Resolution vs format.

Let's say we have two sensors, one twice the size (4x the area) as another, and, for the sake of simplicity, assume no AA filter. Let's say we use two lenses that each have the same resolution (lp/mm) at the same DOF (e.g. f/4 and f/8).

How will the resolution in the photos (lw/ph) compare if:
  • the sensors have the same pixel count?
  • the sensors have the same pixel size?
Repeat the question where the lens used on smaller sensor is twice as sharp (lp/mm) as the lens used on the larger sensor.

Do the answers depend on the contrast level at which the sharpness level is measured?
As I understand it, then lenses designed for a smaller image circle can theoretically be sharper, measured as lp/mm on a sensor with infinite MP count. A mFT lens on a 20mp mFT camera (with smaller pixels) has to be sharper in order to resolve the same lp/ph as a FF lens tested on a 20mp FF camera (with larger pixels). Or to be more accurate, then it should rather be same vertical pixel count, because of the different aspect ratios.

So, are mFT lenses sharper than FF lenses in practice? Have been discussed in many long threads, but not so many hard facts, because the lenses are tested on cameras with different pixel size. Though, should be relatively simple to find out. If testing some good mFT lenses and some good FF lenses + adapter on the same mFT camera, then that should give us a good idea about how sharp the lenses actually are.
 
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Let's say we have two sensors, one twice the size (4x the area) as another, and, for the sake of simplicity, assume no AA filter. Let's say we use two lenses that each have the same resolution (lp/mm) at the same DOF (e.g. f/4 and f/8).

How will the resolution in the photos (lw/ph) compare if:
  • the sensors have the same pixel count?
  • the sensors have the same pixel size?
Repeat the question where the lens used on smaller sensor is twice as sharp (lp/mm) as the lens used on the larger sensor.

Do the answers depend on the contrast level at which the sharpness level is measured?
As I understand it, then lenses designed for a smaller image circle can theoretically be sharper, measured as lp/mm on a sensor with infinite MP count. A mFT lens on a 20mp mFT camera (with smaller pixels) has to be sharper in order to resolve the same lp/ph as a FF lens tested on a 20mp FF camera (with larger pixels). Or to be more accurate, then it should rather be same vertical pixel count, because of the different aspect ratios.

So, are mFT lenses sharper than FF lenses in practice? Have been discussed in many long threads, but not so many hard facts, because the lenses are tested on cameras with different pixel size. Though, should be relatively simple to find out. If testing some good mFT lenses and some good FF lenses + adapter on the same mFT camera, then that should give us a good idea about how sharp the lenses actually are.
Hi,

Yes they are sharper. But not proportionally sharper. Small format makers probably save a lot of money on lenses.

Best regards

Erik
 
And since we are dipping our toes in reality we might as well talk about the fact that if one is not shooting on a tripod with a focus rail two of the biggest issues are going to be camera vibration and focusing performance, both of which problems are amplified on a smaller sensor.
On the one hand smaller pixels will show more vibration due to greater enlargement, on the other hand a longer focal length will magnify vibration. Seems to me this is a wash.
 
Let's say we have two sensors, one twice the size (4x the area) as another, and, for the sake of simplicity, assume no AA filter. Let's say we use two lenses that each have the same resolution (lp/mm) at the same DOF (e.g. f/4 and f/8).

How will the resolution in the photos (lw/ph) compare if:
  • the sensors have the same pixel count?
  • the sensors have the same pixel size?
Repeat the question where the lens used on smaller sensor is twice as sharp (lp/mm) as the lens used on the larger sensor.

Do the answers depend on the contrast level at which the sharpness level is measured?
With my own simplistic model of how cameras work I would say the following:

The same lens is capable of projecting twice as many lines on the larger sensor than it is on the smaller sensor.
It should be noted that on a sensor that is 2.25x larger (FX versus DX for instance) the photosites are 50% larger on the larger format, not 100% larger. Besides that, as a practical matter I have not seen any more appreciable resolution from 12 MP FX sensors versus 12 MP DX sensors. One more thing here, doubling the size of the format increases the difference in DOF by one stop, not two.
If the sensors have the same pixel size, then the larger sensor will capture all of the lines, just like the smaller sensor, so larger sensor captures two times more lines.

