This post is not about macro, so in that regard it is off-topic. I do think there are a few things to point out that are relevant and might help, as per Steve Hendrix’s request. At least for those of us who don’t have access to Gerald’s CapCam! Also, as I mentioned above, I look at this stuff a bit differently than most so this post may help dispel how crazy I am (I’m still a little crazy, but hopefully not that crazy).
I noticed over several years that most people think of lens tilt as tilting the plane of focus. In other words, there is a causation we have in our brains between the degree of tilt and the degree to which the plane of focus is “laid down” flat. In my opinion, this perceived connection is one of the major sources of confusion associated with lens tilt and the Scheimpflug principle.
There is a correlation between lens tilt and plane of focus angle, but not when focused at infinity. In fact, even when focused in from infinity the rear DoF plane angle does not change at all as you dial in more or less tilt, so I find it more useful to think of it this way: As you dial in more tilt, you are simply pulling the DoF wedge up through the ground closer to the camera because the hinge point is moving up.
First, a model description. To keep this simple, everything described below is with the camera level to the horizon both in pitch and roll:
Imagine a threaded rod attached to the bottom of the camera that extends down through the ground infinitely far. The threaded rod is fixed and in line with the film plane, but the threads spin as you dial lens tilt in and out.
As soon as you dial in any small amount of tilt, say 0.01 degrees, something magical happens: the normal parallel planes in the standard DoF (near DoF, plane of focus, far DoF) flip from being parallel planes out in front of the camera to being a wedge, or cone of DoF, with a point of origin (where the lines converge) mounted on that threaded rod. I will refer to that as the “head” of our cone of DoF. As we dial in more tilt, the threads rotate and pull that point of origin (head) up from infinitely far underground toward the base of our camera.
If the lens is focused at infinity, the plane of focus is 90 degrees from the film plane and, since our camera is oriented with the horizon, the plane of focus is also parallel with the ground that extends out to infinity in front of the camera. It remains 90 degrees from the film plane regardless of how much tilt we dial in. Focused at infinity, the only thing more tilt does is pull that hinge line up through the ground closer to the base of the camera; the plane of focus remains flat, 90 degrees from the film plane.
Now we add the focusing variable: Adding to the threaded rod model, let’s add a rope that extends from the lens down, and is tied some point out from the head, at the “waist” of the plane of focus. Close to the point of origin where the near DoF, plane of focus and far DoF converge, but just a wee bit out from that point of origin. Like this:
I know that picture isn’t an accurate description of the angles and the math. But for this explanation it should be good enough…
Now a little more magic: Whenever the lens is focused at infinity, the rope is just long enough to keep the plane of focus 90 degrees from the film plane. As we pull in focus from infinity, the rope will get shorter and pull the plane of focus up from horizontal.
To prove all this, I need to give a shameless plug to Torger’s Lumariver DoF app:
www.lumariver.com. Below are several screenshots from Lumariver.
First, I show what happens as more tilt is dialed in with the lens focused at infinity. Note how the hinge line gets pulled up through the ground closer to the base of the camera, from 11 ft @ 1 degree to 5.6 ft at 2 degrees:
Second, showing the “standard” landscape application, where the far DoF is set along the horizon, 90 degrees from the film plane. We do this by dialing in focus from infinity:
Third, now that the rear DoF plane is horizontal we dial in more tilt.
A few things to highlight:
- More tilt pulls the point of origin up the threaded rod
- More tilt scrubs (diminishes) DoF
- The far DoF remains horizontal if we don’t change the focus distance dialed on the lens.
- The plane of focus does, indeed, “lay down.” But I like to think of this as being due to the DoF being scrubbed or squashed. You, of course, can look at it however you want!
Fourth, a sequence of maintaining the same tilt (1.5 degrees), but dialing in focus from infinity. Hinge point doesn’t move, but our rope gets reeled in, which pulls up the cone of DoF.
Fifth, the difference between dialing in more tilt to get something close in focus, vs reeling in the focus point. In many cases, focusing closer helps because the DoF remains the same width. More tilt brings the plane of focus closer to the ground, but at the expense of height. The ground is all sharp, but the top of the tree or mountain might get blurry as you dial in more tilt. The upper right corner of each image depicts the DoF wedge projected at infinity on the film plane. In the third image, it is the highest, 31mm above the center line of the film/sensor (assuming no rise/fall, but that's another story...).
In summary, I think it is more useful to think of focus as the tool that tilts the plane of focus and cone of DoF. The degree of lens tilt defines how far the head of that cone sits below the camera. It is true that when focused in closer than infinity, changing the degree of tilt does “tip” the plane of focus. But it does not change the angle of the rear DoF line at all.
Again, thanks to Torger!
Dave
GO TRIBE!