### the relationship between DOF and diffraction

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I have a question about the relationship between DOF and diffraction. (cont'd from my last post "replacing shutter to stop down beyond f45 (240mm on 8x10)" Now, I am shooting 6 people, who are standing very closely each other in front of black seamless, in the studio using 8x10 with 165mm super angular lens. Because I want to make people just fit in the frame, the lens is very close to them. (about 30 in.) Then, to make everything in focus I think I have to stop down to f64 or even more. (Near distance 30in. Far distance 70in) Then, I'm going to make 30in x 40in and 40in X 60in prints from the neg. I'd like to ask you how noticeable and obvious the degree of diffraction is if I use f64 or smaller apeture and make large prints like this, because I have not noticed the soft and blur image caused by diffraction before, but I was wondering if I make the image look a little more sharper. I just didn't see the prints carefully. The diffraction affects whole image look softer, or a part of image? Anyway, I may have to sacrifice the DOF in order to obtain the prints which give me sharper impression. Thank you, Joe

-- joe (joe266@aol.com), January 05, 2001

Firstly. Do you really need to get that close? The perspective at 30 inches ain't gonna be very flattering.
There really is no relationship between diffraction and depth-of-field. They are completely separate. The only thing that links them is that they both increase as the lens is stopped down.
Diffraction affects the whole of the image, and is constant across the film plane. It is independent of lens focal length or format, and depends only on the f stop used. The recognised formula is that the size of the 'Airy disc' (the diffraction equivalent of circle of confusion) = 0.0007f mm, or alternatively, that the resolution in line pairs per millimetre is given by 1390/f. (This is only approximate, as diffraction varies with the colour of the light. Blue light will give less diffraction effect, and red light more.)
However, we can definitely say that in a theoretically perfect lens, the resolution degrades in proportion to f number. In the case of f/64, the maximum resolution acheivable will be only about 21 lppm.

Moving on to depth-of-field. DOF on film is solely dependent on the physical size of the lens aperture. A 150 mm lens at f/16 will give exactlty the same DOF as a 75mm lens at f/8, because the physical size of the 'hole' is the same.

Right. Working back from your intended print size, and saying that you need 5 lppm in the print for critical sharpness, it's easy to work out that a resolution on the negative of 30 lppm is desirable. This limits your aperture to (1390/30) ~ f/45.
If this isn't sufficient for your required DOF, then you'll just have to compromise on sharpness.

One final point. Remember that diffraction affects your enlarger lens too, and that the effective aperture number is multiplied by the magnification. In other words, an enlarging lens stopped down to f/8 with a 6 times enlargement, has an effective aperture of f/48 as far as diffraction is concerned. This means you should use your enlarging lens at f/5.6 if you don't want to degrade the sharpness further.

-- Pete Andrews (p.l.andrews@bham.ac.uk), January 05, 2001.

Doing the math on the above has brought home to me the fact that for modest print sizes, say up to 20"x16", where grain isn't really an issue, there is absolutely no advantage to using a format larger than 5x4. In fact, at greater print sizes, the only gain comes in less diffraction at the enlarging stage.

-- Pete Andrews (p.l.andrews@bham.ac.uk), January 05, 2001.

Crap! (I'll say it before anyone else does)
Forget that about the enlarger lens needing to be at f/5.6. Yes, the effective aperture is f/48 when the marked aperture is f/8, but of course the diffraction limited resolution of 30 odd lppm is at the paper, not the film.
This means that larger formats show no advantage until grain becomes apparent at about 8 or 9 diameters.

-- Pete Andrews (p.l.andrews@bham.ac.uk), January 05, 2001.

First, let me agree with Pete... the math shows that there is no "sharpness" advantage to larger formats for given print size... but the image is more than sharpness... tonality, grain matter alot. There is a nice whitepaper on this subject on photodo.com. That said, I shoot 6x9cm and print digitally up to 20x30 with results that are virtually identical to 4x5 even a ridiculously close viewing distances. At larger print sizes, the detail is technically the same (same number of pixels), there is a subtle advantage to the larger format. The pixels are "better". Since their numerical values result from a larger area of film, there is less noise and better tonal smoothness.

As for Joe's concerns, my recommendation is to stop worrying about the diffraction boogyman... the VERY slight softening of edges and reduction in absolute resolution caused by diffraction are going to be very subtle (unless you start using apertures like f/256!). Use the f-stop to get the DOF you need, period. Just don't stop down more than you need. I suspect the number of disappointing images from lack of DOF exceeds the number of disappointing images from diffraction effects by at least 100 to 1.

-- Glenn Kroeger (gkroeger@trinity.edu), January 05, 2001.

Glenn, the way I understand it, all lenses are pretty much diffraction limited at about F/22. My question is, are there certain lenses, or rather types of lenses that hold up better than others when stopped way down?

-- Steve Clark (agno3@eesc.com), January 05, 2001.

Steve: A great lens design cannot "beat" diffraction limits... however there are some aberrations that do not get better with smaller apertures, particularly some types of chromatic aberration. So a lens with a bad case of chromatic aberration will be worse than a lens well corrected for chromatic aberration at smaller stops. But by definition, when any lens becomes "diffraction limited" it means that diffraction outweighs other aberrations, so if two lenses at the same f-stop are both TRULY diffraction limited, their performance will be essentially equal.

-- Glenn Kroeger (gkroeger@trinity.edu), January 05, 2001.

To clarify, Glenn, suppose I have one lens which is an APO lens and another which suffers significant chromatic aberration. Let's consider, say, f45.

Won't the APO lens produce sharper results away from the point of critical focus due to the fact that the different color light rays in the non-APO lens diverge due to chromatic aberration? In other words, won't there be an "effective depth of field" which is superior for an APO lens?

-- lloyd chambers (photo@llc4.com), January 08, 2001.

If I can jump in and answer that last point.
For chromatic errors, the answer is no, the smaller difference between the in focus, and out of focus image 'blobs' will actually make the non-apo lens appear to have greater depth of field. In any case, chromatic aberration is unaffected by stopping down, so the specific aperture is fairly irrelevant.
The effect on DOF is greater with spherical aberration, which spreads the focus of a lens through several planes. The result of this, is that at wider apertures the apparent DOF of a lens suffering from spherical aberration does not change as much as expected when stopped down. Again, the lens suffering from aberration will appear to have greater DOF than a better corrected one.
All these effects are pretty much only of academic interest to the large format user, where lens aberrations have to be very undercorrected to affect the image to a noticeable extent.

-- Pete Andrews (p.l.andrews@bham.ac.uk), January 11, 2001.

It is incorrect to make a statement like "f22 is the upper limit for diffraction," etc. Why? Because, just like DOF, diffraction is dependent on the PHYSICAL SIZE of the aperture hole, not the f number. F22, on a 35mm lens, is significantly smaller in diameter than f22 on a 150mm lens. Thus, f22 with the shorter lens will produce more diffraction.

-- Josh Slocum (jayslc@yahoo.com), January 12, 2001.

Actually, in photography, it IS correct to say that diffraction only depends on f stop. Diffraction IS a function of the physical size of the aperture. However, diffraction patterns are angular patterns and are thus also a function of how far the aperture is from the screen used to view the diffraction pattern (i.e., the film). Note that a shorter lens is closer to the film than a longer lens. So even though the shorter lens has a smaller physical size of the aperture (greater diffraction), it is closer to the film and the diffraction pattern spreads less than it would with a longer lens which is further away from the film. So, in photography, it is absolutely accurate to say that the diffraction pattern is determined only by the f stop. Cheers, DJ.

-- N Dhananjay (ndhanu@umich.edu), January 12, 2001.