# Why are full fstops the numbers they are?

Discussion in 'Beginner Questions' started by http://www.photo.net/martinw, Mar 27, 2018.

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1. ### Norma Desmond

"There is geometry in the humming of the strings, there is music in the spacing of the spheres."
—Pythagoras

“There is one thing the photograph must contain, the humanity of the moment.”
—Robert Frank

2. ### alan_marcus|2

Having years of experience making test films and prints for the photofinishing industry, I can attest to the fact that when it comes to precision film developing, it is barely possible to process film and maintain the process parameters at 1/6 f-stop (± 0.05 density units). To maintain 1/6 f-stop it takes incredible due diligences. Also, 1 find it difficult to believe that one can set the camera exposure, better than 1/3 f-stop with repeatable accuracy.

Just for the record except for a 1 f-stop change, the delta is not what you guys think it is.

1 f-stop change equals 100% increment --- 50% decrement

1/2 f-stop change you would think is 50% increment --- 25% decrement

1/2 f-stop change is 41% increment --- 29% decrement

1/3 f-stop change is 26% increment --- 21% decrement

As an example let’s look at 1/3 stop change and how the surface area of the lens works out. The set is the 6th root of 2 = 1.122

1 – 1.1 – 1.3 – 1.4 – 1.6 – 1.8 – 2 – 2.2 – 2.5 – 2.8 – 3.2 – 3.6 – 4 – 4.5 – 5 – 5.7 – 6.3 – 7.1 – 8

If you construct a circle (aperture), calculate its area, increment its diameter by multiplying by 1.122, you construct a series of circles that enlarge by 26% or decrease by 21%. Similar to the math of compounding interest with money.

3. ### rodeo_joe|1

Bebu, what exactly do you do with your desired 1/10th stop metering precision? Because there's no way you can set your camera or lens to that degree of accuracy.

It would be much more sensible and understandable if the meter simply showed the nearest 1/3rd, 1/2 and 2/3rd stop steps as an aperture number, since that's how the camera displays it. It's not difficult to set up a lookup table (LUT) in the programming and show the nearest reading. The meter could still be accurate to 0.1 stop*, it just wouldn't display that accuracy in a nonsensical way.

*And if you think any commercial meter on the market is sufficiently temperature compensated to actually be accurate to 0.1 stop, then I fear you're quite mistaken.
The temperature coefficient of a silicon photodiode is quite high. To compensate it properly would require an exactly matched dark diode in perfect thermal contact with the sensor. That's not going to happen in the real world.

Truth is that most photographic equipment tolerances are extremely sloppy, because they don't need to be any better.

Last edited: May 19, 2018
4. ### AJG

I agree that 1/10 stop readings are overkill given the lack of accuracy possible with camera settings. I do appreciate the Seknoic readout which more closely resembles a needle readout that can be interpolated rather than the digital readouts (f/11.2, for example) that I have a hard time using or interpreting.

5. ### Bill C

I've used that sort of thing quite a lot in years gone by; not necessarily for setting the camera, but used nonetheless. One example, getting a largish white background evenly illuminated; I can use a spot meter from the camera position then make fine adjustments on, say four lights.

Another use is setting lighting ratios to get to a preset spec. Now someone may say, ya know, 1/3 of a stop should be plenty good for that, but it really can be worse than meets the eye. Consider that an ideal meter reading in 1/3 stops doesn't really nail a number down precisely; if you start gradually increasing the light power the meter reading won't (shouldn't) change until you pass the halfway point to the next reading increment. So there is a "band," roughly 1/3 stop wide, where the meter reading is the same but you can't tell (from a single reading) if you are on the high end or the low end of that range. Now here's how this can be a bigger problem than one might think. Imagine that you have two lights setups, side by side, that you are trying to match. Say that both give the same meter reading (to the 1/3 stop). Ok, it is possible that that one lighting system floats around a little on the high side of the range, whereas the other floats on the low side. It is possible that you could get the same meter reading on both systems, but they could, in reality, sometimes differ by as much as (nearly) 2/3 stop. This really depends on the precision/repeatability (I may not be using the proper term) of both the meter and the lighting system.

Regarding a readout to levels that may seem to be overkill, well, there is a principle in what they call "statistical process control" that you aim for precision levels that may not be achievable (within the economic realities of the business) much of the time. But when a lot of interacting tolerances add up, they often tend to partially cancel each other out - they seldom all go in the same direction. Anyway, if you try to hold a numbers of things tighter than they can really be sensibly controlled then you typically have a better result, statistically.

Anyway, in my work, I've found Minolta meters reading to the "1/10 stop" to be very useful. Much more so than earlier meters reading to "1/3 stop."

One last note, I've spent a great deal of time working in photofinishing qc, and my experience is that we could hold results much tighter than commonly accepted here. My department would typically supply what we call "master negs" (aka printer control/slope negs) for all of our corporate lab use. We could shoot a 100 ft roll of 70mm film, and if a measured point had a density aim of, say 0.75, typically everything would read from 0.74 to 0.76 (perhaps a couple of negs would exceed this and be discarded). This is the end result of a combination of variations of the film, the power of the flash, processing considerations (time, temperature, and agitation fluctuations), and repeatability of the densitometer. Metering and aperture selected didn't really place into this, as it was fine tuned by an actual shoot/process test (metering didn't have enough precision for our purposes).

