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  1. #1
    gainer's Avatar
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    F/64 is where its at.

    F/64 is Where It's At

    I have noticed that the older I get, the more likely I am to remember things from long past and forget things from 10 minutes ago. While I was reminiscing, I happened upon some memory waves, no doubt put there by a Large Format Pictorial Photographer I knew about fifty years ago. Those waves said "F/64 is where it's at." Along with those waves came some others saying that 4 mm is always the optimum lens opening. Is it possible?
    Such rules of thumb are, as often as not, discovered through experience. The user of an 8X10 view camera sooner or later finds a comfort zone, a sweet spot in the iris where things come together. Is there a reason why the comfort zone for, say, a 5X7 or a 4X5 should be the same, in terms of the diameter of the pupil, as the 8X10 or the 11X14? The statement "4 mm is always optimum." implies that to be so.
    I got out my ancient copy of Hardy & Perrin, "The Principles of Optics" and rediscovered these interesting facts: the resolving power of the human eye increases to a maximum of about 1 arc minute as the pupillary diameter increases to about 2 mm. Up to that point the system is mostly diffraction limited. Coarseness of the retina then controls and resolution stays constant as pupil diameter increases to the maximum of about 5.5 mm. Thus, about the only thing the human visual sense gains by opening wider than 2 mm is a brighter image.
    In most optical systems the resolution depends upon the diameter of the entrance pupil of the system and the wavelength of the observed light. The larger the diameter, the smaller the angle that can be resolved between two points of light. An equation describing this relation is:

    alpha = 1.22 lambda/D
    where alpha is the angle between two just-resolved points of light, lambda is the wavelength of the light and D is the diameter of the entrance pupil.

    Look at a scene you would like to record. What would it take to create a photographic image that contains as much detail as can be resolved by your eye? Strangely enough, the entrance pupil of whatever camera you use should be at least as large as that of your eye in order to capture the angular resolution you see. Our photo ought to have all the detail we see in the original scene if the camera lens had only a 2 mm entrance pupil.
    The problem is that when we look at the photo we are not seeing the original scene, but a copy whose information content has already been attenuated by the camera's lens, and perhaps again by the lens of an enlarger. Knowing that the angular resolution of the lens is inverseley proportional to the diameter of its entrance pupil, we might propose doubling the pupil to 4 mm to make up for the loss in the photographic process.
    You will have noticed that I have not taken into account the focal length of the camera's lens. It does not appear in the equation for resolving power. According to that equation, every well-made lens of, say, 4 mm entrance pupil should have the same angular resolution. In visible light it should resolve two point sources 0.5 arc minutes apart, which is twice as good as the average human eye.
    The maximum size is set by depth of field, or perhaps by lens abberrations. There is not much point in a pupil greater than 5 mm unless for the sake of illumination or artistic effects such as selective focus.
    It begins to look as if the diameter of the entrance pupil of the camera is going to wind up somewhere between 2 and 5 mm. If I use 4 mm as a rule of thumb, the resolving power of the camera lens will be made to be 0.5 minutes of arc. Angular resolution is non-dimensional, thus independent of focal length. Diameter of the aperture alone affects maximum resolving power.
    A 4 mm aperture is f/76 for a 12 inch lens, f/38 for a 6 inch lens, f/12.5 for a 50 mm lens, and so on. All would be expected to resolve 1/2 arc minute, and about 24, 48 and 136 lpm respectively.
    What if the lens is not so good? Well, you may improve its chromatism, astigmatism, etc. by stopping it down more, but not its resolution. The objective of this game is to get a photograph that matches the resolving power of your eye even when you view it from closer than the proper perspective point. Stopping down more is not going to do that. Higher resolving power requires greater entrance pupil diameter, not lesser. On the other hand, how bad can a reasonably priced lens be at 5 mm? I have seen some very fine rapid rectilinear lenses.

    If this little paper does not stir something up, I'll be disappointed.

  2. #2
    Sean's Avatar
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    comments from the previous article system:

    By Markok765 - 07:38 AM, 09-03-2006 Rating: None
    what would be the optimum apeture for a 50, 35mm, 105mm ect? ive heard 3 stops from wide open

    By L Gebhardt - 05:25 PM, 09-03-2006 Rating: None
    I like the though of that sort of simplistic rule. In large format that seems to hold true from my experience. On the 90mm lens things seem to go down hill past f/22. On the 135mm it is around f/32. On the 300mm I try not to go above f/45 - maybe I should extend that to f/64.
    However my Mamiya 7 65mm lens produces very sharp looking images all the way upto f/22. They seem (I have not measured it) much sharper than the LF images. So for large format that rule of thumb may work well, but not for all.

