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I was reading this paper which states that

enter image description here

My question is in regards to the first paragraph. I was first imagining, that if I were to try to take the same photo on a smaller sensor as on a large sensor, I would obviously need to use a wider-angle lens, to obtain the same AOV. This would also, as they mention, lead to the sensor needing to resolve more detail per millimeter on the sensor. However, they then mention that the sensor must have a higher resolving power and from my knowledge, when talking about spatial resolving capabilities of a lens (spatial frequency) it has solely with its pixel count.

So when I read the statement, to me it reads that the smaller format sensor needs a higher k value (pixels) than the larger sensor. However, wouldn’t the same K value suffice to obtain the same resolution as limited by the Nyquist limit, albeit as mentioned the SNR will be worse.

Edit: I was also thinking about it that measuring the same resolution (lines/mm) in real life, would lead to more lines/mm on the smaller sensor compared to the larger sensor, but with this thinking the resolution of the real life object imaged is still the same, so idk why we would describe the smaller sensor to have a higher resolving power.

I’m sure there is something I’m misunderstanding, perhaps it relates to the fact that I did ignore contrast or rather assumed both to have equal contrast. I also added an image from Edmund optics to perhaps help show what I was talking about.

enter image description here

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  • \$\begingroup\$ I was also thinking about it that measuring the same resolution (lines/mm) in real life, would lead to more lines/mm on the smaller sensor compared to the larger sensor, but with this thinking the resolution of the real life object imaged is still the same, so idk why we would describe the smaller sensor to have a higher resolving power. \$\endgroup\$
    – vannira
    Nov 23, 2023 at 7:24
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    \$\begingroup\$ Does this answer your question? Why is FF sharper than crop body for the same framing of the same object? \$\endgroup\$
    – Michael C
    Dec 6, 2023 at 10:25
  • \$\begingroup\$ Thank you for your link. It does perhaps address the same points, although I felt like in your answer, you were talking more about changing the distance and how that will lead to smaller sensors needing to resolve more line pairs per mm in addition to their smaller sensor which already needs to resolve more line pairs per millimeter, to achieve resolve the same test chart as on a bigger sensor. However in my example I am strictly talking about , as you also mentioned using different lenses to keep the composition and perspective, practically the whole shot the same. \$\endgroup\$
    – vannira
    Dec 8, 2023 at 23:13
  • \$\begingroup\$ And I was wondering if, I guess as you mention, the fact that the smaller sensor needs a lens with a better resolving capability than the larger sensor, already puts it at a disadvantage. So I am guessing from an optical-engineering standpoint its much easier to obtain a resolution with better contrast from the bigger sensor. I suppose this is due to things like diffraction, as smaller sensor would have smaller pixel pitch, leading to the pixels becoming unresolvable sooner. Is what I have mentioned so far correct? \$\endgroup\$
    – vannira
    Dec 8, 2023 at 23:15
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    \$\begingroup\$ If they're equally blurry as projected on the sensor, and you enlarge what is projected onto the sensor more for one than the other, you also enlarge any blur by the same increased enlargement ratio. That's why. \$\endgroup\$
    – Michael C
    Dec 10, 2023 at 2:00

3 Answers 3

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The resolving power of a sensor is (roughly) its pixel/sensel density. Conveniently, for the same pixels count and aspect ratio, when you decrease the sensor size, you mathematically increase the pixel density, so as long as you don't worry about signal/noise ratio, you are fine.

For instance, assuming a full-frame (FF) and micro-four-thirds (MFT) sensors with 7200 pixels on the long dimension, they can theoretically see 3600 lines pairs (a black and a white line in a regularly spaced vertical grid). This means a line pair is 10µm wide on the FF sensor but only 5µm wide on the MFT, or if you prefer, that the FF sensor sees 100 line pairs per millimeter when the MFT sensor sees 200 line pairs per millimeter.

