Adjusting the focus point - 1/3 in or half way?

[Julian Boulter]

Adjusting the focus point - 1/3 in or half way?

OK - I have read Quang-Tuan Luong's article 'How to focus the view camera' http://www.largeformatphotography.info/how-to-focus.html and I am a little confused regarding placement of the focus point.

In procedure 1 he begins by saying - 'when you establish a Scheimpflug relationship, the subject plane (plane of focus) is one where depth of field behind that plane remains double the distance of depth of field in front. This is just as when the subject plane is parallel to the film. If your camera is on top of the rock, you would have the subject plane defined by one point about two thirds of the way up the rock, the other two thirds the way up the mountain'.

This makes sense to me, if DOF behind the plane is approx double DOF in front of the plane then focusing 1/3 into the subject should place the plane optimally, indeed I have seen many various references advising to 'focus 1/3 in' to make best use of DOF.

But in procedure 2 he talks about adjusting the focus point by focusing on the closest and furthest points and adjusting the plane so that it's midway between the 2 points. Again I have seen many various refenences advising this method including Leonard Evens http://math.northwestern.edu/~len/photos/pages/dof_essay.pdf

I know I'm simplifying things and the rules change if ininity is involved and for close ups but am I missing something here? - why do some reference 1/3 and some reference 1/2 ? If making the closest point and the furthest point equally sharp is optimal (provided the far point is not at the horizon), why does he advise defining the subject plane as 2/3 up the mountain in procedure 1 and not 1/2 way up?

Also where does the hperfocal technique fit into this? where does focussing hyperfocally place the plane? is it closer to 1/3 way in or 1/2 way in?

[steve simmons]

The proper place to focus floats according to the reproduction ratio (the size of the object in reality vs the size of the image of the objest on the gg). For a distant subject that appears much smaller on the gg than it is in reality the proper focus point is about 1/3 of the way in to the scene. However, if the size of the object in reality and the size of the image of the object on the gg are the same (a 1:1 reproduction ratio) the proper focus point as about half way in to the scene.

For this reason I have always suggested that people focus so that the closest thing they care about and the farthest thing they care about are equally soft. This is done after all movements, etc. Then as they close the lens down the dof area will spread to include these areas at the same time. With care and practice, and one of the gg brighteners and a 4-6X loupe, it is usually possible to bring everything into the dof area by f22 or so. The only time this might be a problem is if the near far perspective is being forced or if it is a dimly lit scene.

steve simmons

[Arne Croell]

Julian,

the two numbers refer to different "spaces": the 1/3rd -2/3rd rule refers to object space, i.e. if you focus on an object about 1/3rd of your DOF at a given aperture and circle of confusion is in front of the object and about 2/3rd behind it. The 1/2 rule is in image space, i.e. when you focus the back standard on the farthest point and then on the nearest point to be in focus the optimum position for the film is just in between the 2 extreme positions - that is what Tuan describes. Both rules are equivalent in the end. I personally use the 2nd technique and have never bothered imagining or calculating the DOF in object space.

[Leonard Evens]

I'm not sure exactly where the various---different---one third rules come from, but let me tell you the facts as I see them.

First let me address the situation without tilts.

Let me look at the situation a couple of ways.

It is often proposed in this case that you should focus one third of the way into the subject. It may be that the suggestion is that there is twice as much far depth of field as near depth of field. But this is wrong except for one specific subject distance. It is certainly wrong for closeups where the near and far depth of fields are very closely equal. For subjects at normal distances, the following formulas are good approximations

far DOF = D^2/(H - D)

near DOF = D^2/(H+D)

where D is the subject distance and H is the hyperfocal distance. By simple algebra if you solve

far DOF = 2 x (near DOF)

for D, you get D = H/3. In other words, this applies just when the subject distance is one third the hyperfocal distance. At that subject distance, using the approximate formulas HD/(H+D) and HD/(H-D) for the near and far limits of DOF, everything from H/4 to H/2 should be in focus. Note that even the hyperfocal distance is outside this range. So if distant objects are of interest, this rule is not appropriate. Even if you take it as an approximation which applies in a range, it doesn't really apply very often. For example, using a coc of 0.1 mm, my 150 mm lens at f/16 has a hyperfocal distance of about 16 meters. So the relevant subject distance is about 5 1/3 meters. At that distance, everything from 4 meters to 8 meters would be in focus. Note that if you stop down enough, you will approach the closeup range because the hyperfocal distance decreases, and in that case the approximate formulas no longer apply in any case.

The usual rule about hyperfocal distance is that if you focus at infinity, everything from infinity down to the hyperfocal distance will be in focus, and if you focus at the hyperfocal distance, everything from infinity down to half the hyperfocal distance will be in focus.

