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