    By phfitz - 02:03 AM, 09-04-2006 Rating: None
    Running the numbers with CoC at f/1720, that would make the hyper-focal point for any lens with a 4mm iris approx. 23ft, so anything from 12ft to inf. should be in sharp focus. Getting down to this small should be a waterhouse stop, I think an iris would create diffusion from the little jaggies. I think I will try this tomorrow and see what it does. Thanks for the thought.

    By gainer - 03:18 AM, 09-04-2006 Rating: None
    What I dealt with here was really what is called diffraction limiting. The f-stop, as you see from the equation, is not the "magic number". It is used with the focal length to set the f-stop that gives the maximum depth of field obtainable with the maximum resolution comparable to the eye. The 4 mm diameter is fairly well universal for cameras from 35 mm to 8 x 10. Rules of thumb such as 2 0r 3 stops down from wide open may or may not work. As you stop down, you will actually lose resolution, though you may improve chromatic abberation.
    For most of us, it is usually an academic excercise, but it is an interesting one. It was especially fun for me to find that the true limit of resolution is that of diffraction, which has little to do with focal length or f-stop as such. I have known that limit for more years than I like to admit, but have not considered it in exactly this way.
    4 mm turns out to be f/12.5 for a 50 mm f. l., f/22.5 for 90 mm, f/26.5 for 105 mm. Just divide the focal length by 4.

    By gainer - 04:07 PM, 09-04-2006 Rating: None
    The Mamiya 65 mm lens at 22 is still at about 3 mm which gives it potentially more resolution than the average eye. It would be interesting to compare f/22 with f/16 on consecutive frames.
    Belay what I said about chromatic aberration. I need to read some more. There are two kinds IIRC, and one is affected by stopping down.

    By commiecam - 10:28 PM, 09-04-2006 Rating: None
    Personally, I have tested a number of lenses from my long-gone Minolta SRT system,
    my Zeiss Ikoflex IIa and Rollei 3.5, and two Yashica MAT124 G's. as well as all of the lenses from my Braun Super Paxette system. Almost without exception they were sharpest at f/5.6 to f/8 or f/11,but most usually at f/5.6 qand 8 being just about even. This, for most of the lenses, was two stops to three stops from wise open. I never tested my 15cm f/4.5 Xenar or Symmar, but I did test the 9CM f/6.8 Angulon, and it was sharpest at f/11 or 16. As I read it, the diffraction effects are proportional to the circumfrence of the aperture while the resolving power is area related, thus there
    might be a square-law problem, i.e., the smaller the aperture the greater the portion of
    the image's forming energy that has been formed by light which has been diffracted
    by the aperture's edge.
    Suffice to say that all the testing (on Tech Pan developed in Delagi-8 or highly modified Leica Divided Developer to normal CI's) led me to believe that most lens designers are careful to make sure that all major and most minor aberrations are
    pretty well gone before diffraction effects become a major factor in resolution.
    Strangely, in almost every case, the diaphragm's aperture is in the neighborhood of 8mm to 10mm in diameter! Hmmmm....
    Now that I have an 8x10, I have not even bothered to do any further testing. I am using LOMO 300mm and 480mm f/10 graphic arts repro lenses with a Packard shutter. I am usually shooting at f/22 to f/45 (or f/64 with long lenses) and the results are excellent. Though it is not a scientific test, using the 480mm negative (J&C Pro-100, their cheapest film) scanned at 1200dpi on my Epson 4870 scanner with no enhancement, I can read clearly both the large and small print in both streetnames on a corner street sign that is 1800 feet away. The image is still sharp and I cannot see grain yet, so I suspect the limiting factor is the scan resolution and not the film resolution.
    What's the aperture diameter? 300mm at f/22 to f/45 is 15mm to 9mm, 480mm at f/32 to f/64 is 15mm to 7mm. Good enough for me.
    Regards, Ed Lukacs

