High ISO Labels - why not simplify?

I was just musing the other day about a technicality that puzzles me. In a nutshell it is this - why do camera manufacturers slavishly double ISO numbers to increasingly precise figures, rather than rounding them? In my opinion they missed their best opportunity when they labelled the one after 12800 25600, rather than 25000. Then the next ones would have been 50000, 100000, 200000, rather than the "spurious precision" represented by the figure 204800. You'll have noticed that there are two shifts in the doubling sequence of shutter speeds, to simplify the numbers; once in going from 1/8 to 1/15 (not 1/16) and again going from 1/60 to 1/125 (not 1/120). The fact is that the difference is not noticeable. In the case of digital ISO equivalents, I don't think you can even measure them accurately enough to distinguish between ISO 200,000 and ISO 204,800, which is what I mean by spurious precision. Technically, if you say 204,800 and don't specify any error, you are implying the true value lies between 204,750 and 204,849. I say simplify. You may say I'm just a geek who wasted 5 minutes (plus or minus 30 seconds).

Manufacturer ISO is sometimes wildly different from actual measured ISO, just check out some examples on DxOMark, the actual ISO of some cameras may be ISO1500 when the camera is set to 2000.

Other than that, I dunno... They still need two numbers between each full-stop, like ISO100/160/320/400, so they can't be too lenient. But other that it has no bearing on actual ISO, just that you are roughly doubling exposure with each full stop.

Same with lenses, f/1.2 lenses are a lie, in actuality, the 85L is something like a t/1.4 lens. And f/1.4 lenses are more like t/1.6... Only cinema lenses list the aperture in t-stops, which is the actual amount of light transmitted, and not the theoretical amount. So just like that f-stops are only a rough guide line and have nothing to do with how much light the lens lets though. With the 85L and Sigma 85 both at f/1.4, the 85L actually lets in a fraction more light.

Edit: Having used computers for so long and getting used to the bit system where everything is a multiple of 2, this isn't a concern for me and perhaps others raised on computers, so precise ISO labels are as easy for me to read as calculating bytes.

Probably because it implies precision.

Saying "Yeah its round about 2500, give or take" doesnt sound quite so convincing to someone who's looking to spend several thousand on a camera.

I agree with the OP completely. realistically if these high levels ever become usable in normal situations then you will see people referring to them as 25K, 50K, 100K, 200K etc. Nobody is going to say "I shot this at two hundred and four thousand, eight hundred ISO".

Because if they weren't precise, people would be making posts on message boards complaining about that

Madweasel wrote in post #15202732
...I'm just a geek who wasted 5 minutes (plus or minus 30 seconds).

I agree!

JeffreyG wrote in post #15203081
I agree with the OP completely. realistically if these high levels ever become usable in normal situations then you will see people referring to them as 25K, 50K, 100K, 200K etc. Nobody is going to say "I shot this at two hundred and four thousand, eight hundred ISO".

Me too. Never really thought about it until I put Magic Lantern on my 5DII which gives the more accurate shutter speeds. Someone was asking why their 30s shot actually took 32s on the ML forum.

I don't know if this thread is serious of not, but assuming it is, here goes.

First off, aperture, shutter speed, and ISO are labeled for photographers, not mathematicians. Great liberties were taken in the rounding-off of the values.

The tables below are third-stop tables, with whole-stops indicated by a "<--" at the right.

APERTURE:

Aperture for DSLR cameras is quasi mechanical and quasi electronic. This means that the physical aperture iris is mechanical, but it is fully computer controlled. How close the actual aperture comes to the theoretical aperture is determined by the programming in the camera's computer as well as the limitations of of the physical aperture iris.

Apertures are conventionally labeled as shown on the left, but would more accurately be labeled as shown in the center, based upon the actual aperture values shown on the right:

