On Sharpness, ISO and Shutter Speed

A mechanical resonance in a complex system is quite complex.

The problems with most sensor-stabilized systems are well known, and there's even been some formal attempts at quantifying them. Falk Lumo, also present here on DPR, among others have some material in the public domain concerning mirror and shutter vibration effect on image sharpness.

Recent cameras (modern constructions) have very low mirror-slap impact on sharpness, but stronger shutter-induced vibrations.
Do you have links to any studies showing that such is the case? I am not at all questioning your claim, just interested in how it might be substantiated.
This is an informal summary account of the experiments I did which convinced me.

Back in the days of film SLRs I was taking long exposure long focal length available light shots of distant murals in a dim church. Bafflingly soft unfocused looking results. Then I learned about mirror vibration. My SLR didn't have mirror lock up. I swore then I would never buy another SLR without mirror lock up.

In fact I managed to finesse that requirement by making my next camera mirrorless, the excellent digital Sony R1 with an APS-C sensor. I was waiting for DSLRs to become mirrorless. But fate stepped in in the shape of a huge American tourist with a huge backpack who managed to swipe over my tripod mounted R1. The fall killed it. Sony at the time were making the most promising progress away from the Victorian clockwork clackery of the SLR, but did not yet have a mirrorless model. They also didn't have mirror lock up, saying that with modern damped mirror machinery it wasn't needed.

I reluctantly and sceptically bought a Sony A350 DSLR. Quick tests showed no obvious evidence of mirror vibration. So it was clearly much less at least. But had it gone? I acquired a Sony 500mm reflex lens. Its focal length and very small rotational inertia made it the ideal lens for revealing mirror vibration. And I found it. At shutter speeds below around 1/300th sec I got a ghost image a few pixels vertically displaced. As the shutter speed went down it turned into a vertical smear, then it spread out into a general fuzziness. As the shutter speed continued to go down it started to sharpen again. Exactly what you'd expect from a sharp vertical shock which set up high frequency vibrations which quickly died away.

Or was it shutter shock? Or a combination of both mirror & shutter shock? Now I knew what to look for I found it happening to a lesser but still annoying degree at 200mm on an ordinary zoom.

So I was very interested when I got a Sony A77, which had no moving mirror, and a mechanical front shutter curtain which could be optionally switched in the menu for an electronic front curtain. The ideal experimental camera to answer my question!

Tests showed that the mechanical shutter produced exactly the same vertical ghosting and smearing as I'd seen before, at similar shutter speeds. Switching to electronic shutter completely removed it. So that strongly suggests to me that where the smaller APS-C sensors were concerned Sony at least had successfully removed mirror shake in their DSLRs. What I had originally identified as mirror shake in my A350 looks in retrospect to have been shutter shake.

Of course the much bigger and more violent shutter and mirror machinery of full frame DSLRs is a more serious problem. I'm surprised more people haven't remarked on that as a reason to prefer APS-C.
 
A mechanical resonance in a complex system is quite complex.

The problems with most sensor-stabilized systems are well known, and there's even been some formal attempts at quantifying them. Falk Lumo, also present here on DPR, among others have some material in the public domain concerning mirror and shutter vibration effect on image sharpness.

Recent cameras (modern constructions) have very low mirror-slap impact on sharpness, but stronger shutter-induced vibrations.
Do you have links to any studies showing that such is the case? I am not at all questioning your claim, just interested in how it might be substantiated.
This is an informal summary account of the experiments I did which convinced me.

Back in the days of film SLRs I was taking long exposure long focal length available light shots of distant murals in a dim church. Bafflingly soft unfocused looking results. Then I learned about mirror vibration. My SLR didn't have mirror lock up. I swore then I would never buy another SLR without mirror lock up.

In fact I managed to finesse that requirement by making my next camera mirrorless, the excellent digital Sony R1 with an APS-C sensor. I was waiting for DSLRs to become mirrorless. But fate stepped in in the shape of a huge American tourist with a huge backpack who managed to swipe over my tripod mounted R1. The fall killed it. Sony at the time were making the most promising progress away from the Victorian clockwork clackery of the SLR, but did not yet have a mirrorless model. They also didn't have mirror lock up, saying that with modern damped mirror machinery it wasn't needed.

