Numbers, F-Stops, and Good Pictures

By David Vestal Back to

Before f-stops, there was a consistent set of lens aperture numbers, the Uniform System. Its lens openings were US settings. As you stopped down, each US lens opening had half the speed of the one before it. But that system left no place for openings larger than ƒ/4. The ICP Encyclopedia of Photography gives the US system’s equivalents to f-stops as follows: US 1=ƒ/4;US2=ƒ/5.6;US4=ƒ/8;US8=ƒ/11;US16=ƒ/16; US 32 = ƒ/22; US 64 = ƒ/45(?); US 128 = ƒ/90(?); US 256 = ƒ/90(?!); US 512 = ƒ/128(?). Something fishy there. The encyclopedia is wrong. Those are typos and/or errors of calculation. It skips ƒ/32 and ƒ/64 and says that both US 128 and US 256 are equal to ƒ/90. I suppose it meant to say,“US64=ƒ/32;US128=ƒ/45;US256= ƒ/64; and US 512 = ƒ/90, and so on. I’m not sure. But not many lenses marked in US numbers can still be in use, so let’s not worry.

Let’s look at f-numbers: each represents an opening whose diameter is a corresponding fraction of the lens’s focal length (which in turn is roughly the distance from the diaphragm to the film plane with the lens focused at infinity). Thus in a 50mm lens, ƒ/8 = 1⁄8 the lens-to-film distance or 6.25mm, and ƒ/2 = half of 50mm, or 25mm in diameter, and so on. ƒ/16 is half the size of ƒ/8 because they are really 1⁄16 and 1⁄8. Each stop’s number is approximately 1.4× the next larger opening’s num- ber. 1.4 is also close to the square root of 2, which is 1.41421356237, according to my calculator.

Here’s a table, multiplying each result by 1.4:

If each whole f-number is considered true and multiplied by 1.4 we get:

My first cheap-but-good camera was a Foth Derby, half- vest-pocket size. It took 127 film and made 16 exposures to a roll when you wound to the next number in the little red window on the camera back. It had a decent 50mm ƒ/3.5 lens, and its stops were marked ƒ/3.5, ƒ/4.5, ƒ/6.3, ƒ/9, ƒ/12.5, and ƒ/18. That was another standard f-stop series. With only one whole f-number, how would you figure it? Multiplying by 1.4, rounding to one decimal place, and starting from the largest opening, we get ƒ/3.5, ƒ/4.9, ƒ/6.9, ƒ/9.6, ƒ/13.4 and ƒ/18.8. Dividing by 1.4 from the smallest opening, etc., we get ƒ/3.3, ƒ/4.7, ƒ/6.6, ƒ/9.2, ƒ/12.8 and ƒ/18. We have it surrounded, even if it’s not exactly as marked.

Shutter speeds

The late Bob Schwalberg, a technical stickler, told me that a Foth Derby he’d tested had remarkably accurate shutter speeds. On mine they were marked 25, 50, 100, 200 and 500. Or was it 250 instead of 200? It had no slower speeds than 1⁄25, and its focal-plane shutter banged loudly. No sneaked shots went unheard. For consistency its highest speed probably should have been 1⁄400 second instead of 1⁄500. Or else—but why go there? Early Leicas had 1⁄30, 1⁄40, 1⁄60, 1⁄1, 1⁄200, and 1⁄500 second. Later they went to 1⁄25, 1⁄50, 1⁄75, 1⁄100, 1⁄200, and 1⁄500 second.

My old M2s are marked 1, 2, 4, 8, 15, 30, 60, 125, 250, 500 and 1000. That’s now the international standard. Don’t forget T for time and B for bulb, the thing old-time photographers squeezed after telling us to watch the birdie. Squeeze to open, release to close. Now it’s press and release. T is usually absent. It meant the shutter stayed open until you tripped it again to close it. It’s still found on many leaf shutters built around lenses.

Folklore that I learned as a photo magazine editor says that, on the whole, the photo industry is satisfied when its numbers fall within plus or minus 20 percent—a 40-percent spread. The makers of the Leica were considered superior because they insisted on errors no greater than plus or minus 10 percent. I don’t know the source of this belief, but I imagine that it may be true, within plus or minus 40% error.

My next good camera was a Contax II, pre-war rival to the Leica G. Its shutter speeds were 1⁄2, 1⁄5, 1⁄10, 1⁄25, 1⁄50, 1⁄100, 1⁄250, 1⁄500, and 1⁄1,250 second, again if I remember right. The Leica G only had 1⁄1000 for its top speed but had one second for its lowest speed. Corporate rivalry at work. Logic would change the international standard to 1, 2, 4, 8, 16, 32, 64, 128, 512, 1024, 2048 and so on, like the K numbers of the computer business.

The amount of actual error we experience—difference from marked shutter speeds, apertures and film speeds— must vary widely. We are saved by latitude, a word that means, in photography, what we can get away with. Trial and error experiment that includes our personal variables is the way to find out how great or small our latitude is.

