# Thread: Regarding depth-of field curvature with tilt

1. ## Regarding depth-of field curvature with tilt

I’d like to pose a question I asked once before, stating it in a more specific way now, to see if someone can add clarity to my slightly fuzzy view. It pertains to quantification of depth-of-field. While in practice we use the image on the ground glass, there are times when it's hard to see, e.g., indoors with small apertures. Let me emphasize at the outset, that this is just a matter of curiosity for me regarding the principle involved. My work does not (thank goodness) require the sort of measurement that could be undertaken to determine the information suggested below. I'm just interested in understanding the general forces at work here a bit better, if this be possible without resort to cosines, integrals, etc.

In elaborate optical calculations I can not begin to follow, Harold Merklinger in his exhaustive treatments makes this point, among others: When tilting or swinging the lens and/or back, the DOF is 1) always equal on either side of the plane of focus 2) the DOF extends into the distance along straight lines, forming a constant angle.

While I recently discovered that, with camera standards parallel, the DOF stays nearly equal in front and behind the plane of focus to a much greater focused distance than I had previously thought (e.g., to nearly 10 feet with a 210mm lens stopped down as far as f/16), the rate of increase of DOF per unit of subject (plane of focus) distance accelerates rapidly at a certain point, forming a non-constant-angle, "trumpet bell" sort of curvature along its outer limits, and the increase of DOF beyond the subject compared with that between the lens and subject increases likewise.

It would seem at first to make sense that, with a swing or tilt, the total DOF at near and far points of the plane of focus in our image would be the same obtained if the lens, without a movement applied, were focused on the distance given. For example, here's an approximated total DOF chart for my 210 at f/8:

5 2"
6 4"
7 6"
8 8"
10 1'
12 1.5'
15 2.5'
20 4.7'
25 7.5'

My presumption, above, would seem to indicate that if I aimed my lens at an angle to a long wall, such that the near point was 5 ft. and the far one 25 ft. from the lens, and swung the lens to make the plane of focus coincide with the wall, I would get the respective total DOF given above at those two points, which is to say, half to somewhat less than half of it extended on this side of the wall (or strictly half by Merklinger's acocunt). Thus, almost none at the close point, but 3'2" (according to an online calculator, or 3'9" by Merklinger) on this side of the wall at the far point, so that, say, a bushy ornamental plant next to the wall at the far point could fall within the DOF.

However, all that may be dreamland, because, if I'm not mistaken, once we swing or tilt, the DOF decreases as the amount of swing/tilt increases. So, in the example, the DOF would depend on the camera's angle to the wall—and the plot thins.

Again, I'm not interested in wasting anyone's time as if this were critical to me; this is simply a matter of interest to me, and I will appreciate understanding it better. I had noted in my earlier query on this that Stroebel illustrated the principle with curved, dotted lines in The View Camera, but makes no mention of details.

2. ## Re: Regarding depth-of field curvature with tilt

It would be a lot easier if you just got yourself the Rodenstock pocket DOF/Scheimpflug calculator. You are leaving magnification out of your equation as well as the COC.

3. ## Re: Regarding depth-of field curvature with tilt

Originally Posted by Ulophot
In elaborate optical calculations I can not begin to follow, Harold Merklinger in his exhaustive treatments makes this point, among others: When tilting or swinging the lens and/or back, the DOF is 1) always equal on either side of the plane of focus 2) the DOF extends into the distance along straight lines, forming a constant angle.
For typical photography with subject much larger than film (non-macro), the "depth of focus" in the image space at the film is equal on either side of the plane of best focus. The "depth of field" in the object space is not equal forward and back, because the relation between object distance and image distance is nonlinear.

The depth of field is greater in meters at a larger object distance in meters (you can put numbers to this by looking at the focus scale of a small-format lens with DOF marks, for example). As you mention, Stroebel's View Camera Technique has figures showing this; in my copy of the 5th edition they are in section 2.5. There's no contradiction between Stroebel's figures and what I guess Merklinger said, because of the difference between object and image spaces. Edit to add: I suppose there might be a question about whether the boundaries of the depth-of-field region in object space are straight or curved, but for practical purposes it doesn't matter. The practical aspect is that tilts control where the region of acceptable focus is, not how much of it there is.