I reluctantly and sceptically bought a Sony A350 DSLR. Quick tests showed no obvious evidence of mirror vibration. So it was clearly much less at least. But had it gone? I acquired a Sony 500mm reflex lens. Its focal length and very small rotational inertia made it the ideal lens for revealing mirror vibration. And I found it. At shutter speeds below around 1/300th sec I got a ghost image a few pixels vertically displaced. As the shutter speed went down it turned into a vertical smear, then it spread out into a general fuzziness. As the shutter speed continued to go down it started to sharpen again. Exactly what you'd expect from a sharp vertical shock which set up high frequency vibrations which quickly died away.

Or was it shutter shock? Or a combination of both mirror & shutter shock? Now I knew what to look for I found it happening to a lesser but still annoying degree at 200mm on an ordinary zoom.

So I was very interested when I got a Sony A77, which had no moving mirror, and a mechanical front shutter curtain which could be optionally switched in the menu for an electronic front curtain. The ideal experimental camera to answer my question!

Tests showed that the mechanical shutter produced exactly the same vertical ghosting and smearing as I'd seen before, at similar shutter speeds. Switching to electronic shutter completely removed it. So that strongly suggests to me that where the smaller APS-C sensors were concerned Sony at least had successfully removed mirror shake in their DSLRs. What I had originally identified as mirror shake in my A350 looks in retrospect to have been shutter shake.
That seems pretty likely, yes.
Of course the much bigger and more violent shutter and mirror machinery of full frame DSLRs is a more serious problem. I'm surprised more people haven't remarked on that as a reason to prefer APS-C.
I understand what you mean. Nevertheless, it doesn't seem to work that way in practice. While I am certainly not saying that FF DSLRs or DSLRs in general are free from the problem, it appears, if anything, to be worse with small and light mirrorless cameras, like micro four thirds, although these have shutter blades with only about a quarter the area of an FF camera.

Note, also, that mirrorless cameras, including your R1 and A77, have mechanical shutters that perform "double duty", i.e., the shutter action includes four phases (close-open-close-open) rather than only two (open-close). The first of these four phases (shutter closing to prepare the sensor for exposure) is known to make things worse although it is not the sole culprit. Some signs of shutter shock remain even if you introduce a delay (as is possible on Olympus cameras), analogous to mirror lock-up, between the first phase of shutter action and subsequent phases.
 
Chris Malcolm wrote: Of course the much bigger ...shutter and mirror machinery of full frame DSLRs is a more serious [sharpness] problem. I'm surprised more people haven't remarked on that as a reason to prefer APS-C.
Not hard to guess why lighter, smaller-shutter APS-C cameras would be sharper (and in my experience are, in the field) than heavier, bigger-shutter, perhaps flipping mirror, full frame sensor cameras, on a tripod, on average. Particularly for typical portraiture angle of views.

F/2.2 is not exactly this (literally throw-away/cheapest of all Minoltas AF) 50/1.7 lens' optimum aperture. Here on APS-C mirrorless camera sensor, with no first curtain electronic shutter feature or remote activation, on a fairly flimsy 1200 gram tripod.
F/2.2 is not exactly this (literally throw-away/cheapest of all Minoltas AF) 50/1.7 lens' optimum aperture. Here on APS-C mirrorless camera sensor, with no first curtain electronic shutter feature or remote activation, on a fairly flimsy 1200 gram tripod.

[ATTACH alt="Let's define "perfect sharpness" as resolving single-pixel-width details, to within the symmetrical-blurring contrast capability of the lens, camera body/sensor and anti-aliasing filter."]406056[/ATTACH]
Let's define "perfect sharpness" as resolving single-pixel-width details, to within the symmetrical-blurring contrast capability of the lens, camera body/sensor and anti-aliasing filter.

