You need to do a systematic series of exposures to verify which combination of f/stop and hyperfocal setting maximizes your DOF at infinity focus. Find a repeatable scene that has objects in the near ground, mid ground, far ground, and everything in between to work with.

The hyperfocal setting depends on the circle of confusion number that you choose. The markings on prime lens barrels are usually based on an overly optimistic COC. Most experienced photographers will use an f/stop setting one or two stops more conservative than that indicated on the lens barrel.

After much experimentation and theorizing, my own approach - based on some work by Merklinger - is rather different. I have found that for my 35mm system f/11 gives me the best compromise between DOF and diffraction loss. I mostly use f/11 and set my plane of focus to the plane of the most important element of the composition.

Frank,
It's good to see someone giving such a thorough exposition of a topic. Now who needs to know more about hyperfocal focusing?

But I would like to add to your reference to Rayleigh's formula for calculating maximum resolution at a given f stop. 1500/16 = 93 lp/mm. That's damned good! However, it needs to be said that those 90 or so line pairs are close to the threshold of visibility. They've lost 90% or more of their contrast. (According to Norman Koren, they're at 9% MTF).

For a long time, I've refused to use F11 and F16 with 35mm (being a bit resolution obsessed). However, I'm beginning to change my opinion on this. In some circumstances, with some 35mm lenses, I find that resolution at f16 is hardly distinguishable from resolution at f8 (I'm using a D60). And of course, there's a huge DoF advantage at F16 as opposed to F8. For me, f22 is the point where things become decidedly fuzzy.

If the circle of confusion is in your head now  :D you could do what I do:

I set the lens on the hyperfocal distance I want (say at 6 meters for sharpness from 3 meters to infinity), I read what aperture the scale says, say f16.

Then I set the aperture to f22 (for the Rollei I use, one stop is enough) and I am pretty sure everything is within the zone of sharpness.

Hope this will help you as well,

Wim

Agreed! This is probably why a 1.4x converter on my 100-400 zoom focussed at infinity serves no purpose. There's nothing reaching the lens that's beyond the Nyquist limit of the sensor. Dust, water vapour and the general distortion of the atmosphere is filtering or blocking the very fine detail. However, train the lens on a test chart 20 or 30 metres away and the superior resolving power of the lens plus converter becomes very apparent.



Agreed again, but whether or not we see much more than 40 lp/mm depends on the size of the print, doesn't it? Erwin Puts would no doubt have laughed at the idea of making a 22"x33" print from 35mm, but that's the same degree of enlargement as a Super A3 size print from the D60's 22mmx15mm sensor.

I've recently been using my Canon 50mm F1.8 as a portrait lens (on the D60 it's 80mm). With a Speedlite 220EX in conjunction with a Metz 45 CL-1, I've been able to take fully exposed head and shoulder portraits at F8 and 180th sec, indoors. I'm amazed at the clarity of individual strands of hair on some of the 13"x19" enlargements on Epson Premium Gloss. In fact, I had an uncanny experience whilst gazing at one particular enlargement of a lady with flowing, platinum blonde hair. It appeared for a fleeting moment there was hair lying on the surface of the print, fallen from my own head or wherever. I reached out to brush it away and realised it was part of the image. (No, I definitely wasn't drunk.)

40 lp/mm on the sensor translates to less than 2 lp/mm on a 22x enlargement. These prints look a lot sharper than that. When I get back to my studio, I'll see if I can measure the width of some of these individual strands of hair. (I've never tried doing something like this before. I suppose the best way would be to make a much bigger enlargement from a small crop so I can take a ruler to it.)

I have been trying to use hyperfocal focusing to achieve maximum depth of field in landscape photography with my Pentax 645N and 67II. I have been placing the infinity focus mark on the lens barrel at the F stop in use, utilizing a tripod and activating the self timer to release the shutter. I have noticed that when I enlarge and print my negatives to 16X20 the backround detail is not in sharp focus but rather soft. Has anybody had this experience. My thoughts concerning this problem include the possibility of stopping down too far (F 16 and 22) where the les resolution may not be at its best or perhaps not utilizing the hyperfocal focusing technique properly. Please help!

The standard DOF scales were determined before World War II and were decreed as being the best resolution available at the time on a print from the newly developed 35 mm camera. This was 4 lp/mm on a print (see below) or 33 lp/mm on the 35 mm film and to date the standard has not been changed. So, if you use the DOF scales on your camera lens you are limiting yourself to DOF available with 1930’s equipment and you will be disappointed. If you don’t believe me read Camera Lens News #2 (1997) on the Ziess (Germany) web site.

Required DOF is determined by the print and the viewing distance and I will assume that your 16 x 20 prints will be viewed at the standard distance of approximately one major dimension (20”). I am not sure how familiar you are with optics but this is an optical problem and optical resolution is measured in line pairs per mm (lp/mm) and this is half the number of pixels per mm if you refer to digital systems.

