it is as if you take the canvass off the wall and tilt it to match the floor. Things above and below the floor, the tilted plane/canvass, are now out of focus.

Aperture choice controls the acceptable range of DOF on either side of the tilted or vertical canvass.

[Scott Knowles]

It works because it's proven, see description and the patent application. And it's proven when you use it.

[poco]

Thanks, guys. But it's not the theory behind tilt that I'm confused about. It's why it should work if rays of light enter through the entire (tilted) lens before being focused onto a specific point on the film that I don't understand.

[Paul Metcalf]

Thanks, guys. But it's not the theory behind tilt that I'm confused about. It's why it should work if rays of light enter through the entire (tilted) lens before being focused onto a specific point on the film that I don't understand.

I think I see (ha!) what you're having a hard time with. Remember, "rays" of light (waves actually if you're thinking wave-theory and photons if you're thinking particle-theory of light propagation) travel in parallel, or actually the wave-fronts travel parallel to each other and perpendicular to any point/line/surface in space, in our case the lens front face. That is why lenses are curved (convexly or concavely) so the wavefront at the outer edges of the lens are refracted to different angles than the wavefront at the center, thus focusing the refracted wavefront evenly on a film plane or sensor as best at possible. In this way it's easy to see that when the lens axis is tilted wrt to the film plane, the refracted wavefront is now also tilted. If you think of the wavefront as hitting the front of the lens radially (i.e. equally in all directions), then it is hard to see that the refracted wavefront would be in fact tilted.

Add "ray tracing" to your google searches.

[poco]

Thanks, Paul. I'll do some google hunting and noodling on it, but I'll probably end up settling for "it works because it does."

[aduncanson]

As I mentioned privately, by creating a numerical (Excel) model of the phenomenon I described above, I was able to confirm the classic formulation of the Scheimpflug rule based on how the object distances lengthen or shorten as you tilt the lens.

Below, I am posting a graphic to help you understand how tilting the lens lengthens or shortens the object distance.

- Alan

To further explain the diagram. Before tilting the lens the object distances for points O1 & O2 are identical, OD1 = OD2. After tilting the lens, you measure the object distance along the new lens axis, A', and these object distances diverge to become OD1' and OD2'. Different object distances imply different image distances through the lens equation and therefore the image plane is tilted even though the object plane is not.