On "smaller-sensor" cameras (e.g. APS-C), you end up, on average, getting "perfect sharpness in the field", i.e. something close to the potential sharpness of ordinary lenses and sensors compared to full frame cameras because you are using
  1. Lenses that are usually physically shorter and lighter for a given angle of view, thus the camera rig jiggles less on a given tripod. Sure the new Sony FE 35/2.8 is only 130 grams, but the not-terribly-different-angle-of-view Sony 20/2.8 for APS-C is 70 grams. And someone please inform me if there are 220-gram full format 28-85-type kit zooms of decent optical quality, like there are for APS-C.
  2. Camera bodies that are physically shallower and lighter, thus the camera rig jiggles less on a given tripod.
  3. The smaller-sensor cameras tend to be mirrorless, since people buy them instead of "full frame" to get to some configurations that are smaller than full frame cameras. So there goes the mirror vibrations.
  4. As Chris Malcolm mentioned above, what shutter vibrations one does get from a certain design, are from a smaller shutter in any case.
  5. Lenses that are shorter focal length, thus tending to have higher (at least central) sharpness
  6. For portrait (mild telephoto) focal lengths, on APS-C the compact lenses you get to use usually have a relatively simple and symmetrical, certainly well-refined planar/double-Gauss lens designs
    Quick, which of these lenses is the Zeiss Planar designed about a century before the other one.
    Quick, which of these lenses is the Zeiss Planar designed about a century before the other one.

    instead of harder-to-get-perfectly-sharp-at-wide-apertures telephoto lens designs. Consider the near-worthless plastic kit "normal" lens from the 1980's, used above for mild telephoto portraiture on a smaller APS-C sensor. Most of those lenses function at the same clarity level, at the quite wide apertures of many a portrait, as a high-​
    end full-frame sensor telephoto optic, that is on average more massive and jiggly on a tripod.
  7. For a given travel kit weight budget, the smaller format cameras make it practical to carry a collection of ridiculously light (e.g. 70 gram!), fast prime lenses, instead of a single larger-format 500-1000 gram fast zoom lens. Maybe the kit weight is the same, but the weight and thus stability of the bunch-of-little-primes rig on the tripod for any given photo is much, much less.
My not-remote-actuated mirrorless APS-C Nex C3 portraits with cheap, decades-old lenses are on average noticeably sharper than was ever able to get out of my relatively huge, flipping mirror medium format Mamiya, Which had rather expensive and well-made, conservatively designed F/4 portrait and macro prime lenses. Even though used a remote shutter release for the medium format cam that was on a tripod much heaver and more solid than would tolerate today.
 

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Chris Malcolm wrote:Of course the much bigger and more violent shutter and mirror machinery of full frame DSLRs is a more serious problem. I'm surprised more people haven't remarked on that as a reason to prefer APS-C.
Anders W wrote: I understand what you mean. Nevertheless, it doesn't seem to work that way in practice.
This sounds like you are referring to your own practice, hence you would have plenty of examples available.
Anders W: While I am certainly not saying that FF DSLRs or DSLRs in general are free from the problem, it appears, if anything, to be worse with small and light mirrorless cameras
Then it will be falling off a log for you to show us the full frame flipping-mirror DSLR photo, that you took, say one that was taken on a portable tripod, a real photo not some test setup, with or without a remote shutter release or self-timer, of normal to portrait angle of view, that represents the lesser vibration problem of that type of larger flipping-mirror rig that you describe.

Make sure it's a long exposure, say 1 second like the one below, let's not muddy the waters by you posting an electronic flash photo at 1/8000th of a second or whatever.

Feel free to show us something from a much finer lens and aperture setting than the $50 dollar e.bay Alpha mount plastic kit zoom at F/13 used for this small-cam mirrorless APS-C example. Be nice if your example was from a sensor with an anti-aliasing filter, to further level the playing field.


My own experience is that this kind of close-to-sensor-theoretical clarity is attained less often on the average with full-frame or larger, flipping-mirror camera setups. Alpha mount 18-55 kit zoom, 1 second exposure.


Wish had used something less than ISO 800 for this 1/30th second exposure. But then it was with a mint 1985 Tokina SD 70-210, the world's first ultra compact telephoto zoom, that's just no good wider than F/8.


Darn it, moire becomes a (admittedly and literally tiny) problem when there's no flipping mirror to soften things up a bit. Older-tech Nex 5 sensor.

Few days ago with more modern Nex C3 sensor, 1/4 second exposure, 1200 gram tripod, cheap Minolta 50/1.7 AF lens.
Few days ago with more modern Nex C3 sensor, 1/4 second exposure, 1200 gram tripod, cheap Minolta 50/1.7 AF lens.

Looking for presence or absence of single-pixel-wdith features.
Looking for presence or absence of single-pixel-wdith features.
 

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very interesting indeed!

If I understand correctly you analyze the studio scene raw files downloaded from dpreview.