f/0.7 — f/0.71 — f/0.70711 <--
f/0.8 — f/0.79 — f/0.79370
f/0.9 — f/0.89 — f/0.89090
f/1.0 — f/1.0 — f/1.0000 <--
f/1.1 — f/1.1 — f/1.1225
f/1.2 — f/1.3 — f/1.2599
f/1.4 — f/1.4 — f/1.4142 <--
f/1.6 — f/1.6 — f/1.5874
f/1.8 — f/1.8 — f/1.7817
f/2.0 — f/2.0 — f/2.0000 <--
f/2.2 — f/2.2 — f/2.2449
f/2.5 — f/2.5 — f/2.5198
f/2.8 — f/2.8 — f/2.8284 <--
f/3.2 — f/3.2 — f/3.1748
f/3.5 — f/3.6 — f/3.5636
f/4.0 — f/4.0 — f/4.0000 <--
f/4.5 — f/4.5 — f/4.4898
f/5.0 — f/5.0 — f/5.0397
f/5.6 — f/5.7 — f/5.6569 <--
f/6.3 — f/6.3 — f/6.3496
f/7.1 — f/7.1 — f/7.1272
f/8.0 — f/8.0 — f/8.0000 <--
f/9.0 — f/9.0 — f/8.9797
f/10 — f/10 — f/10.079
f/11 — f/11 — f/11.314 <--
f/13 — f/13 — f/12.699
f/14 — f/14 — f/14.254
f/16 — f/16 — f/16.000 <--
f/18 — f/18 — f/17.959
f/20 — f/20 — f/20.159
f/22 — f/23 — f/22.627 <--
f/25 — f/25 — f/25.398
f/28 — f/29 — f/28.509
f/32 — f/32 — f/32.000 <--
f/36 — f/36 — f/35.919
f/40 — f/40 — f/40.318
f/45 — f/45 — f/45.255 <--
f/51 — f/51 — f/50.797
f/57 — f/57 — f/57.018
f/64 — f/64 — f/64.000 <--
f/72 — f/72 — f/71.838
f/81 — f/81 — f/80.635
f/90 — f/91 — f/90.510 <--
f/100 — f/101 — f/101.59
f/110 — f/114 — f/114.04
f/128 — f/128 — f/128.00 <--

SHUTTER SPEED:

Shutters on DSLR cameras are mechanical, and use true divide-by-two mechanical timing functions. This means that shutter speeds tend to be true powers-of-two representations within the limits of the camera.

Shutter speeds are conventionally labeled as shown on the left, but should have the two-significant digit label shown in the center for the actual shutter speed shown on the right:

60s ----- 64s ---- 64.000s <--
50s ----- 51s ---- 50.797s
40s ----- 40s ---- 40.317s
30s ----- 32s ---- 32.000s <--
25s ----- 25s ---- 25.398s
20s ----- 20s ---- 20.159s
15s ----- 16s ---- 16.000s <--
12s ----- 14s ---- 13.699s
10s ----- 10s ---- 10.079s
8.0s ---- 8.0s ---- 8.0000s <--
6.0s ---- 6.3s ---- 6.3496s
5.0s ---- 5.0s ---- 5.0397s
4.0s ---- 4.0s ---- 4.0000s <--
3.0s ---- 3.2s ---- 3.1748s
2.5s ---- 2.5s ---- 2.5198s
2.0s ---- 2.0s ---- 2.0000s <--
1.5s ---- 1.6s ---- 1.5874s
1.2s ---- 1.3s ---- 1.2599s
1.0s ---- 1.0s ---- 1.0000s <--
0.80s --- 0.79s --- 0.79370s
0.60s --- 0.63s --- 0.63000s
0.50s --- 0.50s --- 0.50000s <--
0.40s --- 0.40s --- 0.39685s
0.30s --- 0.31s --- 0.31498s
1/4s ---- 1/4s ---- 1/4.0000s <--
1/5s ---- 1/5s ---- 1/5.0397s
1/6s ---- 1/6s ---- 1/6.3496s
1/8s ---- 1/8s ---- 1/8.0000s <--
1/10s --- 1/10s --- 1/10.079s
1/12s --- 1/13s --- 1/12.699s
1/15s --- 1/16s --- 1/16.000s <--
1/20s --- 1/20s --- 1/20.159s
1/25s --- 1/25s --- 1/25.398s
1/30s --- 1/32s --- 1/32.000s <--
1/40s --- 1/40s --- 1/40.319s
1/50s --- 1/51s --- 1/50.797s
1/60s --- 1/64s --- 1/64.000s <--
1/80s --- 1/81s --- 1/80.635s
1/100s -- 1/100s -- 1/101.59s
1/125s -- 1/130s -- 1/128.00s <--
1/150s -- 1/160s -- 1/161.27s
1/200s -- 1/200s -- 1/203.19s
1/250s -- 1/260s -- 1/256.00s <--
1/300s -- 1/320s -- 1/322.54s
1/400s -- 1/410s -- 1/406.37s
1/500s -- 1/510s -- 1/512.00s <--
1/600s -- 1/650s -- 1/645.08s
1/800s -- 1/810s -- 1/812.75s
1/1000s - 1/1000s - 1/1024.0s <--
1/1200s - 1/1300s - 1/1290.2s
1/1600s - 1/1600s - 1/1625.5s
1/2000s - 1/2000s - 1/2048.0s <--
1/2500s - 1/2600s - 1/2580.3s
1/3200s - 1/3300s - 1/3251.0s
1/4000s - 1/4100s - 1/4096.0s <--
1/5000s - 1/5200s - 1/5160.6s
1/6400s - 1/6500s - 1/6502.0s
1/8000s - 1/8200s - 1/8192.0s <--

