Impact of film size and Circle of Confusion

[Michael Heald]

Hello! I read Robert B. Hallock's article on what makes a print sharp in the current issue of View Camera magazine. My initial impression was that the larger film size always makes better prints because of less enlargement required and less restrictions on the CoC. However, looking at the graphs, if one takes into account the depth of focus, the advantages (based solely on CoC) are minimized.
However, this appears to depend on the depth of field that a person accepts at the larger format and longer lens.
For example, a 4x5 negtive with a 150mm lens and a 10mm spread between lens/GG distance gives an effective focus range of 8 feet to infinity. According to the figure, with an optimum fstop of 60 and CoC=0.12mm.
For a 305mm lens, for a 10mm spread, the depth of focus is 30 feet to infinity, again yielding an optimum f-stop of 60 and CoC=0.12
In this case, if the photographer accepts less depth of focus, then the enlargement will be sharper from the CoC consideration.
However, to obtain the same depth of field, the GG spread goes up to 43mm. Extraplating the curves out suggest that the CoC is double that of the 150mm lens. So to obtain the same depth of focus, the high f-step is needed and the higher CoC results. Hence, no increased sharpness based solely on CoC.
I'm not sure I am interpreting this correclty, but it appears that 8x10 is superior to 4x5 (purely form a CoC standpoint) in those situations where less depth of focus is needed. Is this true? Best regards.

Mike

[scott_6029]

Boy, I am clearly in the circle....I got lost early on in the article, perhaps just got bored with it.....but, all I need to do is look at an 8 x 10 contact print or 7 x 17 contact print and compare it to an enlargment....

[Brian Ellis]

Boy, I am clearly in the circle....I got lost early on in the article, perhaps just got bored with it.........

I'm glad to see that I wasn't the only one.

[Capocheny]

Me three!

I started to read the article and got a short way into it. But then... my head started hurting and I had to stop! :)

Cheers

[Leonard Evens]

I've just read through the Hallock article quickly, but I think I understand roughly what he is saying. It appears that he is using a method similar to that of Paul Hansma to choose the optimal f-stop which minimizes the combined effect of defocus and diffraction. (Hansma's method is described elsewhere on the Large Format webpage, and there is a link to his article showing the mathematics behind it.) Since Hallock doesn't explain the mathematics he is using, I can't be sure of how his analysis goes, but let me try to explain what I think is going on.

Subject points out in the scene come to focus at different distances from the lens. But you can only put the film at one position, so these other subject points will produce small discs, rather than point images, in the film plane. These are usually called defocus discs. The sizes of the defocus discs depend on the relative aperture, getting smaller as you stop down. Now suppose you want everything within a certain range to be in focus. You focus first on a far point and then on a near point and measure the distance on the rail, or focus spread, between them. If you ignore diffraction, you can calculate for any given position of the film plane, the sizes of the defocus discs from subject points at the near and far distances. This a a simple function of the focus spread and f-number. You can then decide just where to place the film plane and how to choose the f-stop so that the defoucs discs are below some specified size called the maximum allowable circle of confusion, usually just called coc. At the limits of DOF, the defocus discs will be equal to the coc and as you move closer to the exact plane of focus, they will decrease in size, approaching points in that plane.

But that ignores diffraction. Because of diffraction, no subject point is every imaged exactly as a point, but rather by a certain blur pattern, the primary component of which is also a small disc called the Airy disc. The diameter of the Airy disc goes up as you stop down. Now what is the effect of diffraction on a typical defocus disc arising from a subject point off the exact plane of focus? Instead of a disc with sharp edges, you will get a somewhat larger disc with blurry edges. To calculate exactly what happens is a difficult problem in physical optics, and there is no easy way to do it. (See Jacobson's Optics Tutorial for some discussion of that.) However, one can try roughly to estimate how much the defocus discs are enlarged by diffraction. Hansma uses one such method. I don't know which method Hallock uses, but my guess is that it is essentially the same as Hansma's. I think when Hallock refers to the coc, he means the enlarged disc combining the effect of defocus at the limts of DOF with diffraction. The curves he gives in his first figure show how this coc varies as a function of the f-number. There is a different curve for each focus spread. The aim then is to choose the aperture so that disc will be as small as possible, and certainly less than your limit on acceptable sharpness. He gives a curve and a table telling you how to do that.