I am well aquinted with fvbergh 's excellent MTF mapper, as I used it to investigate focus shift (not posted so far).

did you plainly apply the MTF mapper to the full raw and then select a useable slanted edge? Which edge is it actually ?
 
Bernard Delley wrote: If I understand correctly you analyze the studio scene raw files downloaded from dpreview.
Correct
I am well aquinted with fvbergh 's excellent MTF mapper, as I used it to investigate focus shift (not posted so far).
Most excellent indeed
did you plainly apply the MTF mapper to the full raw and then select a useable slanted edge? Which edge is it actually ?
I feed MTFMapper the two slanted edges separately (labeled Horizontal and Vertical in the graphs), in the form of TIFFs cropped from the grayscale full resolution image obtained by clipping to zero and white balancing the relative Raw data. The data thus obtained is undemosaiced and as raw as it gets - you can read a bit more about my procedure here . Keep in mind that it only works with neutral subjects lit by a well behaved illuminant (such as D50)

What did you find out with your tests?

Jack



Vertical and Horizontal results are virtually the same on D4's DPR captures.  MTFMapper's results' accuracy decreases with increasing noise (see here )

Vertical and Horizontal results are virtually the same on D4's DPR captures. MTFMapper's results' accuracy decreases with increasing noise (see here )
 
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Good idea. People with affected cameras and strobe/lights will want to try it.
I did the test with the A7R, the results are here, scroll down to part II:


I found that there is no discernible difference between an image taken with a strobe while the shutter was open for 10 seconds ie. no shutter vibration and a normal exposure with shutter vibration. I checked with a 35mm FE lens and a Nikon 85mm 1.4 and metabones adapter. I also did not see any difference in the A7R mounted on a sturdy tripod or resting on a table top. Both had image quality matching the strobe image with no shutter vibration.

I feel very comfortable in my conclusion that the A7R is not losing image quality due to shutter vibration.

Comments, criticisms, suggestions welcome.



Here is a summary screen capture:



0fd9633eba1548088a20a021af0b6830.jpg



--
www.beforethecoffee.com
 
Good idea. People with affected cameras and strobe/lights will want to try it.
I did the test with the A7R, the results are here, scroll down to part II:

http://beforethecoffee.com/sony-a7r-vibration-comparison-with-nikon-d3-and-sony-nex-7/

I found that there is no discernible difference between an image taken with a strobe while the shutter was open for 10 seconds ie. no shutter vibration and a normal exposure with shutter vibration. I checked with a 35mm FE lens and a Nikon 85mm 1.4 and metabones adapter. I also did not see any difference in the A7R mounted on a sturdy tripod or resting on a table top. Both had image quality matching the strobe image with no shutter vibration.

I feel very comfortable in my conclusion that the A7R is not losing image quality due to shutter vibration.

Comments, criticisms, suggestions welcome.
Shutter vibration/shock isn't an issue at 1/3 sec. The critical shutter speeds are between 1/40 and 1/250 sec, or so (worst at 1/80 to 1/100 sec).
Here is a summary screen capture:

0fd9633eba1548088a20a021af0b6830.jpg

--
www.beforethecoffee.com
 
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Chris Malcolm wrote:Of course the much bigger and more violent shutter and mirror machinery of full frame DSLRs is a more serious problem. I'm surprised more people haven't remarked on that as a reason to prefer APS-C.
Anders W wrote: I understand what you mean. Nevertheless, it doesn't seem to work that way in practice.
This sounds like you are referring to your own practice, hence you would have plenty of examples available.
Anders W: While I am certainly not saying that FF DSLRs or DSLRs in general are free from the problem, it appears, if anything, to be worse with small and light mirrorless cameras
Then it will be falling off a log for you to show us the full frame flipping-mirror DSLR photo, that you took, say one that was taken on a portable tripod, a real photo not some test setup, with or without a remote shutter release or self-timer, of normal to portrait angle of view, that represents the lesser vibration problem of that type of larger flipping-mirror rig that you describe.

Make sure it's a long exposure, say 1 second like the one below, let's not muddy the waters by you posting an electronic flash photo at 1/8000th of a second or whatever.

