[AstroDave]

Towards the end of this discussion (Optical Measurements of Pentax ME Super Shutter Speed - PentaxForums.com , forum member swanlefitte notes

What do these models report as half steps? I notice my ks-2 uses f/4 f/4.5 f/5.6, not f/4.8.

This prompted me to check my K-1 and K-3. They, too, display the (incorrect!) value of 4.5 for the step selected between 4 and 5.6 when in half-step EV mode.

What gives?! Is this just a mis-labeling or do these cameras actually shoot at the incorrect value? Let’s find out (I’ve got nothing much better to do during these days of stay-at-home orders).

So, off to take some photos of my Kodak gray card with my K-1 and the SMC Pentax-DA 50mm 1.8 lens across a range of f-stops. I chose the 1.8 lens so that I could measure over the widest range of stops.

I took frames at half-step and third-step values from f/1.8 to f/22. On the way up and down, the full-step values were shot 2 or 3 times. The repeatability is very good (a testament to my lights and power supply!).

I used RawDigger to extract the actual R,G,B pixel values averaged over a small rectangle in the center of the gray card, similar to what I did when I checked camera linearity a while back (How Linear Are Some Pentax Camera Sensors? - PentaxForums.com)

Just as with shutter speeds, it is important to note that the f-stop values reported for just about all cameras are not quite correct. The numbers have been rounded for convenience. This article has a comprehensive discussion: https://www.scantips.com/lights/fstop2.html

Here are the results, plotted with the (expected/hoped for) mathematically correct aperture values (a lot of fourth and sixth roots of 2 involved) - including the correct value (nearly f/4.8 rather than f/4.5) for the half EV step between f/4 and f/5.6




The data are pretty consistent, although not nearly as good as for the shutter speed results referenced above, and with some systematic deviations. The data clearly show some curvature - peaking in the middle, for all three colors. If pixel value versus aperture were exactly linear, the power law fits should have exponents of 2.00 , rather than the somewhat larger values here (typically 2.12 to 2.13). These values suggest that at the smallest aperture (largest f values), not as much light gets to the sensor as it “should.”

All in all, though, I am fairly impressed with the consistency and goodness of the data. The mechanical tolerances in lens aperture at the smallest openings have to be a small fraction of a millimeter. (At f/16, the aperture here is around 3mm (=50mm/16), and a 0.1mm error results in an aperture area (same as exposure) error of almost 7%.)

So, what about the original question: what is going on with our Pentax cameras when used in half-step mode between f/4 and f/5.6?

Here’s the same plot as above, except I have used the exact value of 4.5 for the half-step value. The points (circled) are clearly out of place.



Looks like Pentax has just mis-labeled this value, and it carries over to the EXIF data, too. Maybe in a future round of updates, this could be fixed.

This dichotomy appears here in the Forum article The Fundamental of Exposure (The Fundamentals of Exposure - Aperture - In-Depth Articles), where on page 5 the half-step values list F4.8, whereas the animated GIF on the same page has the lens stepping through F4.5 !

What value do you see for your camera(s) (including non-Pentax?) for this mystery stop? Does this error go all the way back to the first digital bodies, or even back to the film SLRs?

[swanlefitte]

Thanks for doing the work. I guess you have literally proved you are a gentleman and a scholar. Glad to see it is the half. I just googled aperture charts and it is not unusual but not common to see this 4.5 as both third and half step. such as this https://oberphotographytips.wordpress.com/2013/04/24/aperture-2/

[photoptimist]

Interesting! Yes, in theory, the half steps should be 4, 4.8, & 5.6 and the 1/3 steps should be 4, 4.5, 5.0, & 5.6.

This is not unlike the issue that the labeled "15" second shutter time is really 16 seconds long (and "30" is really 32).

It seems clear that the text of the exposure-value labels is stored in some firmware file, not numerically calculated.

[swanlefitte]

I just checked my k100d and it also displays f/4.5. more importantly I found my a50mm 1.7 lens on the camera!

[AstroDave]

Thanks for doing the work. I guess you have literally proved you are a gentleman and a scholar.

I'll agree with the scholar, but some might argue the gentleman part (although I usually do try!).

Interesting on the K100d (which was my first digital Pentax, by the way, but is long gone). So this seems to pretty much go all the way back to the earliest digitals.

Can somebody chime in with film camera values? I never had a fancy Pentax film SLR, so I am not sure what they display. The ME Super was as good as I got in the film line.

[stevebrot]

What value do you see for your camera(s) (including non-Pentax?) for this mystery stop? Does this error go all the way back to the first digital bodies, or even back to the film SLRs?