Looked at this way, the best aperture to use seems dependent just on the focus spread and not on the focal length of the lens or the format. But these enter indirectly since the focus spread will depend on the focal length. (See below.) In addition, as he points out, there may be reaons to use something other than the best possible aperture for a perfect lens. For example, you may want to use f-stops for which your lens aberrations are small. So he shows you how, if you specify an acceptable coc, you can determine from his graphs the range of f-numbers which will do that well or better. What you consider an acceptable coc will depend on the degree of enlargement needed (hence on the format) and how a final print is viewed.

How does focus spread depend on focal length? If you are not in the close-up range, and you fix the position of the nearest and furthest planes you want in focus, then the focus spread on the rail will be roughly proportional to the square of the focal length. Also, with those restrictions in mind, the focal length you use for a given angle of view will be propotional to the format diagonal. So for the same picture, you would use double the focal length with 8 x 10 as you would use with 4 x 5 and the focus spread would be roughly four times as large. Hansma's method gives a best f-number which is proportional to the square root of the focus spread. If Hallock is using the same method, which I think he is, that means that his best f-number would be roughly doubled if you go from 4 x 5 to 8 x 10 with the other constraints on the scene being the same. Moreover, the size of the (blurred) coc at this best f-number is proportional to the focus spread, so this too would be doubled.

So, when will 8 x 10 be superior over 4 x 5 from this point of view? For the same size final print, you can accept a combined coc twice the size of that for 4 x 5, so the two should be the same. On the other hand, your best f-number is twice as large requiring you to stop down two stops further with appropriate increases in exposure time. This is generally true across all formats. For the same scene, you do better with smaller formats. There is no significant change in the range of usable f-stops for a desired depth of field, but you have to stop down further and use slower shutter speeds for larger formats. What a larger format gives you is a need to enlarge less, which minimizes the effects of grain, puts less strain on lens design, and gives you better tonality.

I hope this answers your questions.

[Leonard Evens]

As a postscript, let me note that Hallock, in the beginning of his article, repeats the old rule of thumb that you should focus one third of the way into the scene. I started a thread on why this rule seems to be so popular when technically it has merit only at one focus distance. Generally the ratio of the near DOF to far DOF in the scene is the same as the ratio of the near distance to the far distance. So in the example he gives with near distance 20 feet and far distance 50 feet, you should actually focus 2/5 ths of the way into the scene. In the previous thread I gave some reasons why the rule persists, and others elaborated further.

[Brian Ellis]

Thanks for the clarification Leonard. So he was just repeating the Hansma article in more complex language? I cut out the table of optimum apertures from the Hansma article (or the one that accompanied it, I forget in which one the table appeared) when it was published many years ago and I've been carrying it (and the similar Linhof table) around with me and using the focusing methodology outlined in that article ever since. As I was struggling with the Hallock article I had a vague idea that he was talking about the same things as the Hansma article but he lost some credibility when he said to focus 1/3 of the way into the subject and then when he talked about the distance between the lens and the ground glass (rather than the film) I decided it was unlikely that I'd find anything in the article of sufficient importance to justify the struggle involved in reading it.

[Jim Jones]

By juggling DOF formulae, one can derive this rule: When the final prints are viewed from the same perspective, DOF in different formats is determined only by the diameter of the entrance pupil of the lens. In some photography this means there is not a dramatic difference in DOF between 35mm and LF. However, in many large format cameras the plane of sharp focus can be adjusted to extend the practical DOF. Also, when producing large images from small film, grain and negative flaws become significant. Several decades ago, before calculators were commonly available, I spent many hours with the help of an old copy of Rudolf Kingslake's Lenses in Photography calculating DOF. It was worth the time, pencil, and paper. Even though I've forgetten many details, the exercise gave me a better feeling for the practical application of DOF that one or two readings of the [I]View Camera[I] article wouldn't. However, the article does nicely summarize important information.