On the other hand the resolution of a lens is independent of what it is used for (film, FF sensor, MFT sensor...). A lens with a 100LP/mmm resolution can project on its focal plane a pair of distinguishable light and dark lines every 10µm but a denser grid is going to be a blurry mess. So, when used with a FF sensor, everything is fine, but on the MFT sensor it is unable to project a pair of lines every 5µm (assuming you are shooting a finer grid or put it twice as far of course), all the MFT sensor sees is a blurry mess, and to take advantage of the full resolution of the MFT sensor, you would need a lens capable of 200LP/mm.

So, if you want to compare a lens for a full-frame camera with a lens for a smaller sensor (MFT or APS-C), you cannot compare the "raw" lens resolution and have to correct it by the sensor "crop factor".

And, by the way, this isn't only the crop factor. Sensor have evolved quite bit since the beginning of digital photography, and between the 6Mpix sensors of early DSLR and the 40+Mpx of current full-frame cameras, the resolution of sensor in LP/mm has more than doubled (about 2.5x), so lenses with an acceptable resolution from 10 years ago are no longer that good on a recent camera.

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  • \$\begingroup\$ So when you mention “that the FF sensor sees 100 line pairs per millimeter when the MFT sensor sees 200 line pairs per millimeter.“ you are talking about the lines being projected on the sensor right, because theoretically if we shot a test chart of 50 LP/mm and this was the resolving limit of both the large sensor and the smaller sensor, to me as a user, I would say that their resolving capabilities are the same, as they can both resolve 50LP/mm in the real world (object plane), even though at the sensor level the smaller sensor can, in this case, resolve more LP/mm. \$\endgroup\$
    – vannira
    Nov 23, 2023 at 19:08
  • \$\begingroup\$ That’s the part that kind of confuses me. \$\endgroup\$
    – vannira
    Nov 23, 2023 at 19:08
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    \$\begingroup\$ The resolution of the actual test chart is irrelevant. It will often be printed at a much larger size than the sensor. A 36cm test sheet with a 10LP/mm projected on the 36mm of the FF sensor will produce a 100LP/mm pattern on the sensor. But on the MFT it will produce a 200LP/mm pattern... if the lens is good enough. \$\endgroup\$
    – xenoid
    Nov 23, 2023 at 20:44
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    \$\begingroup\$ Furthermore, you also mentioned that a smaller sensor will most likely have more trouble trying to resolve the same amount of LP/mm than a larger sensor as due to their tight densities, the image because a bit more of a mesh... No I didn't say that. The small sensor requires a denser pattern, and this requires more resolution from the lens. \$\endgroup\$
    – xenoid
    Nov 23, 2023 at 20:45
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    \$\begingroup\$ Yes, and yes... But diffraction is a problem at small apertures, poor resolution is a problem at all apertures and especially at the more open ones, that are the ones you want to use to avoid diffraction. \$\endgroup\$
    – xenoid
    Nov 23, 2023 at 22:01
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Resolution as discussed in the article is MTF; which is measured as line pairs per millimeter.

So, the smaller sensor with greater pixel density (same MP) has a higher resolution potential. Whether you make use of that potential (same lens), or not (wider lens), doesn't negate that fact.

Sensor size is rather irrelevant in the discussion of a lens' MTF. And the MTF resolution can be compared across formats as long as the test equipment (bench/camera/sensor) has a resolution at least as high as what you are wanting to use the lens with. I.e. a sensor of lower resolution capability (regardless of size) does not reduce the lens' capability.

What you cannot necessarily do is compare the system MTF of a lens tested on a certain camera body to that of another system. I.e. if the reference system (camera/sensor) may be limiting the MTF results (e.g. low pass filter).