Feel free to show us something from a much finer lens and aperture setting than the $50 dollar e.bay Alpha mount plastic kit zoom at F/13 used for this small-cam mirrorless APS-C example. Be nice if your example was from a sensor with an anti-aliasing filter, to further level the playing field.
With regard to long exposures on a tripod, I thought it was common practice among SLR users to use mirror lock-up. At least that's what I did with my SLRs. So I fail to see that blur due to mirror-flap should be much of a practical problem in this particular context. Nor is shutter shock any problem at these shutter speeds. The problem is known to peak at shutter speeds of approximately 1/100 s and disappear more or less gradually as you go faster or slower than that.

Aside from that, I consider visual illustrations like those you show pretty uninteresting as pieces of evidence with regard to the general (and statistical) question at issue here: whether blur due to shutter shock is more prominent with certain camera types than with others.

What you might want to do is utilize the search function here on DPR or on Google and search for "shutter shock" and have a look at the what you come across that way. Not saying that this is in any way conclusive evidence with regard to the objective situation. But I am sure it shows quite convincingly that "shutter shock" is currently perceived to be a far greater problem in MFT circles than in FF DSLR circles.

You might also find this post in the present thread and the subthread it spawns of interest:

http://www.dpreview.com/forums/post/52630115
 
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Good idea. People with affected cameras and strobe/lights will want to try it.
I did the test with the A7R, the results are here, scroll down to part II:

http://beforethecoffee.com/sony-a7r-vibration-comparison-with-nikon-d3-and-sony-nex-7/

I found that there is no discernible difference between an image taken with a strobe while the shutter was open for 10 seconds ie. no shutter vibration and a normal exposure with shutter vibration. I checked with a 35mm FE lens and a Nikon 85mm 1.4 and metabones adapter. I also did not see any difference in the A7R mounted on a sturdy tripod or resting on a table top. Both had image quality matching the strobe image with no shutter vibration.

I feel very comfortable in my conclusion that the A7R is not losing image quality due to shutter vibration.

Comments, criticisms, suggestions welcome.
Shutter vibration/shock isn't an issue at 1/3 sec. The critical shutter speeds are between 1/40 and 1/250 sec, or so (worst at 1/80 to 1/100 sec).
I tested 1/5 1/3 1/10 1/20 1/40 1/80 1/160 1/320..... None looked discernibly different with either lens: 35mm FE28 or the 85mm 1.4. The camera was mounted on a Really Right Stuff tripod, not a rink-dink one.


--
www.beforethecoffee.com
 
Thanks for your quick and precise answer. And sorry for my slow reply.
I feed MTFMapper the two slanted edges separately (labeled Horizontal and Vertical in the graphs), in the form of TIFFs cropped from the grayscale full resolution image obtained by clipping to zero and white balancing the relative Raw data. The data thus obtained is undemosaiced and as raw as it gets - you can read a bit more about my procedure here . Keep in mind that it only works with neutral subjects lit by a well behaved illuminant (such as D50)

What did you find out with your tests?
I have been looking into PAF behavior like accuracy, repeatability, focus shift, AF tuning and AF color sensitivity using MTFMapper profiles. The trouble is to provide a clean data set supporting a clear message that will not be misunderstood. -- It gets too time consuming to do it. -- I may post focus shift data in a new thread later today.

In this thread we have the riddle of 20% difference between vertical and horizontal resolutions occurring one way with A7 and the other way around with D610. Obvious possible causes include vertically running shutter shake, decentered lens, misaligned Bayer filter etc. The A7r at 1/200s seems consistent with vertical shutter shake.

One would wish further investigation to confirm the effect and narrow down on possible causes; or dismiss the effect as not repeatable. 'Easy' to do for somebody with a camera in question (not me) and prepared with MTFMapper; just set up a single slanted edge against a uniform background (perhaps blue or overcast sky) and analyze the images.
 
Thanks for your quick and precise answer. And sorry for my slow reply.
I feed MTFMapper the two slanted edges separately (labeled Horizontal and Vertical in the graphs), in the form of TIFFs cropped from the grayscale full resolution image obtained by clipping to zero and white balancing the relative Raw data. The data thus obtained is undemosaiced and as raw as it gets - you can read a bit more about my procedure here . Keep in mind that it only works with neutral subjects lit by a well behaved illuminant (such as D50)

What did you find out with your tests?
I have been looking into PAF behavior like accuracy, repeatability, focus shift, AF tuning and AF color sensitivity using MTFMapper profiles. The trouble is to provide a clean data set supporting a clear message that will not be misunderstood. -- It gets too time consuming to do it. -- I may post focus shift data in a new thread later today.