Sharpness and DOF can be studied as a purely scientific subject. This is useful, but not adequate. The ultimate presentation of an image and the qualities of the subject are important considerations. Some printing techniques obscure fine detail. Others emphasize detail and grain. Some subjects have detail that should be sharply rendered. This is often true in Ansel Adams photos. Others rely more on masses of light and dark for effect. For example, some Edward Weston macro photos were diffraction limited, but have not lost important detail. Sometimes the limitations of small formats is an asset. The gritty quality of David Douglas Duncan's combat photography was appropriate for recording the harshness of war.

[Leonard Evens]

Brian,

I had a somewhat more positive take on the article than you did. The article is the second in a series of two, and the first article, I thought, was really excellent. Perhaps there was some afterglow effect for the second article.

The article does contain a few useful ideas that might not be available elsewhere. For example, he does show graphically how the combined coc varies as a function of f-stop. In particular, as I noted earlier, he tells you how to use that to choose a range of acceptable f-stops rather than fixing on one supposed best f-stop. His tables and graphs might also be enlightening to some readers who don't feel qualified to deal with the usual mathematical approach. Soemtimes, such an approach is more enlightening than fiddling with formulas. But, since I know all of this quite well, I can't really judge how useful the article would be to others who are not so familiar with the ideas. I must say that the comments here haven't been too promising in that respect.

There is one other minor point in the article where I think the emphasis is wrong. He has an appendix on bellows extension and comments that it is less important for wide angle lenses. What he says there is correct, but I think it is misleading. In fact, the crucial factor is the magnification, rather than the focal length. For the same magnification, you would just be closer if you used a wide angle lens, but you would use the same correction for bellows extension.

[Michael Heald]

Hello! Thank you for the replies. I am curious how lens tilt affects teh optimum f-steop. The article dealt with parallel planes. An advantage of view cameras is the ability to tilt planes to bring images into focus. With my 4x5, with proper tilt of the lens, for landscapes, there seems for be minimal near/far difference to the GG.
Given that 8x10 has less DOF because of the use of longer lenses, how much can front lens tilt help for landscape focusing? Best regards.

Mike

[Leonard Evens]

What you do when you tilt is to change the plane of exact focus. You can arrange so that plane passes through a specified near point and far point. If you get it right, all points in the plane, including the near and far points will be in exact focus. In addition, just as in the untilted case, there is a region about the exact plane of focus which is in adequate focus in more or less the same sense as in the untitlted case; the images of such points in the film plane will be blurred 'discs' smaller in size than some specified coc. This region is bounded above and below by two planes which meet the exact plane of focus in a line below the lens called the hinge line. It is best described as a wedge, with quite limited vertical extent close to the lens which increases as you move further from the lens. As you stop down, the upper bounding plane swings upward and the lower one swings downward, and as a resul the size of the region increases.

To choose the proper f-stop, you choose additional references points, one above the exact plane of foucs and one below it which delineate the upward and downward limts of what you want in focus. As in the non-tilted case, ignoring diffraction, you measure the focus spread, and you use it to determine the f-stop in a manner similar to that used in the untitlted case. Namely, you take the focus spread and divide it by twice your chosen coc. I don't think anyone has generalized Hansma's method to combine defoucs and diffraction in the tilted case, but if you use the method suggested above, it actually overestimates how far you have to stop down. If you stop down an additional stop or two, you are probably doing a reasonable job of balancing diffraction and defocus, even in the tilted case.

One of my projects is to extend Hansma's method (presumably also Hallock's method) to the tilted case. I have a pretty good understanding of what happens to defocus when you tilt, but I still have to learn about how tilt affects diffraction discs. My guess is that things don't hange very much except for a small correction factor to take account of the tilt. For the modest tilts commonly used in practice, that correction factor is going to be close to 1. If you just used Hansma's table (or Hallock's graphs or tables) my guess is that you wouldn't be significantly off.

[robc]

Given that 8x10 has less DOF because of the use of longer lenses, how much can front lens tilt help for landscape focusing?

A lot but it depends on the subject. For example, using a 300mm lens to photograph a planar subject such as a beach, it is possible to get evrything in focus from very near to very far. But as soon as you have something in the scene which protudes outside the cone on sharp focus you are in trouble. For example, a small building which is near to the camera would soon protude above the cone of acceptable sharpness as you tilt the lens forward. You need to be very precise and very picky about your subjects.