If the sensors have the same number of pixels, it now depends what was the limiting factor for the smaller sensor, if it was the lens or the pixel pitch:
  • If lens was the limiting factor, then the larger sensor will be able to capture more lines.
  • If the pixel pitch was limiting then the larger sensor captures the same number of lines.
If one lens is twice as sharp, then both sensors will have projected the same number of lines.
This ignores issues with corner resolution, which (again) as a practical matter and in my experience can be significant. Indeed, I have seen a couple of inexpensive mid-range FX zooms come up short against the lowly Nikkor 18-70 kit lens in the corners at the wider equivalent AOVs and DOF (that is, both being used on my D800 so the FX lens started out with significantly more MP and still couldn't compete in this parameter). I also had problems getting decent corner performance from my A850 at wider than 72° (measured diagonally) over what my D300 could do with a Nikkor 14-24/2.8 attached to it; ultimately this lead me to a Schneider Super Angulon 28mm f/2.8 PC lens (which is now my favorite landscape lens). The bottom line for me has been I will give up some absolute resolution in the center for across the frame performance, and I give up resolution for other things too like perspective control and the ability to tilt the focus plane because those sorts of things do add up in the real world.
If the sensors have the same number of pixels they will be able to capture the same number of lines.

If the sensors have the same pixel size it depends on what the limiting factor was for the smaller sensor:
  • If the pixel size was limiting, then the larger sensor will be able to capture more lines
  • If the lens was the limiting factor, then the larger sensor will capture the same number of lines.
Correct except that a lens doesn't have to be twice as sharp to accomplish this in the real world we live in now, so maybe that becomes an issue in a higher MP future.
 
This ignores issues with corner resolution, which (again) as a practical matter and in my experience can be significant. Indeed, I have seen a couple of inexpensive mid-range FX zooms come up short against the lowly Nikkor 18-70 kit lens in the corners at the wider equivalent AOVs and DOF (that is, both being used on my D800 so the FX lens started out with significantly more MP and still couldn't compete in this parameter). I also had problems getting decent corner performance from my A850 at wider than 72° (measured diagonally) over what my D300 could do with a Nikkor 14-24/2.8 attached to it;
not the same AOV.
ultimately this lead me to a Schneider Super Angulon 28mm f/2.8 PC lens (which is now my favorite landscape lens). The bottom line for me has been I will give up some absolute resolution in the center for across the frame performance, and I give up resolution for other things too like perspective control and the ability to tilt the focus plane because those sorts of things do add up in the real world.
I do not see any reason why corner resolution should be better for smaller formats. My experience is exactly the opposite. The Canon 17-55/2.8 I owned had more problems in the corners than my 24-105/4 on FF (which has a better range, and it is not a particularly spectacular lens).

If you are using FF lenses on crop, you are getting a more uniform performance but you lose AOV and light; but then you can use tilt and shift lenses on FF which are very uniform.
 
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This ignores issues with corner resolution, which (again) as a practical matter and in my experience can be significant. Indeed, I have seen a couple of inexpensive mid-range FX zooms come up short against the lowly Nikkor 18-70 kit lens in the corners at the wider equivalent AOVs and DOF (that is, both being used on my D800 so the FX lens started out with significantly more MP and still couldn't compete in this parameter). I also had problems getting decent corner performance from my A850 at wider than 72° (measured diagonally) over what my D300 could do with a Nikkor 14-24/2.8 attached to it;
not the same AOV.
Sure it is. The AOV of that lens on the D300 ranges from 91.7° to 62° and 72° is around 20mm. In fact, that lens on the D300 offered a wider AOV than the lenses I looked at to use on my A850 which only went to 84°.
ultimately this lead me to a Schneider Super Angulon 28mm f/2.8 PC lens (which is now my favorite landscape lens). The bottom line for me has been I will give up some absolute resolution in the center for across the frame performance, and I give up resolution for other things too like perspective control and the ability to tilt the focus plane because those sorts of things do add up in the real world.
I do not see any reason why corner resolution should be better for smaller formats.
It depends on the lens. As I wrote, for several lenses my results were a step down from what I was accustomed to and I had to do some searching and ended up spending some money to get better results. Indeed, the two copies of the Sony 24-70/2.8 ZA I had when used at focal lengths shorter than 30mm had terrible corners.
My experience is exactly the opposite. The Canon 17-55/2.8 I owned had more problems in the corners than my 24-105/4 on FF (which has a better range, and it is not a particularly spectacular lens).
I'm not saying my experience is universal, but it's something to watch out for and either way it's not being taken into consideration much when comparisons are being made.
If you are using FF lenses on crop, you are getting a more uniform performance but you lose AOV and light;
If you use them in an equivalent fashion than you get the same AOV and the same amount of light (the latter is accomplished by using them more wide open).
but then you can use tilt and shift lenses on FF which are very uniform.
Sure, and then AOV are not going to be the same, so any comparisons there of edge performance when used on a different format would be meaningless.
 