It has been well established that the human eye with 20-20 vision can resolve objects with 1 minute of arc which is 7 lp/mm (actually 6.88) or 14 pixels/mm at 250 mm (10”). Typically an adult can resolve around 5 to 6 lp/mm on a print at 250 mm (this equates to 254 to 305 dpi on the printer) and 2.5 to 3 lp/mm at a viewing distance of 20”. The magnification from say your 67 camera to the 20” print is 20x2.54/7=7.3 and so if we say we want 3 lp/mm on the print this equates to 3 x 7.3=22 lp/mm on the film (assuming no enlarging or scanning losses in resolution) and 40 lp/mm should be achievable on the film, so the resolution requirement is acceptable.

Lp/mm is related to the circle of confusion or the size of an out of focus dot and the size of this dot is 1/lp/mm and for 22 lp/mm this is 0.05 mm and so the smallest dot that we can have on the film to look like it is in focus on the print is 0.05 mm (0.002”).

The limiting factor setting DOF is not the distance (as shown on the lens scales) but the f-stop and this is why the lens manufacturers show the f-stop as well as the distance on the DOF scales, so the main thing we need to be concerned with is the aperture. The diffraction limit for any lens using white light is set by the approximate relationship 1500/f-stop in lp/mm and so f10 has a diffraction limit of 150 lp/mm, but you do not have to calculate this but you need to realise that for current film and lens technology and for optimum resolution, you should not stop down a 35 mm camera more than f8, or f11 to f16 for medium format or f16 to f22 for a 4x5 otherwise the sharpness of the photograph will be diffraction limited.

For those comfortable with math and who have the time, you can calculate everything out, however for those without the time (or can’t be bothered with the math), there are some simple rules of thumb based on the Merklinger approach. When you take a photograph, decide what is the closest thing that you want to resolve in the picture and estimate it’s size. Then stop down the lens to the aperture you are thinking of using and if the object you want to resolve is larger than the aperture then focus on infinity and take the shot or you change the aperture to suit provided you stay in the diffraction limits. If the object you want to resolve is smaller than the stopped down aperture size you will need to focus between infinity and the object.

In this case use the focusing ring on the camera (or a range finder if you have one) to estimate the distance of the nearest and farthest objects of equal size that you want to resolve (say a 5 mm (0.2”) twig in the foreground and a 5 mm (0.2”) crack in a door in the background). Now determine the distance between the objects from these estimates and the focus distance will be half way between the two objects. For example say the distance to the twig is 50 m and to the crack in the door is 150 m so the distance between them is 100 m and the focus distance is 50 + 100/2 = 100 m.

To determine the f-stop required you will need to ratio the sizes and the distances. Some people believe that long focal lenses have narrow depth of field and therefore DOF has something to do with focal length This is not true, DOF relates only to the aperture and the magnification ratio for otherwise optically identical lenses of different focal lengths. Consequently, with identical f-stops and with all other things being equal a 50 mm lens focused at 5 m has the same DOF as a 500 mm lens focused at 50 m, because the magnification ratios and the f-stops are the same.

Since the sizes of the objects in the example are the same, whatever is worked out for the front object will also be true for the far object. Hence the ratio of the twig to its distance is 5/50 = 0.1 and consequently the ratio of the focus distance to the aperture size must be the same and so the lens aperture must be: focus distance x 0.1 = 100 x 0.1 = 10 mm (in this case it does not matter if we mix m and mm). All that is necessary now is set the lens to an aperture of 10 mm, take a light reading, adjust the shutter speed, compose and take the shot.

In this example, if you are using a 50 mm lens then the f-stop will be 50/5 = f5 (say 4.5), which may not be at least two stops down from fully open. If you used a 100 mm lens the f-stop would be 100/10 = f10 and setting the lens at f8 for 35 mm would be perfect. For medium format if you used an 80 mm lens the f-stop would be 80/10 = f8, which is okay but for a 160 mm lens the f-stop would be 160/10 = f16 which is probably a bit better for 6x7. if you used a 500 mm lens then the f-stop would be 500/10 = f50, which would be well and truly diffraction limited to apply to a 35 mm film size and so you would not use this lens.

This consideration is only optical and not aesthetic and so you would have to use all your normal judgements and procedures. This procedure will give you much better results than DOF lens scales or tables and is about the best you will do with a camera that has fixed lens and film planes. It is not as complicated as it appears and once you get used to it, it will become second nature and you will hardly have to think about it. I have used a Linhof 617 for some time and it has no range finder and no way to look through the lens, consequently you are forced to use techniques such as these to get decent shots with anything in the foreground.

If you are a perfectionist and want to have better sharpness than this gives you, then I suggest that you buy a view camera and the possibilities of photography will open up to you. Just ask Alain Briot or read his “The Agony And The Ecstasy” article on Michaels web site.

This is the best I can do in a relatively small space and I hope it helps.

To play with different values for your acceptable circle of confusion, try Bob Atkins site, http://bobatkins.com/photography/technical/dofcalc.html

There you can select different COF values (by selecting different film formats) to see how much the hyperfocal distance changes as you beocme more exacting in your COF standards.