This following web site has much info and some useful little .mov files and pdf's to help visualise what is happening.

http://www.trenholm.org/hmmerk/

[Michael Graves]

I must admit, I've been following this thread with an increasing degree of (ahem!) confusion. None of the eloquent answers explain how image size relates to Capitol Hill. Wasn't that the original question?

[Leonard Evens]

Perhaps my last answer wasn't explicit enough. Let me try to supplement it.


Hello! Thank you for the replies. I am curious how lens tilt affects teh optimum f-steop.

Using a tilt requires two steps. First, you use a near and far point to establish the plane of exact focus. Then you select points above and below that plane, with accompanying focus spread, to determine the f-stop you need to get those points in adequate focus. To the best of my knoweldge, no one has provided a complete theoretical analysis of how to do this, but it appears that essentially the same method works as you would use to determine the f-stop from the focus spread in the untilted case.


The article dealt with parallel planes. An advantage of view cameras is the ability to tilt planes to bring images into focus. With my 4x5, with proper tilt of the lens, for landscapes, there seems for be minimal near/far difference to the GG.

Before you tilt, you choose near and far points on the gg and measure the focus spread between them. The point of titling is to reduce that focus spread to zero. In practice, you may stop short of that and be satisfied if it is very small. That has nothing to do with choosing the optimal f-stop to get everything you want above and below the plane of exact focus in adequate foucs. As noted above, you have to choose two additional points to accomplish that.


Given that 8x10 has less DOF because of the use of longer lenses, how much can front lens tilt help for landscape focusing? Best regards.

First let me correct the statement aboe about what is given. 8 x 10, compared to 4 x 5, has less depth of field for the same angle of view (hence a longer lens) fonly if you insist on using the same f-stop. But if you stop down two additional stops it has the same depth of field. At the same time, the effect of diffraction is also less by about two stops because you only have to enlarge half as much for the same size final print. Similarly, the number of accpetable f-stops, as described by Hallock, remains the same, but everything is just shifted two stops in the direction of smaller apertures. You shouldn't think of 8 x 10 as providing less depth of field. Instead, you should think of it as requiring longer exposure times for the same depth of field.

With respect to the use of tilt, remember that tilting doesn't increase depth of field. It just distributes it better for the scene. Instead of a slab between a near plane and a far plane, you have a wedge between upper and lower planes. So you use tilting for landscapes with 8 x 10 in essentially the same way you do it for 4 x 5. For the same angle of view, the fact that you use a longer focal length lens means that you have to tilt more to yield the same plane of exact focus---step one above For example, suppose you needed the plane of exact focus to pass 1.5 meters below the lens. If you used a 150 mm lens, you would need to tilt about 5.7 degrees. If you used a 300 mm lens, you would need to tilt about 11.5 degrees. This would be true whatever format you would be using, and the way the format enters the analsyis is that you use double the focal length with 8 x 10 for the same angle of view.

In Hallock's article, he points out that in the untilted case, for a longer focal length lens, you get more focus spread, for the same near and far points in the scene. That means, using any of the methods based on focus spread (such as in the article) to choose the optimal f-stop will yield a smaller f-stop. In fact, in the untilted case, if you double the focal length, you will have to stop down four additional stops, at least if you keep the same criterion for sharpness. But if you double the focal length because you have gone from 4 x 5 to 8 x 10, you should also reduce the criterion for shaprness by half, which means you would end up only needing to stop down two additional f-stops, which is what I said above.

So how does that change in the tilted case, using points above and below the plane of exact focus to choose the optimal f-stop? I would have to go back and check explicitly what the calculations show, but I believe it works essentially the same way. Longer focal length lenses result in greater focus spread if you use the same upper and lower points. But if you also change format, you should change the criterion for shaprness. The net result should be that for the same scene, you would end up with an optimal f-stop about two stops smaller for 8 x 10 than for 4 x 5. The only posible complication is that there is a correction factor needed because of the tilt. If you tilt more, the correction factor has more of an effect, and as noted above, you do end up tilting more using the longer focal length lens with 8 x 10. My memory of how the calculations go is a bit hazy, but I think in either case, for practical situations, the correction factor can be safely ignored. But, as I said, I would have to go back and redo the calculations to be absolutely sure of that.

[Alan Davenport]

I am curious how lens tilt affects the optimum f-stop.