ISO:

ISO is purely electronic, but is a mix of analog and digital circuitry. Because of this, ISO is notoriously inaccurate. That is to say, a camera set to ISO 1600 may actually have an ISO anywhere between 1200 to 1900, or worse, and with a tendency to be lower rather than higher.

ISO is a film-based function carried over into the digital world. In the digital world, it may be thought of a sensitivity value for the sensor. In practice, however, a given sensor has only one sensitivity, its so-called native ISO. All other ISOs are obtained by amplifying or reducing that native ISO. This amplification or reduction is done partly by analog means and partly by digital means.

Standard ISO values are normally labeled as shown on the left, versus the two-significant-digit labels (more digits for whole-stops) shown in the center, and the actual ISO values shown on the right:

ISO 6 ------ ISO 6.25 --- ISO 6.2500 <--
ISO 8 ------ ISO 7.9 ---- ISO 7.8745
ISO 10 ----- ISO 9.9 ---- ISO 9.9213
ISO 12 ----- ISO 12.5 --- ISO 12.500 <--
ISO 16 ----- ISO 16 ----- ISO 15.749
ISO 20 ----- ISO 20 ----- ISO 19.843
ISO 25 ----- ISO 25 ----- ISO 25.000 <--
ISO 32 ----- ISO 31 ----- ISO 31.498
ISO 40 ----- ISO 40 ----- ISO 39.685
ISO 50 ----- ISO 50 ----- ISO 50.000 <--
ISO 64 ----- ISO 63 ----- ISO 62.996
ISO 80 ----- ISO 79 ----- ISO 79.370
ISO 100 ---- ISO 100 ---- ISO 100.00 <--
ISO 125 ---- ISO 130 ---- ISO 125.99
ISO 160 ---- ISO 160 ---- ISO 158.74
ISO 200 ---- ISO 200 ---- ISO 200.00 <--
ISO 250 ---- ISO 250 ---- ISO 251.98
ISO 320 ---- ISO 320 ---- ISO 317.48
ISO 400 ---- ISO 400 ---- ISO 400.00 <--
ISO 500 ---- ISO 500 ---- ISO 503.97
ISO 640 ---- ISO 630 ---- ISO 634.96
ISO 800 ---- ISO 800 ---- ISO 800.00 <--
ISO 1000 --- ISO 1000 --- ISO 1007.9
ISO 1250 --- ISO 1300 --- ISO 1269.9
ISO 1600 --- ISO 1600 --- ISO 1600.0 <--
ISO 2000 --- ISO 2000 --- ISO 2015.9
ISO 2500 --- ISO 2500 --- ISO 2539.8
ISO 3200 --- ISO 3200 --- ISO 3200.0 <--
ISO 4000 --- ISO 4000 --- ISO 4031.7
ISO 5000 --- ISO 5000 --- ISO 5079.7
ISO 6400 --- ISO 6400 --- ISO 6400.0 <--
ISO 8000 --- ISO 8100 --- ISO 8063.5
ISO 10000 -- ISO 10000 -- ISO 10159
ISO 12500 -- ISO 12800 -- ISO 12800 <--
ISO 16000 -- ISO 16000 -- ISO 16127
ISO 20000 -- ISO 20000 -- ISO 20319
ISO 25000 -- ISO 25600 -- ISO 25600 <--
ISO 32000 -- ISO 32000 -- ISO 32254
ISO 40000 -- ISO 41000 -- ISO 40637
ISO 50000 -- ISO 51200 -- ISO 51200 <--
ISO 64000 -- ISO 65000 -- ISO 64508
ISO 80000 -- ISO 81000 -- ISO 81275
ISO 100000 - ISO 102400 - ISO 102400 <--

Two things should be borne in mind: with digital camera ISOs being horrendously inaccurate across the board, the actual label used is completely irrelevant; and there is no standard for labeling ISOs above ISO 10000 (those in the table above were created by extension).

Cheers Roger. The thread is sort of serious - I was mainly interested in what others thought - obviously it is inconsequential, and just a matter for academic interest/amusement. I hadn't known what you say about shutter speeds. I do know that some old cameras used different sequences, such as 1/50, 1/100, etc.