There is another argument which might apply. If you've studied the material elsewhere in this website about focusing using the focus spread method, you may have noticed that some people argue that you shouldn't focus at the center of the focus spread on the rail. For more distant subjects, the near DOF is a relatively small fraction of the far DOF, certainly well less than one third. So if you use the one third into the subject rule to focus, you will be sacrificing the foregroud in favor of the background. Some people argue for doing exactly that, but there doesn't seem to be any universal way to do it. Clearly, it doesn't make any sense if you want infinity to be in focus because one third of infinity is still infinity. Merklinger has argued that for distant subjects, you should just focus at infinity, which eliminates the usual far DOF. Joe Englander suggests an approach based on the focus spread method using distances on the rail. He says you should put the standard one third of the focus spread from the far focus point and two thirds from the near focus point. But don't be misled, this has nothing to do with the one third into the subject rule.

My feeling is that there are certainly circumstances in which you want to favor distant subjects over near subjects. Near subjects tend to be larger and can often tolerate some loss of sharpness. But I don't think there is any formula which can tell you just how to do it. In each case, you should start off using the focus spread method and set the focus point half way between the near point and the far point. Then you should examine the gg image, stopped down if you can still see anything that way, and make adjustments that seem appropriate. You may want to do this to favor the background as noted above. You may also want to do it if you use shifts and, as often happens, field curvature changes the point of focus from the center to the periphery. You have to use your best judgement, and hope for the best.

Let me now address the case where there is a tilt.

For simplicity I assume the back standard is vertical. Then the applicable rule is the following. Imagine a vertical plane at some distance. There will be a certain vertical distance in this plane above the plane of exact focus and a distance below the plane of exact focus, and within these distances everything will be in focus. These distances depend on the distance from the lens and on the hyperfocal distance. The important thing is that THEY ARE EQUAL. At the hyperfocal distance, it is known what these distances are, and using that information, you can calculate them at any distance. (At the hyperfocal distance, the distances above and below are very close to the distance from the lens to the hinge line. See my essay or Merklinger.)

So why does Luong's article suggest making the distance above twice the distance below? There is no argument that I know based on optics that justifies such a rule. However, there are some qualitative arguments---like those above---which could justify it. Suppose you have such a scene with a relatively flat foreground and a mountain in the distance. If you use the halfway up rule on the mountain, you will have the foreground at the lower limits of the DOF wedge for the tilted lens. Since usually you want to be sure the foreground is sharp, you may want to move the plane of exact focus down somewhat. In so doing, you will sacrifice some part of the DOF wedge which in principle is usable, and you may lose some sharpness on the upside, but that may be appropriate for your purposes.

Again, I don't think there is anything magic about any particular fraction like one third here. What I suggest is the following. First determine the tilt as best you can to get a reasonable subject plane of exact focus. You might start by setting that subject plane halfway or some other fraction "up the mountain" or you could have it coincident with the relatively flat foreground. Then, without changing the tilt, focus on something high that you want in focus and something low and note the positions on the rail. As in the untilted case, start off by setting the point of focus on the rail halfway between those points. Now look closely at the image, again stopped down if you can still see anything, and adjust the focus so that things that are important to you are sure to be in adequate focus. As you move the standard, the plane of exact focus, together with the DOF wedge about it, will swing on the hinge line. Maybe a one third-two thirds split will be right, maybe not. As before, it is a question of judgement.

Unfortunately, when you tilt the lens, there is the additional problem that you might not have got the plane of exact focus right to start, so you may have to adjust the tilt and refocus as above. I think there is necessarily some element of bootstrapping involved however you go about it.

This still may not be clear, so feel free to ask more questions.

[Leonard Evens]

Julian,

If you read my long explanation, you will see that Arne's comment that the two methods are equivalent is wrong, except at one subject distance, but since he isn't using the one third into the subject rule, that is irrelevant for him.

Steve's method in brief avoids having to think about it all and relies on visual evaluation. It incorporates the objective and subjective sides of the problem in a couple of operations. If you have a very good eye and/or enough experience, it certainly beats trying to use optical principles. Personally, I have neither the eye nor the experience. I have a hard time judging when near and far are "equally in focus" and my elderly eyes can't see much of anything if I stop down below f/16, even with a very bright Maxwell screen. But I think my suggestions amount to a long-winded endorsement of the same ideas, but guided more by an understanding of the optics, which for me compensates to some extent for poor dark vision and less experience.

Perhaps I should amplify one point. In the case of the tilted lens, there are two distinct, but interrelated operations. Determining a provisional subject plane by setting the lens tilt and then placing that plane and the DOF wedge about it by moving the standard. You have to keep these separate in your mind, and understanding how the subject plane and DOF wedge swivel about the hinge line, as I see it, are essential to developing a three dimensional visualization of what is happening in subject space.

[Mark_3632]

leonard

Either it is too early in the morning to wrap my brain around your explanation or I really did not get it. I think it is the latter. I have a question for you.