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I'm not saying my experience is universal, but it's something to watch out for and either way it's not being taken into consideration much when comparisons are being made.
This has been discussed a lot and GB even included in his essay as one of the myths ("smaller formats have sharper corners"). Of course, then the reason was that people did not understand equivalence. Then the discussion would drift towards equivalent settings. Still, there is nothing indicating some inherent advantage of the smaller formats. In Canonland, the 17-40, for example, was soft in the corners and when the EF-S 10-22 appeared, if was better in the corners. But then the Nikon UWA (for FF) was considered the gold standard. Then Canon released the 16-35/4 IS which is stellar. Then they released a very sharp 10-18 for the M system, etc. Then the EF 11-24 (for FF) which is considered almost perfect, etc.
 
I'm not saying my experience is universal, but it's something to watch out for and either way it's not being taken into consideration much when comparisons are being made.
This has been discussed a lot and GB even included in his essay as one of the myths ("smaller formats have sharper corners"). Of course, then the reason was that people did not understand equivalence. Then the discussion would drift towards equivalent settings. Still, there is nothing indicating some inherent advantage of the smaller formats.
I didn't say there was an inherent advantage; I said it's something to watch out for and that I have had personal experience having issues with back when I went from shooting with a D300 to an A850 (with lesser pixel density but with more MP). Also, I understand there are equivalence issues, and I stopped the lenses down accordingly to compensate for that.
 
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And since we are dipping our toes in reality we might as well talk about the fact that if one is not shooting on a tripod with a focus rail two of the biggest issues are going to be camera vibration and focusing performance, both of which problems are amplified on a smaller sensor.
On the one hand smaller pixels will show more vibration due to greater enlargement, on the other hand a longer focal length will magnify vibration. Seems to me this is a wash.
Vertical/Horizontal hand shake, for instance, affects the smaller format proportionally more, all else equivalent. DM produced a paper suggesting that most hand vibration is angular in nature but I remember thinking when I read it that it was not focused on the typical photographic setups discussed here. A reason why 3-axis IBIS has quickly been superseded by 5-axis?

Jack
 
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And since we are dipping our toes in reality we might as well talk about the fact that if one is not shooting on a tripod with a focus rail two of the biggest issues are going to be camera vibration and focusing performance, both of which problems are amplified on a smaller sensor.
On the one hand smaller pixels will show more vibration due to greater enlargement, on the other hand a longer focal length will magnify vibration. Seems to me this is a wash.
Vertical/Horizontal hand shake, for instance, affects the smaller format proportionally more, all else equivalent.
All else isn't equivalent though. Focal length for any given FOV is greater for the larger format so that will magnify any shake more. On top of that the longer focal length is a bigger lens, unless we are compensating for maximum apertures, so on telephoto lenses that's likely to add to shaky handling.
DM produced a paper suggesting that most hand vibration is angular in nature but I remember thinking when I read it that it was not focused on the typical photographic setups discussed here. A reason why 3-axis IBIS has quickly been superseded by 5-axis?
Whenever I shoot I try to push the shutter speed up enough to compensate for my shaky grip. Now with a longer lens that means raising the ISO more, so again the two formats are fairly balanced in that regard. I would add here that I have seen a bit more mirror induced vibration (probably shutter too) on 135 format than on APS-C format, but that was mostly at shutter speeds that were at the margins (in fact the lens was mounted on a tripod with no MLU in that test, so add potential motion blur of the subject to real world challenges).
 
And since we are dipping our toes in reality we might as well talk about the fact that if one is not shooting on a tripod with a focus rail two of the biggest issues are going to be camera vibration and focusing performance, both of which problems are amplified on a smaller sensor.
On the one hand smaller pixels will show more vibration due to greater enlargement, on the other hand a longer focal length will magnify vibration. Seems to me this is a wash.
Vertical/Horizontal hand shake, for instance, affects the smaller format proportionally more, all else equivalent.
All else isn't equivalent though. Focal length for any given FOV is greater for the larger format so that will magnify any shake more.
Not really since the image is magnified less in the end.
On top of that the longer focal length is a bigger lens, unless we are compensating for maximum apertures, so on telephoto lenses that's likely to add to shaky handling.
Just the opposite in my case. A heavier lens feels more stable in my hands.
 