4. ## Re: Regarding depth-of field curvature with tilt

This all sound correct and good for how depth of focus / depth of field works. The analogous equations in the world of optical design typically get derived into determination of hyperfocal distance, which is the object distance allowing for maximum practical depth of field.

It gets math heavy quickly, but that is how these effects are described.

Optical designers also distinguish between object space and image space: Depth of field for object space. Depth of focus for image space.

Cheers,
Jason

5. ## Re: Regarding depth-of field curvature with tilt

and is image space essential flat

6. ## Re: Regarding depth-of field curvature with tilt

Thanks for the responses.

I pulled out Merklinger's Focusing the View Camera and found one mistake of mine. He does say in his initial definitions that the DOF is not always equal on the near and far sides of the plane of focus. He designates these two distances each as L and says that L1 and L2 may be more appropriate. I was confused by my memory of struggling through the text years ago, and by the various methods of determining DOF and measuring the distance from the plane of focus at different angles.

Nodda Duma (Does this screen name suggest that you are an optimist, New England accent and all, not a doomer?): I am aware, at least, of the difference between depth of focus at the film plane and depth of field in object (subject) space. I am speaking of the latter.

reddesert: "I suppose there might be a question about whether the boundaries of the depth-of-field region in object space are straight or curved, but for practical purposes it doesn't matter." Perhaps you are right; I have not made as many images in as many different kinds of situation with the view camera as I would like. It seems to me that what I referred to as the trumpet-bell curvature could in some situations make a significant difference, but the theory, as you indicate, may be obviated by practical considerations.

(A bit off topic here, Merklinger introduces a hinge line, and a distance J to be estimated, which explain the tilt of the plane of focus relative to front or back camera tilt in a very useful manner. I found, to my disappointment, that I could not estimate J well in practice, let alone single degrees of tilt; some others have experienced similar difficulty. Back to the ground glass and loupe.)

7. ## Re: Regarding depth-of field curvature with tilt

Merklinger's stuff is great, but as you pointed out unfortunately difficult (or impossible) to apply with any sort of rigor in practice without all sorts of surveying equipment, tools/gauges, depth finders (?) etc. (not to mention having all the formulas committed to memory).

I would say the short of it from Merklinger's perspective is that when dealing with a deep object field, it may sometimes be preferable to bias the focusing decisions toward objects which are further away, rather than necessarily maximizing depth of field, simply because far away objects which are smaller in size on the image plane might need to be sharper (smaller CoC) than nearby objects which are rendered larger on the image plane, in order for the image to give a relatively uniform impression of sharpness/detail. In other words, concepts such as hyperfocal distances etc. consider only the image field, without regard for relative sizes and positions of things in the object field.

Originally Posted by Ulophot
Thanks for the responses.

I pulled out Merklinger's Focusing the View Camera and found one mistake of mine. He does say in his initial definitions that the DOF is not always equal on the near and far sides of the plane of focus. He designates these two distances each as L and says that L1 and L2 may be more appropriate. I was confused by my memory of struggling through the text years ago, and by the various methods of determining DOF and measuring the distance from the plane of focus at different angles.

Nodda Duma (Does this screen name suggest that you are an optimist, New England accent and all, not a doomer?): I am aware, at least, of the difference between depth of focus at the film plane and depth of field in object (subject) space. I am speaking of the latter.

reddesert: "I suppose there might be a question about whether the boundaries of the depth-of-field region in object space are straight or curved, but for practical purposes it doesn't matter." Perhaps you are right; I have not made as many images in as many different kinds of situation with the view camera as I would like. It seems to me that what I referred to as the trumpet-bell curvature could in some situations make a significant difference, but the theory, as you indicate, may be obviated by practical considerations.

(A bit off topic here, Merklinger introduces a hinge line, and a distance J to be estimated, which explain the tilt of the plane of focus relative to front or back camera tilt in a very useful manner. I found, to my disappointment, that I could not estimate J well in practice, let alone single degrees of tilt; some others have experienced similar difficulty. Back to the ground glass and loupe.)