I just checked my Super Program and it displays f/1.7, f/2, f/2.5, f/2.8, f/3.5, f/4, f/4.5, f/5.6 in shutter-priority mode (emphasis mine). Direct setting of aperture is not supported on this body, but according to the camera manual, the increment is half-stop.

Drilling a little further, when George de Fockert decoded the range of maximum aperture values for the KA mount, his work found the sequence: f/1.2, f/1.4, f/1.7, f/2.0, f/2.5, f/2.8, f/3.5, f/4.0, f/4.5, f/5.6, f/6.7, f/8.1 FWIW, the mount contacts on my DA 50/1.8 map to f/1.7 and that is what my Super Program displays. Apparently, the use of f/2.5, f/3.5, and f/4.5 as half-steps is as old as the KA mount as far as the camera side goes.

I said "camera side" because the Pentax A-Series Lens manual shows the click sequence for that series aperture ring as: f/1.2, f/1.4, f/1.7, f/2.0, f/2.4, f/2.8, f/3.4, f/4.0, f/4.8, f/5.6, f/6.7, f/8, f/9.5, f/11, f/13.5, f/16, f/19/, f/22, f/26, f/32, f/38, f/45. "In-between" stops were indicated with a •, with in-between apparently meaning half-steps except towards the upper end.

Are the waters muddy enough yet? Was the sequence designed to mirror intended maximum aperture support?

Yes...I know...I should have put all that stuff in a table.


Steve

1The K-Mount Page | Features and Operation of the KA Mount

[AstroDave]

Are the waters muddy enough yet? Was the sequence designed to mirror intended maximum aperture support?

Very interesting!

I kinda have that "maximum aperture support" idea - make it look like that widest opening is a bit more than it really is.

[stevebrot]

I kinda have that "maximum aperture support" idea - make it look like that widest opening is a bit more than it really is.

...or a bit less, as the case might be for f/2.5. Strangely, I am not sure that this is entirely a Pentax thing. The reason I say that is because the n.5 intermediate stops are extremely prevalent as maximum aperture designations and because very few people actually know the half-stop f-numbers. (I confess that I never noticed the display discrepancy before today. )

On a related topic...how about those shutter speed sequences, eh? Why does EV 6 tabulate as 1/15s at f/2.0 and 2s at f/11?


Steve

[UncleVanya]

Fascinating. Now I need to go check my pz-1...

[swanlefitte]

Did some searching. Did i find a clue?
F/No. The ratio of the focal length to the diameter of the aperture. The numbering of the scale varies, the most common are:
f2, 2.8, 4, 5.6, 8, 11. This was the standard used in Britain.
f2.2, 3.3, 4.5, 6.3, 9, 12.5. This was widely used on continental lenses.
Lens Diaphragms - Antique and Vintage Cameras

[zapp]

You should not mix mathematically correct terms with naming conventions. At the end exposure must be correct. Multiplication of exposure times so also not doubling. 1/60s vs. 1/125s. Between f/4 and f/5.6 you could expect f/4.86621... You will soon find out that to metering and electronic aperture are cool to compensate for exposure tolerances.

[swanlefitte]

You should not mix mathematically correct terms with naming conventions.

The main problem is that f/4.5 is used for both 1/3 and 1/2. Is the n.5 for half stop a naming convention from before cameras did third stops that carries on? That would be similar to a microwave using 100 to denote 1 minute and no seconds instead of 100 seconds.
If a third or half stop is deemed important enough to be differentiated in the working of the camera it is important enough to denote them in a distinguishable way.

[Not a Number]

I never use the half-step setting on my K10D. The ISO settings on film cameras is 1/3 stop, everything else should be too

[BigMackCam]

What an interesting thread on such a strange little quirk! Thanks for the research and well-presented findings, @AstroDave - much appreciated

[Alex645]

Just as with shutter speeds, it is important to note that the f-stop values reported for just about all cameras are not quite correct. The numbers have been rounded for convenience.

And it should be noted this type of rounding is also common in ISO and some memory cards.

The only reason I can think of why 1/3 EV between 50 and 100 is 64 and 80 instead of 67 and 83 is because it's just harder to memorize. Same with ISO 125 and 160 instead of 133 and 166.

In regards to why f/4.5 stuck? My pre-DSLR digital incident light meter has 1/10 EV steps, so instead of f/6.7 for a reading 1/2 EV between f/5.6 and f/8, it reads f/5.6.5. 1/3 EV before f/8 will read f/5.6.7. What is really confusing is that for f/4.5 or the more correct f/4.8, it would read f/4.5....not because that was a half stop on lenses, but because half an EV more than f/4 is a .5 increase, and thus f/4.5.

Memory cards? Last week I got a trivia question wrong: How many MB in a GB? I didn't think and answered 1000. It's actually 1024.

Is there a reason there are 8 bits to a byte instead of 10?