Jack Hogan wrote: Vertical/Horizontal hand shake, for instance, affects the smaller format proportionally more, all else equivalent.
All else isn't equivalent though. Focal length for any given FOV is greater for the larger format so that will magnify any shake more.
There is an easy way to visualize the compromises involved in equivalence: insert the mFT sensor half-way between the lens and a FF sensor. Now move both sensors up and down the same absolute amount. Which image is affected more? From this article :

d6fd2ebe51c34f088c84bbf3ddad4617.jpg.png

On top of that the longer focal length is a bigger lens, unless we are compensating for maximum apertures, so on telephoto lenses that's likely to add to shaky handling.
Of course there is going to be a size/weight sweet-spot for the given application, the D500+500mm/5.6 PF being right in there for birding for instance.

But to put a finer point on it, my birding friends remind me that "there's no substitute for square mm of pupil area". Once you start with that premise, equivalent lenses end up pretty well having similar bulk/weight/cost on all real photography formats.

If they don't it's because the relative manufacturer has taken shortcuts, hoping that its intended audience will not notice that they are no longer comparing apples to apples vs the competition :-)

Jack
 
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And since we are dipping our toes in reality we might as well talk about the fact that if one is not shooting on a tripod with a focus rail two of the biggest issues are going to be camera vibration and focusing performance, both of which problems are amplified on a smaller sensor.
On the one hand smaller pixels will show more vibration due to greater enlargement, on the other hand a longer focal length will magnify vibration. Seems to me this is a wash.
Vertical/Horizontal hand shake, for instance, affects the smaller format proportionally more, all else equivalent.

DM produced a paper suggesting that most hand vibration is angular in nature but I remember thinking when I read it that it was not focused on the typical photographic setups discussed here.
EXPERIMENTAL DETAILS

We measured hand motion as a function of time, using small board with a CMOS sensor. The board form factor was chosen to resemble that of a camera-phone. It is approximately 5cm by 9cm and can be held like a camera-phone. During each measurement, the sensor recorded VGA video at 96 fps. The motion was later extracted from the video sequence. The scene emulated a typical indoor scene (300 Lux, target about 2-3 meters away from subject) and the target to be photographed wasan ISO-12233 test chart.

EXPERIMENTAL PROTOCOL

The protocol was very straight forward. The subject aims the board to the test chard (using
a live view on the PC). The live view is then stopped (as is the case for most mobile handsets). The subject then holds the board as steady as possible for 2 seconds. The video stream (VGA@90 fps) is recorded. We used 25 subjects, 20 males and 5 females, aged between 25 and 50 years.

.


What's your beef with the above, Jack ? Please be specific, so I'll know what you are saying.
 
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Let's say we have two sensors, one twice the size (4x the area) as another, and, for the sake of simplicity, assume no AA filter. Let's say we use two lenses that each have the same resolution (lp/mm) at the same DOF (e.g. f/4 and f/8).

How will the resolution in the photos (lw/ph) compare if:
  • the sensors have the same pixel count?
  • the sensors have the same pixel size?
Repeat the question where the lens used on smaller sensor is twice as sharp (lp/mm) as the lens used on the larger sensor.

Do the answers depend on the contrast level at which the sharpness level is measured?
With my own simplistic model of how cameras work I would say the following:

The same lens is capable of projecting twice as many lines on the larger sensor than it is on the smaller sensor.
It should be noted that on a sensor that is 2.25x larger (FX versus DX for instance) the photosites are 50% larger on the larger format, not 100% larger. Besides that, as a practical matter I have not seen any more appreciable resolution from 12 MP FX sensors versus 12 MP DX sensors. One more thing here, doubling the size of the format increases the difference in DOF by one stop, not two.
This part should not be controversial. Was not making any statements regarding how many lines the sensor would capture. Just that if you have twice the distance, then you will also have twice the lines at the same line density per mm.

The question was to compare sensors differing 4x in area, not 2x. Maybe that explains your remark about DOF and photosites.
If the sensors have the same pixel size, then the larger sensor will capture all of the lines, just like the smaller sensor, so larger sensor captures two times more lines.