I am a relative newbie to camera movements. I was photographing a pile of boulders and saw, when I got everything positioned, the way i wanted, that there was a distinct triangle of points that were in focus, after tilting and swinging. These points were the furtherest point, and the nearest point which happened to line up, and a point on the left of the GG which I guess would be the right most mid point of the scene. There was a little softness in the middle. would a small aperature, of say f/45 pull this area into focus?

[Leonard Evens]

Mark,

From your description, I can't know the exact geometry, but I will try to give it a try. Since you are using both a tilt and a swing, the net result is that the plane of exact focus is at an angle to both the vertical and horizontal. Three points in space determine a plane, so if those three points were all exactly in focus, then the subject plane would have to pass through them. Probably, it is fairly close to those points. The softness "in the middle" is probably some part of the scene which is too far above or below the plane of exact focus.

You have two or three options, which you can try singly or in combination.

First, with your tilt and swing set, try adjusting the focus so the soft area comes more into focus. Some or all of the references points may then go out of focus, but try to pick a good balance. Then stop down to see if that improves the situation. Without knowing the precise geometry, I can't say how far you would have to stop down. Unfortunately, you almost certainly won't be able to see anything on your gg at f/45, so you have to estimate how much improvement there is looking at a wider aperture, say f/22, and guessing.

Second, you can go back and redo your tilt and swing, and then refocus again. Since what you want in focus doesn't lie in a plane, you probably need to choose the subject plane of exact focus so it reasonably cose to the four areas you want in focus. Mathematically, this is a fairly complicated problem, and it requires some not particularly intuitive calculations. I've seen some discussions of how to do this visually on the camera, but none of them seem that easy to use. If I remember correctly, Jim Stone's book has one such method, and there may be others you can find on the web. But I think it comes down to fiddling, and it can take a while. Once you have placed the plane of exact focus optimally, you can try stopping down again. However, given the optical constraints, it may just be something that can't be done.

I haven't often had to use both tilts and swings, and when I have, I've just winged it, usually with reasonable success. But I'll take some time to think of it to see if my geometric insight from over 50 years of doing mathematics can help.

[Al W]

The half way rule refers to physically moving the lens. Move the lens to the farthest point and note where it is on the focusing rail, then focus on the nearest point. The hyper focal point will be the point on the focusing rail directly between these two points.

If you think about what's happening inside the camera at the focal plane it makes sense. When you focus on the near and far points you are determining how far apart the two circles of confusion will be. To have them be equal diameter you need to move your lens to the point directly in between these two points. Look at the depth of field scale on a 35mm camera. It's exactly what they are doing there. You physically move the lens to the half way point by placing the near and far focal points on the same f number on the scale, but if you look at the focal distances to the subject you'll see the 1/3 rule come into play.

Another nice thing is that for a given format you can determine the f stop you need by measuring the distance the lens moves between near and far focus. Here are the numbers.

For a 1/1500 the film diagonal circle of confusion (COF) on 4x5;

Lens Movement = f stop; 1mm = f5.6, 1.5mm = f8, 2mm = f11, 3mm = f16, 4mm = f22, 6mm = f32, 9mm = f45, 13mm = f64, 19mm = f90.

For 5x7;

Lens Movement = f stop; 1.5mm = f5.6, 2mm = f8, 3mm = f11, 4.5mm = f16, 6mm = f22, 9mm = f32, 13mm = f45, 19mm = f64, 27mm = f90.

For 8x10;

Lens Movement = f stop; 2mm = f5.6, 3mm = f8, 4mm = f11, 6mm = f16, 8mm = f22, 12mm = f32, 17mm = f45, 26mm = f64, 38mm = f90.

In my opinion, the half way rule is by far the easiest way to focus.

[David Karp]

I don't understand the physics, but I have used the 1/2 way method, since it was recommended by John Sexton at a workshop. He gave us a table with nearly the same information as that given by Tuan in his article. This method seems to work and is easy to do. Just focus on the near and far, noting the position of the standard, and then set the standard 1/2 way betweent the two points. Then look at the table to set your f/stop.

In addition, it is my understanding that this method is the basis of the focus/dof calculators built into some of the studio cameras by companies such as Sinar, Arca-Swiss, and Cambo, and a table distributed by Linhof.

[Leonard Evens]

Al W.,

That is a nice explanation of just what happens on the film side of the lens in terms of blur circles.

But I'm not sure what you mean by "You physically move the lens to the half way point by placing the near and far focal points on the same f number on the scale, but if you look at the focal distances to the subject you'll see the 1/3 rule come into play." If you go back and read what I've now tried to say twice, putting the focus point half way into the focus spread does NOT generally place the distance to the exact plane of focus in the subject plane one third into the subject DOF range. It only does that if the subject plane is at one third the hyperfocal distance.

While we are at it, there is one further quibble which was mentioned by Paul Hansma in the article linked on this webpage. The correct position to put the focus is not actually exactly halfway between the focus points, but except in very special circumstances, which almost never occur in practice, that is close enough.