I haven't finished reading this month's Hallock article. Moving on anyhow...

Tilts allow you to customize where the plane of focus falls in the subject space.

Assume that you have a certain area in your scene which you need to be in excellent focus; i.e., everything in that area must fall with your DOF (as defined by the CoC.)

For discussion's sake, let's say you're worried about everything from the grass 10 feet away, out to some tall trees near infinity focus. Now let's say that, untilted, your focus spread is 10mm. IOW, you must rack the focus out 10mm from the infinity position in order to perfectly focus the grass at 10 feet. You could set the focus halfway between these points and have to use f/64 to get enough DOF.

By tilting the lens (or back, it makes no difference) you may be able to reduce the focus spread to only 2mm. Weirdly, when you have the lens at one extreme you see the grass and everything on the ground in perfect focus, and when you extend it 2mm further, the tops of the trees snap into focus. You set the focus midway between these extremes and, using Hansma's formula you find that you can use f/22.6.

With a smaller spread, you are able to use a larger aperture to get everthing into the DOF. Because the aperture is bigger, there is less diffraction, so the image is sharper. Referring to Hansma, note that this is an "optimum" f/stop, meaning "the f/stop that will produce the smallest circle of confusion over the area of importance." It's important to remember that this technique does not produce maximum depth of field; it lets you select the aperture that will give the best image quality over the range of distance that is critical to the photo.

[Leonard Evens]

What Alan says is very sensible, but I fear it may be possible to misunderstand it.

Let me emphasize once again. If you specify a near and far point, say where the initial focus spread untilted is 10 mm, then by tilting appropriately, it is possible to reduce the focus spread for those two points to ZERO. Not only is this possible in theory, it is possible in practice to within your ability to focus accurately. There is always a bit a play in setting focus which depends on the degree of magnification as when using a loupe and the mechanical gearing of the focusing mechanism, but I would be surprised if that were ever as great as 2 mm.

Once that is done, you worry about DOF above and below the plane of exact focus containing the original near and far points. That requires the choice of ADDITIONAL reference points above and below that plane and consideration of the focus spread between them. Then as Alan says, the focus spread between those points may be quite small, and a a result you can use a larger f-stop where diffraction is less of an issue. But this depends critically on the geometry of the desired DOF region. Roughly speaking, when you tilt, you gain DOF horizontally, but you lose it vertically, the loss being most severe near the lens. How these two factors balance out for the intended scene determines whether or not tilting is worth the effort.

In practice, the two different processes described above may not always be clearly separated, particularly if you have to do some iterations to get it just right. Also, often you may want to change just where the plane of exact focus goes by focusing between the high and low points, thereby departing from the original near and far points.. But it is important to keep the two issues firmly in mind or you will get throughly confused.

One further point. According to the Hansma/Hallock point of view, the optimal f-stop is that which gives you the f-stop which produces the smallest 'coc' (combining defocus and diffraction) at the limits of the desired DOF that you can obtain. It doesn't think of defocus as good and diffraction as bad, but considers them equally important. But, as Alan says, if the focus spread is smaller, then the optimal f-stop is will be wider, (also somewhat closer to what defocus alone would suggest) and you thereby gain in terms of being able to use a shorter exposure time. The other effect of smaller focus spread is that the actual optimal coc thereby obtained is smaller, which allows for greater enlargement before the image starts to deteriorate under close viewing

[John Kasaian]

I'm confused.

Say I've got a vista approx, 3 miles "deep" so do I focus on, say a rock 1 mile out?

Or do I use tilts to bring into focus on the foreground and horizon thats three miles out and fine focus on that rock 1 mile out? It sounds like a good experiment I'll have to try out to just see which produces the sharpest print.

Or am I missing something? I'm confused!

[Alan Davenport]

If you specify a near and far point, say where the initial focus spread untilted is 10 mm, then by tilting appropriately, it is possible to reduce the focus spread for those two points to ZERO.


Leonard, certainly that is true for any two points. In fact it is true for any given three points, since there is always a plane that contains any given three points. But unless everything in the scene is on that plane, it won't all be in perfect focus and there WILL be some focus spread. Case in point is my imaginary example with ground and trees behind. You can't have the ground in focus AND the tops of the trees, instead you would adjust the plane of focus to pass through the trees halfway to their tops, and stop down until the ground at the base of the trees, and the treetops, came into acceptable focus. Most landscapes aren't a single plane, so focus spread is the rule, not the exception...