If the sensors have the same number of pixels, it now depends what was the limiting factor for the smaller sensor, if it was the lens or the pixel pitch:
  • If lens was the limiting factor, then the larger sensor will be able to capture more lines.
  • If the pixel pitch was limiting then the larger sensor captures the same number of lines.
If one lens is twice as sharp, then both sensors will have projected the same number of lines.
This ignores issues with corner resolution, which (again) as a practical matter and in my experience can be significant. Indeed, I have seen a couple of inexpensive mid-range FX zooms come up short against the lowly Nikkor 18-70 kit lens in the corners at the wider equivalent AOVs and DOF (that is, both being used on my D800 so the FX lens started out with significantly more MP and still couldn't compete in this parameter). I also had problems getting decent corner performance from my A850 at wider than 72° (measured diagonally) over what my D300 could do with a Nikkor 14-24/2.8 attached to it; ultimately this lead me to a Schneider Super Angulon 28mm f/2.8 PC lens (which is now my favorite landscape lens). The bottom line for me has been I will give up some absolute resolution in the center for across the frame performance, and I give up resolution for other things too like perspective control and the ability to tilt the focus plane because those sorts of things do add up in the real world.
True, working assumption was that both lenses resolve same lines/mm.
If the sensors have the same number of pixels they will be able to capture the same number of lines.

If the sensors have the same pixel size it depends on what the limiting factor was for the smaller sensor:
  • If the pixel size was limiting, then the larger sensor will be able to capture more lines
  • If the lens was the limiting factor, then the larger sensor will capture the same number of lines.
Correct except that a lens doesn't have to be twice as sharp to accomplish this in the real world we live in now, so maybe that becomes an issue in a higher MP future.
So you’re saying that the lenses are not currently the limiting factor in sharpness, so going to a smaller format might require sharper lenses to keep the same result, but they don’t have to be sharper by a factor equal the crop factor.
 
Detail Man wrote: What's your beef with the above, Jack ? Please be specific, so I'll know what you are saying.
Hey DM, sure.

I would assume that the 3D pattern of typical hand-motion experienced while taking a smartphone picture is quite different from that experienced while capturing a photo with an advanced ILC setup. What is negligible in one may not be negligible in the other, especially when one would guess that there is an order of magnitude difference in the range of motion. So before discounting V/H motion altogether I'd prefer to see data more relevant to this audience.

Plus there is that nagging question in the back of my head: if V/H motion is so immaterial, why have 5-axis IBIS? Stick with 3, which actually gives better performance on a tripod.

Jack
 
Detail Man wrote: What's your beef with the above, Jack ? Please be specific, so I'll know what you are saying.
Hey DM, sure.

I would assume that the 3D pattern of typical hand-motion experienced while taking a smartphone picture is quite different from that experienced while capturing a photo with an advanced ILC setup.
How so ? Hands still tremble. Higher mass may tend to stabilize range of physical motion. Not clear how much mass (may) affect the frequency spectrum. In your favor, the paper states:

It has been shown that motion blur is affected (among other factors) by camera mass, and so the situation in camera-phones and other hand-held devices might be different.

But that issue is a separate matter from the kind of speculation that you are engaging in ?
What is negligible in one may not be negligible in the other, especially when one would guess that there is an order of magnitude difference in the range of motion.
You mean some (absolute) physical movement distance (as opposed to per image-frame) ?
So before discounting V/H motion altogether I'd prefer to see data more relevant to this audience.
Before discounting Etay Mar Or and Dmitry Pundik altogether, I'd like to know concretely why.
Plus there is that nagging question in the back of my head: if V/H motion is so immaterial, why have 5-axis IBIS? Stick with 3, which actually gives better performance on a tripod.
Regardless of sensor format, linear motion becomes significant at close subject distances. The angular motion-detector output data are converted to a linear equivalent values, and summed together with the linear motion-detector output data to generate a correction signal, anyway. While one is at it, why not throw in linear motion-sensing, and call it "Olympus 5-D Magic" ?

Besides, at less than around 30 cm, lenses on larger image-sensor format cameras cannot focus on subject matter - whereas smaller image-sensor format cameras can focus at 3 cm. Past 30 cm (per Or, Pundik), the large-format (linear motion) advantage diminishes. I myself see your (linear motion) premise becoming rather "boxed-in" on the above multiple fronts.
 