Film speeds

These go by thirds of stops, steps, and zones, though our thinking and practice tend to go by half stops. The reason sensitometry uses logarithmic numbers instead of arithmetical ones is to fit the data conveniently onto graph paper. They compress the facts. In the log numbers used in sensitometry,0=1,1=10,2=100,3=1000 and soon. Log numbers also have the advantage of representing all densities proportionally.

There have been many film and plate speed systems since the 1890s, starting with H&D numbers established by Hurter and Driffield, who invented sensitometry in the first place. The characteristic curve wasn’t known until they discovered it, to their own surprise. Other film speed systems have included American Scheiner, European Scheiner, Weston, ASA, ISO, DIN and GOST. In the USA, film speeds are now given in ISO (International Standards Organization) arithmetical numbers, as follows: .1, .12, .16, .2, .25, .3, .35, .5, .6, .7, 1, 1.2, 1.5, 2, 2.5, 3, 4, 5, 6, 8, 10, 12, 16, 20, 25 (now the lowest common film speed). The range goes on: 32, 40, 50, 64, 80, 100, 125, 160, 200, 250, 320, 400, 500, 650, 800, 1000 (also written 1M) , 1.2M, 1.6M, 2M, 2.5M, 3.2M, 4M, 5M, 6.4M, 8M, 10M, 12M, and 16M. The series 4, 5, 6, 8, 10 is obviously odd: 5 is 1.25 times as much as 4; 6 is 1.2 times as much as 5; 8 is 1.33 (plus more 3s forever) times as much as 6; and 10 gets back to 1.25 times as much as 8. This sequence repeats: we have a slightly irregular gallop. I guess it’s the best we can do. ISO speeds also include logarithmic DIN (Deutsche Industrie Normal) speeds, in which ISO 400 = 27°, and 500 = 28°. ISO film speeds are normally written with both numbers, as “400/27°.” Arithmetical speeds are easier for me to understand: 400 is twice as fast as 200, which is twice as fast as 100. I’m not so used to log thinking, but it should be more true in proportion overall.

The word “accurate” belongs properly to actual film speed, which doesn’t always coincide with the number on the film box. In 1970, I did a film-speed test, giving a long series of exposures to a set-up subject with luminances (measurable brightnesses) of a 1-to-1000 range. A Kodak 18% reflectance neutral gray card was in the middle, and I metered on that. I tested several black-and-white films of the time: Kodak Tri-X (ASA 400) was one, and Ansco Super Hypan (ASA 500) was another. Each was given its recommended development in D-76, a most consistent developer. All discrepancies introduced by inaccuracies in the camera (shutter speeds and apertures) were repeated, so all test shots were comparable. In this test, Kodak Tri-X performed at half its rated ASA 400 speed, or EI 200. Ansco Super Hypan’s performance showed that its true speed was closer to EI 125, which equals ISO 125. (EI = Exposure Index, a term used increasingly by the photo industry.) We who write about film speeds should also use EI for all film speeds not determined by the standard ANSI test method.

All ASA and ISO speeds are determined by two density points per film, according to a rigorously standard ANSI test done with a developer that’s used only for film-speed testing. (I thought of mixing that ANSI developer formula and trying it out for pictures, but never got around to it.) Never mind that D-76 would almost certainly come closer to the results photographers would get. The standards-organization mind doesn’t work like our minds. What started out as ASA, the American Standards Association, became ANSI, American National Standards Institute, before it mutated to ISO. They couldn’t even standardize their name. It’s curious that Weston speeds, much used by photographers before ASA speeds were introduced, used the same numbers as ASA and ISO and EI, but for other film speeds. Weston 160 became ASA 200, and Weston 320 became ASA 400, and so on. I have wondered if that might not reflect the photo industry’s wish to make their films seem faster by giving them higher numbers, but that is an unworthy thought. Or is it? It is certain that the photo industry’s scientists know much more about film and its behavior than we photographers will ever learn. It is not so certain that they know much about pictures.

And now, the Zone System

The Zone System is Sensitometry Lite with Roman numerals. It readily teaches photographers to control the tones of their photos of things that hold still, but it also introduces a thornier problem. It gives people the illusion that their pictures are good. It’s as if anyone who can play scales correctly is thereby a musician. It ain’t necessarily so. Also, Ansel Adams wrote that we should place the brightest subject values in which we want detail and texture on zone seven-and-a- half. And how do you say that with Roman numerals? Well, I found the way. In fact, I found two ways. One is done with a common fraction: VII I/II. The other is decimal: VII.V. And because I have solved this mystery, my pictures are absolutely marvelous.

About the Author

David Vestal
David Vestal is a photographer and teacher whose publications include The Art of Black & White Enlarging (1984) and The Craft of Photography. His photographs are exhibited internationally and are found in numerous private and public collections including New York City’s Museum of Modern Art and the George Eastman House in Rochester, NY. The wit and wisdom of his commentaries have long earned him a strong following among readers.