8. ## Re: Regarding depth-of field curvature with tilt

Philip,

A couple of things. First, depth of field works in proportion to distance from the lens (aperture, to be more specific). That's why there is more depth of field behind (farther) from the plane of sharp focus than in front of it (nearer the lens). This function, as I understand it, is linear, which means that when you tilt or swing, and position the plane of sharp focus so that one "end" is nearer the camera and one is farther from the camera, the depth of field for a point (or line) on that plane that is is nearer the camera will be less than that for a point that is farther from the camera. Another way to visualize this is to think of what the depth of field would be with no movements with the camera focused at those same two near and far distances; less depth of field for the nearer focus, more for the farther.

As for the "trumpet-bell-shaped" area of depth of field when one applies tilts or swings: I illustrated just this in an article on camera movements I did for View Camera magazine some years ago and was promptly corrected by a mathematician. I turns out that the shape is just a plain wedge and that the growth of the depth of field as a function of distance is linear. In this matter, I believe, Stroebel is inaccurate (as was I, who learned from Stroebel).

Also, depth of field does not "decrease" when you apply swings or tilts; it just assumes a variance dependent on the distance any part of the object is from the camera position. In other words, with, say, swing applied, the depth of field for an object five feet from the camera will be the same as if you had focused the camera at five feet without using movements and the depth of field for an object at 20 feet from the camera will be the same as if you had focused the camera at 20 feet without movements. It's just that for each distance, that specific depth of field applies only for the plane that is perpendicular to the plane of sharp focus and intersects the plane of sharp focus at the line that corresponds to that specific distance (hope that's clear - I don't know how to express it more simply).

Lastly, to speak to your dilemma of focusing in dim light and making sure you have a small enough aperture to make sure everything is in acceptably sharp focus: The near-far focusing method and then choosing optimum aperture based on focus spread works fine for me. It's outlined here on the LF home page: https://www.largeformatphotography.info/fstop.html .

Hope this helps,

Doremus

9. ## Re: Regarding depth-of field curvature with tilt

Originally Posted by Michael R
...
I would say the short of it from Merklinger's perspective is that when dealing with a deep object field, it may sometimes be preferable to bias the focusing decisions toward objects which are further away, rather than necessarily maximizing depth of field, simply because far away objects which are smaller in size on the image plane might need to be sharper (smaller CoC) than nearby objects which are rendered larger on the image plane, in order for the image to give a relatively uniform impression of sharpness/detail. In other words, concepts such as hyperfocal distances etc. consider only the image field, without regard for relative sizes and positions of things in the object field.
I had not thought about that in that way. Thanks. Using that concept to maintain or to create a sense of space in an image is helpful. Like 'atmospheric distance', which does partly rely on far distance objects being less sharp than fore/mid ground objects, it is another tool to use. Working only with contact printing of camera negatives it would be a subtle touch.

Some large digital prints have seem too two-dimensional to me...perhaps when sharpening over-all with too heavy of a hand, one loses the subtle touch of the difference between areas of critical focus and those areas that as just sharp.

10. ## Re: Regarding depth-of field curvature with tilt

What you’re seeing in digital prints (if they originated from a digital camera), a kind of “un-natural” sharpness everywhere, could also potentially be the result of focus-stacking. If you do this with care, you can more or less circumvent the laws of optics.

The fact we normally expect far away things to be less clear can make an “unlimited” depth of field an interesting effect - one of those things that can be subtly disquieting to viewers without them necessarily immediately realizing why.

This was/is exploited by some photorealistic painters, who purposely painted near and far objects with essentially equal detail. One of the things this seems to do in my eyes is remove any atmosphere in the literal sense, which gives the work a strange sort of stifling, static quality I find captivating. This might be analogous to the two-dimensional impression you you describe.

Originally Posted by Vaughn
I had not thought about that in that way. Thanks. Using that concept to maintain or to create a sense of space in an image is helpful. Like 'atmospheric distance', which does partly rely on far distance objects being less sharp than fore/mid ground objects, it is another tool to use. Working only with contact printing of camera negatives it would be a subtle touch.

Some large digital prints have seem too two-dimensional to me...perhaps when sharpening over-all with too heavy of a hand, one loses the subtle touch of the difference between areas of critical focus and those areas that as just sharp.