By the way, film accuity for the 35mm lens DOF marks was based on film similar to Tri-X (EI400), now known for its grain.

Another DOF calculator: http://dfleming.ameranet.com/dofjs.html

Yet another: http://www.dudak.baka.com/dofcalc.html

Ray,

I agree with you and Norman Koren that the Rayleigh diffraction limit has an implied contrast transmission of 9% and that this is difficult to see with the human eye. The 50% contrast transmission suggested by Norman Koren is something I also agree with and I generally use this in practical optical considerations. I was trying to keep things non-complicated in my submitted comments to make suggestions to someone that I did not know and to keep the note as short as feasible.

The ideas of Erwin Puts of Leica fame are very interesting and the thought that we cannot normally see anything larger than 40 lp/mm in typical enlargements has interesting implications. The key implication is simple but not instantly apparent and that is that the camera never uses the high resolution unless it has to. That is unless we are trying to resolve things that are small enough, we don’t need or utilise the resolution. Consequently in photographing a mountain in the background we only need say 5 or 10 lp/mm and hence we get a high contrast image, but if we want extreme detail in the mountain then we need higher resolution and we get less contrast. Consequently, we rarely need anything greater than 40 lp/mm unless we are doing close up work. This is why I was suggesting that considering the object size is very important when deciding the aperture.

In regards to your comment about f16. There is nothing that say’s you shouldn’t use f16 unless the object detail you want is smaller than the aperture. If it is smaller then Uncle Rayleigh and Mother Nature is going to stomp all over our lens and film/sensor MTF curves just to show you who’s Boss. I use f16 often and even f45 on my 4x5 it depends on what I am trying to resolve as to whether I use it or not.

I have used a D60 and currently a 1Ds at f16 quite often, and with good results, the only problem I had was with some night “City Lights” shots at 60 seconds exposure and I had to open up to f8 to get the lights pin sharp (luckily I bracketed f-stop on this occasion as well as time).

I have never bought into the digital/film debate because I have not got a certain explanation for the observed facts. I do know that in my experience the D60 and 1Ds blows 35 mm transparency off the planet in regards to enlargement quality and all that this entails.

The 1Ds has a rounded up 114 pixels/mm or a theoretical 57 lp/mm (maybe less depending on where the test target lines fall on the sensor) and Velvia is rated by Fuji at 80 lp/mm at 1.6:1. In my view, the reason for the quality (if not specification) difference in favour of the 1Ds has to do with the Signal to Noise Ratio of the CMOS sensor. I have no definitive evidence except my eye’s, but I think that the SNR of the CMOS is so low that this provides a much higher contrast than Velvia at a slightly lower resolution and if we cannot see much more than 40 lp/mm (Erwin Puts), we sure can see the higher contrast and hence the picture appears to have a much higher detail. For example the MTF curve for Velvia shows a contrast of around 60% at 40 lp/mm and I think the percentage contrast transmission of the 1Ds CMOS must be in the high 80’s or 90’s, or maybe more.

When I first got the 1Ds I tried shooting a resolution target and then realised that nothing over 50 lp/mm could be resolved because of the pixel spacing and decided that this was an unfair test. So I photographed something normal that the CMOS could resolve and this was a steel ruler and I kept on interpolating it upwards in size. Without going through all the detail my first print was such that a 1 mm division measured 0.77 mm (1 cm measured 7.7 mm) and I abandoned the test when a 1 mm division measured 85 mm. Without a densitometer I would estimate that the contrast was at least still 80% and the image was still clear, although the edges were a little fuzzy. This is a final print to CMOS size enlargement of 125 (equivalent to a 118” x 177” 35 mm transparency enlargement). The pixel pitch on the 1Ds is 0.009 mm and I do not know the size of the pixels but if the pixels are half of the pitch then they are 0.0045 mm but I would guess that they are in the order of 0.006 mm with 0.003 between the pixels. If this is the case then on the print each pixel was 0.75 mm wide and although the edge was fuzzy the contrast was amazing being about 4 pixels wide from very light grey to absolute black and no film is going to match that at 125X. So the noise level in the signal must be exceptionally low to maintain the contrast over such a magnification. Even though the edge contrast was about 4 pixels wide, this could be due to light scattering and chromatic aberration just as much as a CMOS limitation, that’s why I gave up and besides I proved that the camera is good and can be blown up by a considerable amount. I would think from this that the equivalent of the MTF of the 1Ds sensor would be like a Leica Summicron M 2/90 ASPH lens; a horizontal straight line.

Anyway, I think the jury is still out on the reason on why the Canon CMOS sensors are so good, unless Canon comes forth and tells us. Maybe the Nikon ones are great too, I don’t know, I have not used Nikon digitals since the 990 days.

Again all this is pointing out is that contrast in the image is just as important as resolution as you point out. Ahhhh, if only Santa would bring me a 4” x 5”, full size 1Ds grade CMOS sensor for my Ebony 45 view camera. Then I could really produce some serious print sizes with serious resolution and DoF. Maybe Alain Briot would go digital then.

Dream on.