What motivated lens makers to now use 1/3 f-stops rather than say 1/4 or 1/2 stops?

Question

I've noticed that many older lens have just hard f-stops for lens (2, 2.8, etc). However, since the aperture wheel for some is continuous you can "stop" are some arbitrary point and shoot. From my post: How did photographers get the exposure right back in the day with only full-stop increments?, people can work with hard stops and fix at most +/- 2/3 EV later in post.

Assuming that's the case, what was the motivation behind creating 1/2 and later 1/3 f-stop lens? I understand that photographs don't need that much precision since we are using f-stops and not t-stops, referenced below. From that and my above example, it seems that 1/2 and 1/3 stops are nice extras? Isn't it enough to have a camera body that has 1/3 stops for shutter speed and ISO but hard stop for lens or is it a requirement that all factors of the light triangle must have 1/3 stops for aperture/shutter priority and auto? Related note, have we stopped at 1/3 stops or are lens makers going to have 1/4, 1/5 or some other smaller value for moving between stops?

EDIT: I am ignoring depth of field as f/stops do control that and I'm specifically focusing on getting the right exposure.

Reference:

• Why are DSLR lenses measured in F stops instead of T stops?

Answer 1

Historically, the unit of exposure was a doubling or halving of the exposing energy. This is the origin of the f/stop. Initially, this adjustment was made by inserting a thin metal plate with a circular hole, into a slit in the lens barrel. The photographer had a series of these metal slides called Waterhouse Stops after John Waterhouse circa 1858. The Waterhouse stop was superseded by the mechanical iris diaphragm. (You can see early examples of both in this video from Roger Cicala at lensrentals.com) To achieve a 2X change the aperture diameter must be enlarged or contracted such that the surface area of the hole is doubled or halved. To accomplish a 2X change, the diameter of the hole must enlarged or contracted using a multiplier of divider of 1.414 (square root of 2).

As an example, say a 50mm lens is mounted and set to f/8. The diameter of the hole in the iris will be 6.25mm. To open up this lens to f/5.6 the revised diameter will be 8.82mm. To stop down to f/11, the revised diameter must be 4.42mm. What I am trying to say is, given that the leaves of the iris are adjusted by a gear train, precision is challenging.

To make a ½ f/stop change, the multiplier is the forth root 2 = 1.19. To make a 1/3 stop change, the diameter modification is the sixth root of 2 = 1.12. In other words, as we make smaller and smaller adjustments the needed precision adds cost.

Please note: With black & white films, the resulting negatives are useless until printed. The printing operation is comparable taking a picture of the negative substituting light sensitive paper for film. This second exposure (printing) allows for adjustments to be made to mitigate errors made during the initial film exposure. In all most every case, a camera precision of greater than 1 f/stop was not necessary.

With the advent of more complex materials like positive black & white and color slide film, the need to improve exposure accuracy is evident. This inspired the 1/2 and 1/3 iris adjustments.

Now long focal length lenses are the “norm” for large film cameras. When we are adjusting longer lens the amount of accuracy of the gear adjustment of the iris is not a problem because the hole size change to make a 1/3 stop change is hefty. If the focal length is short, then 1/3 f/stop changes become problematic. Example: A 28mm set to f/8 has a diameter of 3.5mm. To close down to f/11, the revised diameter works out to be 3.125mm, not an easy mechanical change.

Answer 2

TL;DR: ⅓ stop (doubling of a ratio) is approximately ¹⁄₁₀ of a tenfold increase of a ratio.

While photography likes to use the stop system — linear counting of numbers of doubles or halves (i.e., base-2 logarithms) — most of the rest of science and engineering, including optics, use base-10 logarithms.

Whereas a stop is log₂ of a ratio in photography, a Bel is the log₁₀ of a (typically power/acoustic/optical) ratio. The Bel is somewhat large and unwieldy, so we usually use decibels, or 10×log₁₀ of a ratio. A doubling of the ratio in terms of decibels, i.e. 10×log₁₀(2), is 3.01 dB, or approximately 3 dB.

But a stop is a doubling of a ratio, so 1 stop is the same as 3 dB of optical power. ⅓ of a stop is ⅓ of 3 dB, or 1 dB. You can double-check this by taking 10 dB (which is a power ratio of 10) = ¹⁰⁄₃ of a stop = 2^10/3 = 10.08 ≈ 10.

You see this in photography when talking about neutral density filters. The optical density of a filter, d is related to the transmittance, T, by:

T = 10^-d

So a filter with OD = 1 transmits 10% of the light through it, OD = 2 transmits 1% of the light, etc.

The manufacturers that specify their filters using the ND.number -notation are directly using the optical density. ND0.3 is a 1 stop filter, ND0.6 is 2 stops, ND0.9 is 3 stops, ND3.0 is 10 stops, etc. If you had a ND0.1 filter, it would be ⅓ stop.

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Now, is that why ⅓ stops are used? I don't know. But I assume so, because it provides a nice convenient mapping from the photographic system of doubling/halving to the rest-of-science system of base-10 operations.

Answer 3

Just pointing out that a "proper" exposure depends on many factors, not just F-stop. The exposure time is equally important, and depending on the dynamic range of the film or the solid-state sensor, you can push the print range to match the desired visual appearance of the print. Typical film and sensors have far greater dynamic range than our eyes do, which is why this is possible.

Next, don't leave out the image quality/style other than illuminance. F-stop controls depth of focus as well as light level; shutter speed controls motion blur as well as light level.

So, in the end, the resolution (size of change of F-stop and/or shutter timings) provided is a mix of historical accident, dB deltas between settings, and just plain "more is better" salesmanship.

Answer 4

I suspect that finer f-stop scales were used when more precise exposure metering become available and with introduction of some slide films that had small exposure range. For some simple meters of the past and b&w film finer scales were not too important.