[Alan Davenport]

If you specify a near and far point, say where the initial focus spread untilted is 10 mm, then by tilting appropriately, it is possible to reduce the focus spread for those two points to ZERO.


Leonard, certainly that is true for any two points. In fact it is true for any given three points, since there is always a plane that contains any given three points. But unless everything in the scene is on that plane, it won't all be in perfect focus and there WILL be some focus spread. Case in point is my imaginary example with grass in the foreground and trees behind. You can't have the ground all the way to the trees in focus AND the tops of the trees, instead you would adjust the plane of focus to pass through the trees halfway to their tops, and stop down until the ground at the base of the trees, and the treetops, came into acceptable focus. Most landscapes aren't a single plane, so focus spread is the rule, not the exception...

[Alan Davenport]

In fact it is true for any given three points, since there is always a plane that contains any given three points.
I guess I should qualify that. If the three points are on a plane that passes through the lens, you might not be able to tilt enough...

[Leonard Evens]

Alan,

Three points do determine a plane. And you can match many subject planes by an appropriate choice of both tilt and swing, but you can't necessarily do it with just a tilt. If you use just a tilt, you can be sure that the subject plane will intersect the film plane (assumed vertical here) in a horizontal line. In that case, two points will completely specify the subject plane. If there were a third point you wanted to be in that plane, either you would have to be lucky or else you would have to use a swing in addition to your tilt to get it there.

Your intuition that not every subject plane is possible is correct. For example, by tilting, you can't have the subject plane pass any closer vertically to the lens than the focal length, and in practice, it will be considerably further away than that. For example, for a 150 mm lens, with a 30 degree tilt, the distance of the subject plane below the lens is 300 mm. 30 degrees is, or course, an enormous tilt, much larger than you would use except in exceptional circumstances. For a more realistic 10 degree tilt, it would be about 864 mm.

With respect to your other point, let me suggest you go back and read carefully what I said. I think you will find we are saying the same thing. You have to remember that, ideally at least, there is one plane where the focus is exact. (In reality things are not that neat, of course, but it is close enough for all practical purposes.) That is going to be true whether you tilt or not. That means that all other points, not in that plane, are going to be out of focus to a greater or lesser degree. The object of selecting the proper f-stop is so that all points within some desired region of space will come into adequate, if not exact, focus. To do that, as I keep pointing out, you have to stop thinking about the original near and far point which are used just to choose the position of the plane of exact focus. You then have to do something else, namely consider points above and below that plane to determine the proper f-stop.

As I noted above, things may not be so simple, because you may want to go back and change the position of the exact plane of focus, either by just shifting the position of the standard or even by changing the tilt. Often it makes sense to start with the upper and lower limits of what you want in exact focus and then to try to position the exact plane of focus about halfway between them. You would then choose your near and far points to set the tilt with that in mind. But unless you separate in your mind the process of determining the tilt angle from the process of determining the f-stop, you are going to run into difficulties in doing either.

John,

I'm not sure just what you are asking, but let's suppose you want the near foreground and objects both 1 mile out and 3 miles out to be in focus. If by foregound, you typically mean something quite close to the lens, with anything but a wide angle lens, chances are you will need a tilt. Then you would choose your near point to be some specific point in the foreground close to the lens that you want in focus. With any lens you were likely to be using, it wouldn't matter if you chose for a far point something one mile out or three miles out, since both would be effectively at infinity. Optically, they could be considered to be at the same distance in the sense that in either case their images would be in exact focus basically at the focal lens distance from the lens.

On the other hand if you considered an analogous situation with more realistic distances, and you had a near point, a middle point and a more distant point you wanted in focus, you could choose either the point in the mid distance or in the far distance as your far point. Probably it would work better using the middle distance point. But in either case, you would choose your exact plane so that it passed through the desired two points and then select your f-stop so the third point came into focus when stopped down. In a situation like that you describe, you probably wouldn't have to stop down very far. Problems arise where there are additional points above and below the plane of exact focus which are quite close to the lens and which you want in focus.