    By commiecam - 10:32 PM, 09-04-2006 Rating: None
    300mm at f/22 to f/45 is 15mm to 6.5mm, 480mm at f/32 to f/64 is 15mm to 7mm.
    Sorry... Ed
    By phfitz - 12:18 AM, 09-05-2006 Rating: None
    Hi there,
    Just tried this with a knife-edged 4mm waterhouse stop, 1920's B&L 8x10 Tessar (305mm), 8x10 Berrger 200, divided D76. What I can see:
    1) Kodak's old formula for depth of field (2 min. of arc, f/1720) is rather accurate. It does start a very smooth fade to soft from about 12ft and closer.
    2) don't see any diffaction affects, lose of sharpness, but an f/90 exposure does involve the wind. More than sharp enough for contact prints.
    3) it's really hard to focus stopped down this far.;-)
    I have a few other lenses that take waterhouse stops and will continue playing with this. Think of an 8x10 Hobo style Ansel Adams point-and-shot, with reversible lens cone for easier storage. Fixed focus, fixed f/stop, light weight and unbrakable. Just have nothing in the picture within 15 feet of the camera (where have I seen that before???).

    By gainer - 03:35 AM, 09-05-2006 Rating: None
    Ed, I don't quite fathom your distinction between diffraction and resolution. Diffraction is one of the factors effecting resolution. There are different measures of resolving power. The most general perhaps is angular units, usually minutes of arc. Diffraction is the primary factor in resolving power of astronomical telescopes, where the angular separation between images of two stars is the important factor.
    The criterion I was looking for was angular resolving power greater than that of the eye, but not necessarilly the maximum. When the purpose is to produce a photo that has only twice as much resolving power as the eye, there is nothing to say you must stop there except the requirement for a certain depth of field. Certainly, sharpness can be made greater if you are photographing a flat field.
    So, the question is not "Where is it sharpest?" but "Where is it it that the unaided eye first percieves lack of sharpness" as one stops down?

    By MichaelBriggs - 03:10 AM, 09-06-2006 Rating: None
    I don't the analysis of terms of angular resolving power of the original scene is the best approach. What we care about is what the print looks like. Sometimes a sharp looking print will show more than could have been seen with the unaided eye, sometimes less. What matters on the print re sharpness is the linear size of the blurring caused by any effect, diffraction, aberrations, out of focus, etc. -- if the blur is large enough in linear size, the eye will see it. It doesn't matter whether the detail could have been seen by the unaided eye in the original scene -- the print is what matters. The angular size in the original scene isn't pertinant. A print made from a negative taken with a long lens will cover a smaller angular field of the scene, and to have the same linear resolution as a print made with a short lens, will need a higher angular resolution. Yes, the basic equation for angular diffraction doesn't use the focal length of the lens. But when you make the next step to calculate the linear size of the blur on the film, then the focal length enters the equation, and diffraction becomes a function of f-number.
    The other factor not considered is the amount of enlargement from negative to print. f64 is a reasonable aperture for formats that will be contact printed, but will typically be non-optimum in a smaller format (to a greater extent the smaller the format). This is assuming that one is comparing same size prints -- the smaller format will require a greater enlargement from negative to print, and so, to achieve the same linear blur size from diffraction on the print, will need less diffraction on the film, and hence a smaller f-number.

  3. #3
    Sean's Avatar
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    By gainer - 05:07 AM, 09-07-2006 Rating: None
    Sorry, but that is not correct. The unaided eye will not see with angular resolution greater than 1 minute of arc. Now, if you make a print and enlarge it so that it is to be viewed inside the normal perspective point of the lens with which it was taken, that is a different question, but it can be approached in the same manner. Such a picture is distorted in a way, but if you know ahead what you want to do, you can use the diffraction equation, along with a little logic, to figure out how to do it. When the problem involves maximizing depth of field, setting exposure time and obtaining adequate resolution for an effective print, it is certain that the focal length of the taking lens will enter into the calculations. If there is no depth of field requirement, you may, and should, open the lens to its point of best resolution. If you know that the print is going to require the viewer's eye to be closer than normal (what I called "grain sniffing" distance) by some factor, then you can multiply the normal resolution by the same factor to get the minimum diameter that will give the desired resolution for a sharp-looking print, as you notice I used 4 mm instead of the 2 mm that would have matched the acuity of the unaided human eye. If I used a 90 mm lens on 35 mm, the normal viewing distance of a contact print for correct perspective would be 90 mm. Enlarging the negative by, say 10X would increase the proper viewing distance to 900 mm, or about a yard. The proper viewing distance for a shot from a 50 mm neg would be about 20 inches.
    If you stop down the lens to get the needed depth of field, you may find the definition in the print to be fuzzy. If you open it up to make it sharp, you may lose the depth.
    The equations you need are the one I gave for diffraction and the one for depth of field. If you plan to set depth of field visually, you will have to use a pretty good focusing magnifier. Will you be able to see the onset of both fuzz and loss of depth? I guess we have been doing it for well over a century. As I said, this is largely an academic exercise which I undertook to see if it could really be true what someone told me, that the apertuere was going to wind up at 4 mm anyway.
    We agree, I think, that we want the angular resolution to be greater than the average human eye, which is 1 minute of arc. Whatever lens we use to take the picture will have about that resolution at an aperture of 2 mm, regardless of its focal length. In order to increase that resolution to allow for an enlarging lens or the tendency of some viewers to move inside the point of correct perspective we must open the lens. Opening the lens decreases depth of field. Closing the lens decreases sharpness in the print. It is a trade-off.