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  • \$\begingroup\$ Thank you for the reply and thank you for the link to the paper \$\endgroup\$
    – vannira
    Nov 23, 2023 at 19:13
  • \$\begingroup\$ So the smaller sensor has better LP/mm resolution when compared to the bigger sensor, but needs the better resolution to resolve the same details at the bigger sensor. However, seeing as they ultimately output a similar resolved image then, so would you say to the average user that that they have the same resolution or the smaller lens has a better resolution ? \$\endgroup\$
    – vannira
    Nov 24, 2023 at 10:01
  • \$\begingroup\$ @vannira, too many variables to say... with modern sensors and photosites ≤ 5um it is seldom that the lens/technique resolves to the level of the sensor. E.g a lens at f/8 is only able to resolve an average of 13MP on an APS sensor due to diffraction; and an inexpensive lens would probably resolve less. \$\endgroup\$ Nov 24, 2023 at 14:10
  • \$\begingroup\$ But so in general smaller sensors do tend to have lower resolving capabilities because they require to resolve more LP/mm and to do that, require a lens with better resolving capabilities, plus other factors like diffraction. Is that correct? Although I did also read that larger sensors are more affected by aberrations. \$\endgroup\$
    – vannira
    Nov 24, 2023 at 18:08
  • \$\begingroup\$ @vannira, Yes, that is correct. But larger sensors are not more affected by aberrations. What may have been meant is that it is harder to design a lens that creates a larger image circle, which the larger format requires, and which is free of aberrations. E.g. images taken with a crop sensor tend to be more evenly sharp across the field because they are only using the center part of the image circle. \$\endgroup\$ Nov 24, 2023 at 20:48
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So when I read the statement, to me it reads that the smaller format sensor needs a higher k value (pixels) than the larger sensor. However, wouldn’t the same K value suffice to obtain the same resolution...

I think so, yes. The same number of pixels (alongside a lens that can resolve adequately) should suffice, I think. This still qualifies, according to the paper writer, as a sensor that has a "higher resolving power" just by virtue of having a higher pixel density.

However, I would question why you are looking into this stuff. Are you doing optics research or something? In my humble opinion, what you should be doing is enjoying photography, taking photos. If you have resolution issues in your results, then you can look at getting a lens with better resolving power. But otherwise I would recommend to anyone with analytical tendencies to stop thinking about the physics of it all and try to remember that photography is about taking photos and telling stories.

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  • \$\begingroup\$ I understand and respect your view on it. However, to me personally, it is for one just something I am interested in and two, I am a strong believer that the technical aspects and science behind the Art is (to me) a cardinal aspect in practicing the Art. \$\endgroup\$
    – vannira
    Nov 23, 2023 at 21:48
  • \$\begingroup\$ Simply by looking back at the Renaissance, it is definitely substantiated that many of the great Artists were skilled in a multitude of facets, such as the sciences, mathematics and much more, which in my opinion, was also very evident in the beauty of their art works. \$\endgroup\$
    – vannira
    Nov 23, 2023 at 21:50
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    \$\begingroup\$ I went to a really wonderful small exhibition of photos by Elliott Erwitt in London last week, and over the weekend in Berlin, another haunting exhibition of photos by Mary Ellen Mark. These are our modern-day Renaissance masters of photography. I get ever more disillusioned with this website, as everyone seems to eventually - maybe I'll stop participating here. StackExchange is built for programmers, not artists. Photography is an art. \$\endgroup\$
    – osullic
    Nov 24, 2023 at 11:22
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    \$\begingroup\$ Nobody looks at a good photo and feels that what it lacks is a lens that can resolve 200LP/mm over 100LP/mm. \$\endgroup\$
    – osullic
    Nov 24, 2023 at 11:26
  • \$\begingroup\$ I definitely am not saying that the in depth science / technical knowledge is needed to create beautiful Art, but to me personally it is important. Furthermore, as you pointed out, I have found that stack exchange photography is the place to ask these more in-depth technical questions in regards to photography, hence why I asked this question on this forum. \$\endgroup\$
    – vannira
    Nov 24, 2023 at 19:23

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