I was interested to see what Canon did with the original 1D, with its CCD sensor and electronic "shutter" enabling it to go one stop quicker than 1/8000s - I thought they may have labelled it 1/15,000, like the progression from 1/8 to 1/15, but they called it 1/16,000 and to my knowledge it's still the only (D)SLR to have such a shutter speed.

PhotosGuy wrote in post #15203694
I agree!

Cheers Frank!

It is what it is, pi is almost 3, but not really.

20droger wrote in post #15205998
APERTURE:
Aperture for DSLR cameras is quasi mechanical and quasi electronic. This means that the physical aperture iris is mechanical, but it is fully computer controlled. How close the actual aperture comes to the theoretical aperture is determined by the programming in the camera's computer as well as the limitations of of the physical aperture iris.

Apertures are conventionally labeled as shown on the left, but would more accurately be labeled as shown in the center, based upon the actual aperture values shown on the right:

f/0.7 — f/0.71 — f/0.70711 <--
f/0.8 — f/0.79 — f/0.79370
f/0.9 — f/0.89 — f/0.89090
f/1.0 — f/1.0 — f/1.0000 <--
f/1.1 — f/1.1 — f/1.1225
f/1.2 — f/1.3 — f/1.2599
f/1.4 — f/1.4 — f/1.4142 <--
f/1.6 — f/1.6 — f/1.5874
f/1.8 — f/1.8 — f/1.7817
f/2.0 — f/2.0 — f/2.0000 <--
f/2.2 — f/2.2 — f/2.2449
f/2.5 — f/2.5 — f/2.5198
f/2.8 — f/2.8 — f/2.8284 <--
f/3.2 — f/3.2 — f/3.1748
f/3.5 — f/3.6 — f/3.5636
f/4.0 — f/4.0 — f/4.0000 <--
f/4.5 — f/4.5 — f/4.4898
f/5.0 — f/5.0 — f/5.0397
f/5.6 — f/5.7 — f/5.6569 <--
f/6.3 — f/6.3 — f/6.3496
f/7.1 — f/7.1 — f/7.1272
f/8.0 — f/8.0 — f/8.0000 <--
f/9.0 — f/9.0 — f/8.9797
f/10 — f/10 — f/10.079
f/11 — f/11 — f/11.314 <--
f/13 — f/13 — f/12.699
f/14 — f/14 — f/14.254
f/16 — f/16 — f/16.000 <--
f/18 — f/18 — f/17.959
f/20 — f/20 — f/20.159
f/22 — f/23 — f/22.627 <--
f/25 — f/25 — f/25.398
f/28 — f/29 — f/28.509
f/32 — f/32 — f/32.000 <--
f/36 — f/36 — f/35.919
f/40 — f/40 — f/40.318
f/45 — f/45 — f/45.255 <--
f/51 — f/51 — f/50.797
f/57 — f/57 — f/57.018
f/64 — f/64 — f/64.000 <--
f/72 — f/72 — f/71.838
f/81 — f/81 — f/80.635
f/90 — f/91 — f/90.510 <--
f/100 — f/101 — f/101.59
f/110 — f/114 — f/114.04
f/128 — f/128 — f/128.00 <--

What I haven't ever quite understood is why Canon's ½ stop aperture numbers reuse third stop values at the low end of the scale:
f/1
f/1.2
f/1.4
f/1.8 (why not f/1.7?)
f/2
f/2.5 (why not f/2.4?)
f/2.8
f/3.5 (why not f/3.3?)
f/4
f/4.5 (why not f/4.8?)
f/5.6
After f/5.6 the numbers are as expected. This seems to go back all the way to the EOS 650 of 1987 so it may have historical roots in previous mounts. Apparently the irises in EF lense are controlled in increments of 1/8 stop and are set to the nearest value to the desired value.

However, what I wonder if the camera is set to f/4.5 in the third stop scale for a given ISO and shutter speed, will it take the same or a 1/6 stop darker picture if the camera is set to half stops and f/4.5 is selected? In other words, do you get actually f/4.5 or f/4.8? I'm going to try it a bit later.

Edit: as it turns out both pictures are exactly the same. I tried with two lenses, one where f/4.5 is wide open, one where f/4.5 is stopped down.

whuband wrote in post #15206499
It is what it is, pi is almost 3, but not really.

And sometimes we state numbers too accurately, giving an impression of accuracy beyond what exists.