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You are indeed Detail Man, DM.

Call me St. Thomas, in the absence of data closer to home I remain unfettered - and wondering about the need for 5-axis IBIS (3 is so much thinner:-)

Jack
 
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You are indeed Detail Man, DM.

Call me St. Thomas, in the absence of data closer to home I remain unfettered - and wondering about the need for 5-axis IBIS (3 is so much thinner:-)
Perhaps doubt is the first article of faith, my friend. What matters is what we doubt, why, and when. And indeed, "we call first truths those we discover after all the others." (Albert Camus)

"Bigger" be always "more better" (in the macho nerd-world of shiny gear worship), I'm afraid that they are already up to 6-axis (with more dimensions likely very soon to be discovered):

The iNEMOTH is the new range of inertial motion sensors from ST and includes the 6-axis motion-sensing IC, the LSM5D53H ...

... advantage of a 6 axis quadcopter is that combining the six sensors can detect both unusual attitude and a fall. By centralizing the pitch controls and applying throttle, the 6 axis quad comes to a stable hover. This will help bring it to desired height if it’s flying too high or reposition it to an upright position if it’s flying facing an opposite side like upside down. Even if your quad tumbles while reducing altitude, you just have to increase the throttle before it touches down to make it stable. (I’m sure we have all done that before).

6-Axis Image Stabilization Updates for Most Lumix Lenses

All hail the Consumer State - where power mistaken for knowledge is the engineered outcome.

:P
 
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Let's say we have two sensors, one twice the size (4x the area) as another, and, for the sake of simplicity, assume no AA filter. Let's say we use two lenses that each have the same resolution (lp/mm) at the same DOF (e.g. f/4 and f/8).

How will the resolution in the photos (lw/ph) compare if:
  • the sensors have the same pixel count?
  • the sensors have the same pixel size?
Repeat the question where the lens used on smaller sensor is twice as sharp (lp/mm) as the lens used on the larger sensor.

Do the answers depend on the contrast level at which the sharpness level is measured?
As I understand it, then lenses designed for a smaller image circle can theoretically be sharper, measured as lp/mm on a sensor with infinite MP count. A mFT lens on a 20mp mFT camera (with smaller pixels) has to be sharper in order to resolve the same lp/ph as a FF lens tested on a 20mp FF camera (with larger pixels). Or to be more accurate, then it should rather be same vertical pixel count, because of the different aspect ratios.

So, are mFT lenses sharper than FF lenses in practice? Have been discussed in many long threads, but not so many hard facts, because the lenses are tested on cameras with different pixel size. Though, should be relatively simple to find out. If testing some good mFT lenses and some good FF lenses + adapter on the same mFT camera, then that should give us a good idea about how sharp the lenses actually are.
Hi,

Yes they are sharper. But not proportionally sharper. Small format makers probably save a lot of money on lenses.

Best regards

Erik
Well, lenses for 'small' formats can be expensive enough, so maybe you could also say that they make a lot of money on lenses ;-) But are you saying that if for example comparing FF and mFT lenses, then mFT lenses will be sharper as a general rule (with exceptions) if measured as lp/mm on sensors with same pixel size, but not quite sharp enough to resolve the same lp/ph (or lw/ph) as FF lenses if tested on cameras with same vertical pixel count? If so, that's my impression too.
 
And since we are dipping our toes in reality we might as well talk about the fact that if one is not shooting on a tripod with a focus rail two of the biggest issues are going to be camera vibration and focusing performance, both of which problems are amplified on a smaller sensor.
On the one hand smaller pixels will show more vibration due to greater enlargement, on the other hand a longer focal length will magnify vibration. Seems to me this is a wash.
Vertical/Horizontal hand shake, for instance, affects the smaller format proportionally more, all else equivalent.
All else isn't equivalent though. Focal length for any given FOV is greater for the larger format so that will magnify any shake more.
Not really since the image is magnified less in the end.
That's why it's a wash. On the one hand (smaller format) you have more pixels per mm of sensor area recording more shake, and on the other hand you have more magnification of that camera shake. If the shake is the same in both instances then it's going to end up the same in the end result.
On top of that the longer focal length is a bigger lens, unless we are compensating for maximum apertures, so on telephoto lenses that's likely to add to shaky handling.
Just the opposite in my case. A heavier lens feels more stable in my hands.
For me it depends on how heavy the lens is and for how long I am trying to hold it steady.
 

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