In this thread we have the riddle of 20% difference between vertical and horizontal resolutions occurring one way with A7 and the other way around with D610. Obvious possible causes include vertically running shutter shake, decentered lens, misaligned Bayer filter etc. The A7r at 1/200s seems consistent with vertical shutter shake.

One would wish further investigation to confirm the effect and narrow down on possible causes; or dismiss the effect as not repeatable. 'Easy' to do for somebody with a camera in question (not me) and prepared with MTFMapper; just set up a single slanted edge against a uniform background (perhaps blue or overcast sky) and analyze the images.
Would it make any sense to shoot an image with no shutter shake and remove that as a variable? Set up the camera in a dark room, set the timer for 10s and fire some off camera strobes at 7s - enough time to allow any shutter vibrations to dampen.
 
In this thread we have the riddle of 20% difference between vertical and horizontal resolutions occurring one way with A7 and the other way around with D610. Obvious possible causes include vertically running shutter shake, decentered lens, misaligned Bayer filter etc.
The lens used with the D610 appears to be the same as that used with the D4, which resulted in a 'perfect' graph, so I would exclude lens defects like astigmatism/distortion. I would also tend to exclude shutter shock because the difference seems to be constant throughout the measured shutter speed range.

This leaves out-of-focus effects and sensor related differences (microlenses, filters, fill factor).

Assuming the same 85mm:1.8G was used, I believe the Df's DPR studio scene captures are slightly out of focus:

D4 average MTF50 reading ISO 50-12800: 1834 lw/ph

D4 average MTF50 reading ISO 50-12800: 1834 lw/ph

DF average MTF50 reading from ISO 50-12800: 1701 lw/ph - Why the difference?

DF average MTF50 reading from ISO 50-12800: 1701 lw/ph - Why the difference?

Such different readings using the same lens+sensor would suggest that the Df was not focused properly, unless there is something else at play? And the spread between the vertical and horizontal readings in the Df is minimal, therefore reducing out-of-focus' chances as a primary suspect.

If one excludes all of the above the likely culprit starts to look like the sensor, even because the Df and D4 apparently use the same one made by Nikon as opposed to a Sony in the D610 and A7.

Some AA filters are known to produce a directional response (oval shaped for instance). Whether this is desired or the unwanted result of misalignment of the beam-splitting plates is anyone's guess. The vertical/horizontal switch observed between the A7 and the D610 could simply be due to the AA plates being 'misaligned' 90 degrees off in one vs the other.

It would be harder to explain the A7/D610 V/H switch as a result of the shape of the 'fill' factor, since both sensors were designed by Sony and it is suspected that they come off the same fab line. And I am not sure how the CFA could cause such an effect, especially given how the MTF50 measurements are made off the white balanced raw data only.

Jack
 
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It would be harder to explain the A7/D610 V/H switch as a result of the shape of the 'fill' factor, since both sensors were designed by Sony and it is suspected that they come off the same fab line. And I am not sure how the CFA could cause such an effect, especially given how the MTF50 measurements are made off the white balanced raw data only.
The Bayer CFA and, if present the microlens array, are of very different material than the underlying 'silicon' sensor. So its brought up in registry in a later processing step. Obviously there are fabrication tolerances. I could imagine that a very slight displacement of the CFA would lead to a minor light spill and a concomitant reduction of edge contrast in that direction. The next batch has random other displacements inside the tolerance field.

This displacement is wild speculation. A serious discussion would need V/H data from several samples of a camera model.
 
Ok, since this thread has continued so long, I'll add in a couple of outlandish reasons we might see small differences for horizontal vs. vertical readings:
  1. The light-sensitive areas with sensels might not have a 1:1 aspect ratio, perhaps due to paths for wiring. This could lead to slightly wrong interpolation and a small change in effective resolution.
  2. The sensor and lens mount flange might not be precisely parallel. I don't even want to think about this, but absolutely tiny tilts can cause measurable tilting of the focus plane as per the "Scheimpflug principle." This tilt could even be a dynamic function due to shock-absorbing mounting of the sensor.
I'm not saying I think either of these is likely, but they definitely could happen....
 

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