    By MichaelBriggs - 05:47 AM, 09-08-2006 Rating: None
    It seems that the difference between our analyses is that you are assuming that people view prints at their centers of perspectives. Step 1: angular diffraction is proportional to lambda / D. Step 2: linear diffraction on the film is step 1 multiplied by the focal length of the taking lens. Step 3: linear diffraction on the print is increased, compared to the film, by the enlargement factor, if not a contact print. Step 4: if the prints are viewed at the center of perspective, so that the viewing distance is proportional to the focal length of the taking lens, then we divide by the focal length again, and the factor of step 2 cancels -- the focal length doesn't enter the prediction of the effects of diffraction. But I don't think people actually view prints this way -- how many people adjust their distance from prints based on the focal length of the taking lens? People typically view smaller prints at approximately reading distance, and larger prints at approximately their diagonal. (Many photographers will examine all prints closely.) So I don't think that Step 4 reflects actual practice, which leaves us at Step 3, with the predicted diffraction proportional to taking lens focal length divided by aperture diameter, i.e., f-number.

    By gainer - 04:28 PM, 09-08-2006 Rating: None
    I didn't assume anything about how people view pictures, but I did assume that photographers like their pictures to be viewed as they saw them. That is all you can plan for. When you get out your monocle and get close, you are looking for something other than pictorial quality.
    If you look closely, I gave values of lines/millimeter for various focal lengths used with a 4 mm aperture. These are maximum values for that aperture for the middle of the visible wavelengths. They can be less due to lens properties.
    The focal length always enters the prediction of the effects of diffraction on the photo, but not by changing the angular resolution of the lens. Certainly, the linear distance between two resolvable points in the plain of focus depends on the distance from lens to the plain of focus, but the angle between them does not. The telescope at Palomar can see the elements of a star cluster that my 1 inch lens only sees as a single star. No matter how close I get to what I'm looking at, the parts of it I can see as separate parts are at least 1 minute of arc apart.
    I'm beginning to think you only read the title of my article. F/64 only happens to be the "sweet spot" for 8X10 according to the F/64 Club. 4 mm aperture is a pretty good place to start for any camera we're likely to use, because it is twice as good as the human eye. If you have a good lens and a small depth of field to cover, you can open up for a sharper photo, but your unaided eye will be unalbe to tell it. The normal reading distance is usually 10 to 12 inches. Two points separated by 1 minute of arc at 12 inches distance will be about 0.003 inches apart. That is about 0.08 mm. That is about 12 lines/mm. If I get twice as close, I can see 24 lines per mm, but I will need a magnifier to see if those are separate lines if my unaided vision is 20/20.

    By Gene_Laughter - 01:50 AM, 09-13-2006 Rating: None
    I don't need measurements to determine if I like the artistic merits of an image. Give me emotion, feeling, atmosphere and beauty - not scientific yardsticks.

    By gainer - 02:42 AM, 09-13-2006 Rating: None
    Surely, Gene, you don't need your measurementd but you need somobody's or you wouldn't have the chisels or the paper or the canvas or the film. You would have to express it all with whatever you find lying around. I admit, some of the cave dwellers were very expressive, but wouldn't you rather have our cameras, films, developers and other things that scientific yardsticks can facilitate?

    By jstraw - 08:20 PM, 09-15-2006 Rating: None
    If the 4mm aperture for a 210mm lens is f-52.5 and the lens only stops down to f-45 does that mean that the aperture is 4.66mm and what are the implications for resolution at 4.66mm?



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