Suppose I have a circle with a radius of about 3cm. What is the area of the circle?

a) 28.27 cm^2
b) 28 cm^2
c) 30 cm^2

The correct answer is c). The first answer implies that we know a lot more about the radius of the circle than we do. Even b) at two specific digits is overly precise. I said it was 'about 3 cm' and not 3.000 cm.

One wonders if the ISO numbers we are given are suggesting an accuracy level beyond what they represent. Also, they are becoming cumbersome at the high end.

macroimage wrote in post #15206601
What I haven't ever quite understood is why Canon's ½ stop aperture numbers reuse third stop values at the low end of the scale:
f/1
f/1.2
f/1.4
f/1.8 (why not f/1.7?)
f/2
f/2.5 (why not f/2.4?)
f/2.8
f/3.5 (why not f/3.3?)
f/4
f/4.5 (why not f/4.8?)
f/5.6
After f/5.6 the numbers are as expected. This seems to go back all the way to the EOS 650 of 1987 so it may have historical roots in previous mounts. Apparently the irises in EF lense are controlled in increments of 1/8 stop and are set to the nearest value to the desired value.

However, what I wonder if the camera is set to f/4.5 in the third stop scale for a given ISO and shutter speed, will it take the same or a 1/6 stop darker picture if the camera is set to half stops and f/4.5 is selected? In other words, do you get actually f/4.5 or f/4.8? I'm going to try it a bit later.

Edit: as it turns out both pictures are exactly the same. I tried with two lenses, one where f/4.5 is wide open, one where f/4.5 is stopped down.

It's a matter of rounding, which is historical and not mathematical.

Since the same camera cannot have both half-stop and third-stop aperture intervals at the same time, there should be no confusion when the same rounded value is used for both half- and third-stops. The "official" and actual values for these intervals up to f/5.6 are:

f/0.7 - f/0.7 - f/0.70711
----- - f/0.8 - f/0.79370
f/0.8 - ----- - f/0.84090
----- - f/0.9 - f/0.89090
f/1.0 - f/1.0 - f/1.0000
----- - f/1.1 - f/1.1225
f/1.2 - ----- - f/1.1892
----- - f/1.2 - f/1.2599
f/1.4 - f/1.4 - f/1/4142
----- - f/1.6 - f/1.5874
f/1.7 - ----- - f/1.6818
----- - f/1.8 - f/1.7817
f/2.0 - f/2.0 - f/2.0000
----- - f/2.2 - f/2.2449
f/2.4 - ----- - f/2.3784
----- - f/2.5 - f/2.5198
f/2.8 - f/2.8 - f/2.8284
----- - f/3.2 - f/3.1748
f/3.3 - ----- - f/3.3636
----- - f/3.5 - f/3.5636
f/4.0 - f/4.0 - f/4.0000
----- - f/4.5 - f/4.4898
f/4.8 - ----- - f/4.7568
----- - f/5.0 - f/5.0397
f/5.6 - f/5.6 - f/5.6569

There's a lot to consider here.

First, in the matter of half- and third-stop intervals, the cameras and lenses should both be calibrated for sixth-stop intervals and the appropriate intervals chosen. In practice, few are.

Second, in the matter of accuracy, f/stops should be manufactured to at least two-digit accuracy. And if you believe they are, I have a couple of bridges that might interest you. In practice, most "L"-class lenses have apertures with 10-12.5% accuracy. Others maybe as low as 25% accuracy. Fortunately, accuracy error seem to be unidirectional. For example, a lens that is 10% low at f/5.6 tends to be correspondingly low at all other apertures.

As any engineer will tell you, Murphy's Law states that errors will accumulate. That is, if you have a camera that is 10% low at f/5.6, your brand new "L" lens will also be 10% low at f/5.6. And you cannot anticipate Murphy's Law. If your camera is 10% low at f/5.6, there will be no lenses produced that are 10% high at f/5.6. Learn to shut up and use exposure compensation.

Fourth, shutter speed are surprisingly accurate in good cameras. Premium professional-grade camera typically have shutters that are accurate to within 20% of their fastest speed. At slower speed, this error is truly insignificant.

Fifth, ISO is grossly inaccurate in even the best of cameras. It was pretty bad with film, too. An ISO or ASA 100 film could actually be anywhere between 20% lower or 15% higher. ISO is an "about" function: a camera can be set to about ISO 400; changing from ISO 200 to ISO 800 about quadruples the exposure; etc. There is nothing accurate about ISO.

Because of the gross inaccuracies of ISO, I just smiled when people were so ecstatic when ISOs went from whole-stop to third-stop increments. A third-stop change is lost in the mud.