6. ### BeBu Lamar

Because like most people I now shoot mostly digital and thus there is no need for an exposure meter. I use my exposure meter as a light meter and the 7% resolution is not all that good. I wish I can afford the real light meter that can do 2%.
While I don't do that any more but I can check the T stop by measuring the light intensity at the film plane.

7. ### rodeo_joe|1

If you shoot RAW with 1.5 stops of headroom, then 1/3rd of a stop is plenty accurate enough.

And show me the lens with less than 1/10th stop vignetting that needs a lighting match that close.

I'd also challenge the most finicky of art directors to spot 1/10th of a stop change in light level.

Pointless and false accuracy!

"I wish I can afford the real light meter that can do 2%."

- Why exactly? You still haven't explained what possible use it would be.

I have two Luxmeters. One is purely analogue with a moving-coil readout, the other digital. The best MC meters have a linearity and FSD accuracy of around 2%, and even then have to be carefully levelled and read with a mirrored scale.
Digital readouts have a similar accuracy +/- the LSD. But as explained above, the sensor accuracy, linearity and temperature compensation (lack of) probably far outweighs any display accuracy.

I think what you're asking for doesn't exist outside of a standards laboratory. Even then that accuracy of reading has almost no practical application.

Last edited: May 20, 2018
8. ### rodeo_joe|1

FWIW. The Cos^4 law dictates that any lens will have a difference of at least 1/10th stop image brightness between on-axis and 10.64 degrees off axis.

That means using a lens of >115mm focal length on the 135 format to (theoretically) achieve 1/10th stop evenness across the frame; or equivalent lens angle on other formats.

9. ### Andrew Garrard

Joe - is that universally true? With relatively modern telecentric designs, I thought some effort was made to do better than the expected fall-off - but my optics aren't strong enough to know.

For what it's worth, I don't argue that describing the aperture to a tenth is all that useful - but unless we actually go to a logarithmic system (equal steps) I don't really see how the number is easily going to be written otherwise.

10. ### BeBu Lamar

These have the 2% accuracy
Luminance Color Meters | Konica Minolta Sensing

11. ### stuart_pratt

I doubt any of my collection of antiquated 1960’s and 1970’s SLRs give the same light reading within half a stop, let alone a tenth of a stop. I can appreciate how you could use this, as Bill C says, for getting a very even lighting to a backdrop or something, but I would think there is little practical value measuring this accurately with a modern camera. If you don’t like what your rear screen is showing you after you have taken the shot, I doubt anyone would be thinking ‘I know, I’ll dial in a 10th of a stop compensation’, even if you could do so. After all, the meter reading is only as good as the thing you point it at, so rather than having a much more sensitive meter, learn what to point it at better.

12. ### BeBu Lamar

With the new post in the Nikon forum now I know it's f/1.0, 1.1, 1.2 then 1.4.

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13. ### Andrew Garrard

Get an f/0.95 Nocturnus and report back to us, BeBu?

(\$1900-at-half-price-early-adopter isn't quite sufficiently tempting to me for just over a half a stop faster than the f/1.4 Art I've already got!)

14. ### Richard Williams

I think the familiar whole stops (well, down to f/90, anyway) are truncated, rather than rounded, to a couple of significant figures. Otherwise, f/22.627 would be written as f/23.

William Michael likes this.
15. ### Richard Williams

My older digital Gossen Sixtomat Flash does this (full stops and 1/10 stops) - more recent versions like the F2 also give you the option of conventional 1/3 or 1/2 stops.

16. ### Andrew Garrard

Whole stops, maybe (I've not checked past f/22). It's certainly not that simple for fractional stops, though - f/3.174802 (1/3 stop above "f/2.8") shows as f/3.2, correctly (for nearest) rounding to the larger denominator. But then a third of a stop from that, f/3.563595 gets truncated to "f/3.5".

I'm just going to put it down to historical accident and probably cumulative rounding errors. Sometimes trying to look for a logical explanation doesn't work.

BeBu Lamar likes this.
17. ### BeBu Lamar

Yes the conventional way of rounding off doesn't follow any rules. Because if it's simply truncation then I can certainly program my calculator to do that. Whenever I do any programming related to f/stop or shutter speed I have to do the enumeration and look up table.

18. ### glen_h

At the time that our favorite numbers were chosen, meters weren't all that accurate.

Certainly there wouldn't have been much reason for an f/23 over an f/22.

ISO (and ASA values before them) are rounded to 1/3 stop.

19. ### Andrew Garrard

Oh, yes. The question to me isn't about telling 22 from 23, it's about 22 being a worse approximation to the correct power of two than 23 is. It's like using 4 as an approximation of pi - it's not so much that you didn't use more precision, it's that even at the precision you're using, you don't have the best answer.

I can see how you get there by successive approximation (sqrt(2) is 1.414... or roughly 1.4; 1.4x2 is 2.8, 2.8x2 is 5.6, 5.6x2 is 11.2 is roughly 11, 11x2 is 22), although arguably we should have ended up with f/7.8 (5.6x1.4=7.84) rather than f/8 if we were allowed to do that.

I do agree that f/22 is within a third of a stop of the "right" (f/22.627...) answer though - roughly 8.92 stops down from f/1.0. f/23 obviously gets closer to the desired 9 stops (9.047...)

Executive summary: things invented before the electronic calculator, especially when used by artists rather than engineers, sometimes had somewhat screwy maths. And a cellphone with access to the internet and a calculator app is a dangerous way to allow me to wake up on a Saturday morning.

20. ### Vincent PeriMetairie, LA

Hmm... but "22" is so much
easier to remember than "23"...