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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

vannira
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  • 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. – vannira Nov 23 '23 at 07:24
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    Does this answer your question? Why is FF sharper than crop body for the same framing of the same object? – Michael C Dec 06 '23 at 10:25
  • 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. – vannira Dec 08 '23 at 23:13
  • 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? – vannira Dec 08 '23 at 23:15
  • And then I was asking, if we compare the 4k smaller sensor equipped with a lens that had a better resolving capabilities to fully resolve each pixel, to the 4k larger sensor with a lens of a lower resolving power, but still resolving able to resolve all the pixels. At the end of the day both those sensors would produce the same 4k image, of for example the test charts LP/mm, so would we as a user of the camera say the smaller sensor optical system has higher resolution or are the resolutions the same? – vannira Dec 08 '23 at 23:24
  • "I suppose this is due to things like diffraction, as smaller sensor would have smaller pixel pitch, leading to the pixels becoming unresolvable sooner." No. It is due to the need to enlarge the results from the smaller sensor to display them at the same size as the larger sensor. Shooting from the same distance, an 80mm f/2.8 lens on a FF camera would demonstrate the same amount of diffraction as a 50mm f/1.8 lens on a 1.6X APS-C crop sensor. Both would also yield the same framing and approximate depth of field (at non-Macro subject distances). – Michael C Dec 09 '23 at 05:03
  • Well I wasn't implying that the diffraction is larger on one or the other, but the relative sizes of the airy disks compared to the pixels, wouldn't that have an affect too? The airy disks would be covering more pixels which would reduce its contrast and make it more difficult to resolve, compared to if the airy disks on the larger sensor? Also I don't understand why enlarging the crop factor image would reduce resolution, if the acquisition of both of them were the same, lets say 4k? – vannira Dec 09 '23 at 21:27
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    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. – Michael C Dec 10 '23 at 02:00

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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.

xenoid
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  • 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. – vannira Nov 23 '23 at 19:08
  • That’s the part that kind of confuses me. – vannira Nov 23 '23 at 19:08
  • 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. If I’m correct this is due to contrast / modulation right? And you are saying that you would then need an even better lens for the small sensor with a better MTF.

    Am I understanding correctly ?

     – vannira Nov 23 '23 at 19:11
  • I assume this is also the reason why smaller sensors with equivalent pixel K values as larger sensors have lower resolution (without taking into account lenses), because for the same resolution the Sensor needs to resolve more LP/mm, which have bigger chances of blurring/becoming unresolvable due to diffraction and what not. (Plus larger sensors allowing for more SNR) – vannira Nov 23 '23 at 19:13
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    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. – xenoid Nov 23 '23 at 20:44
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    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. – xenoid Nov 23 '23 at 20:45
  • But the thing I was asking or saying was that to me and I feel like many others, the terminology of saying the MFT sensor has higher resolution than the FF (if allowed by the lens) would make it sound like the MFT can produce higher resolution images but in reality, due to its smaller size it needs to have higher resolving powers to be able to produce the same image.

    I hope what I just tried to convey makes sense, or am I misunderstanding it?

     – vannira Nov 23 '23 at 21:40
  • Regarding the second point: ah I suppose I was inferring too much. So you were just stating that the MTF needs a lens with better capabilities in both in spatial resolution and modulation transfer? However, I guess I’m not sure but wouldn’t the denser line pattern on the MTF also be much more susceptible to things like airy disk diffractions even with a better lens? – vannira Nov 23 '23 at 21:43
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    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. – xenoid Nov 23 '23 at 22:01
  • Okay, thank you – vannira Nov 24 '23 at 10:01
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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).

Steven Kersting
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  • Thank you for the reply and thank you for the link to the paper – vannira Nov 23 '23 at 19:13
  • 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 ? – vannira Nov 24 '23 at 10:01
  • @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. – Steven Kersting Nov 24 '23 at 14:10
  • 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. – vannira Nov 24 '23 at 18:08
  • @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. – Steven Kersting Nov 24 '23 at 20:48
  • Ah I see, that makes a lot of sense. Thank you so much for the information. – vannira Nov 24 '23 at 22:21
  • MTF is measured as a percentage contrast at a specified number of lines per mm. MTF50 measures contrast at 50 l/mm. MTF10 measures contrast at 10 l/mm, and so on. Roger Cicala's excellent blog entry explaining MTF – Michael C Dec 09 '23 at 05:11
  • @MichaelC, MTF50 is when the resolved contrast drops to 50% (0.5). The l/mm has to do with sensor resolution/pixel size; smaller pixels, more l/mm, more resolution, and lower contrast... 10 l/mm isn't really that relevant to modern sensors anymore. – Steven Kersting Dec 09 '23 at 12:10
  • No. MTF50 is when MTF is measured using 50 line pairs per mm. Try telling Uncle Roger he's wrong. When contrast is 50%, that's a 0.5 MTF measurement, not MTF50. MTF = blackest–whitest/blackest+whitest, which means MTF is always a number between 0 & 1. It's never more than 1.0, which is 100% contrast. – Michael C Dec 10 '23 at 01:57
  • @MichaelC; From your own reference: "If you look at the left side of the graph, the MTF (contrast) measurement, it’s a simple matter to find the MTF50 (or MTF 10 or MTF90 for that matter). It’s simply the frequency (lines per mm) at which the image retain 50% of the test target’s contrast. (Or 10% or 90% of original contrast form MTF10 or MTF90)." And if the test was done at 50l/mm, the results could never be other than 50l/mm... – Steven Kersting Dec 10 '23 at 15:08
  • The scales on the left side of the graphs go from 0% on the loser corner to 100% in the upper corner. Those values are ALL between 0.00 & 1.00. The differently colored lines indicate the percentage contrast at different lp/mm measured tangentially or sagittially. – Michael C Dec 12 '23 at 07:33
  • If you're talking about these charts those aren't lp/mm, either. They're lp/IH. IH=Image Height. – Michael C Dec 12 '23 at 07:39
  • "By convention, MTF graphs use thick and thin lines, like Figure 3 below, to represent the MTF of thicker (10 l/mm) and thinner (30 l/mm) lines. (Not every manufacturer does it, but it would probably be a good idea to also test the lens at its widest aperture and its best aperture, say f/8 for most lenses. MTF charts that do this will use one color for f/8 and another for the widest aperture the lens has. I chose black lines for f/8 and blue for wide open for this illustration)." – Michael C Dec 12 '23 at 07:43
  • Above quote is from: Have You Seen My Acutance? – Michael C Dec 12 '23 at 07:44
  • If you're talking about these graphs, the the scale on the left is still percentage contrast. The scale across the bottom shows lp/mm. As one moves from left to right, the lines show the amount of contrast measured at various numbers of lp/mm. The one linked shows from 10 lp/mm to 90 lp/mm. Every measurement is taken using the same part of the lens FoV, presumably the center. – Michael C Dec 12 '23 at 07:57
  • "At a single point on the lens (right at the center, for example) I can measure the MTF at different frequencies (lines /mm) and make a nice graph of the results. Remember, this isn’t across the entire front of the lens like the very first graph. This is measuring one point on the lens at different frequencies (smaller and smaller lines). Every lens, like the graph below, has lower MTF as the lines get smaller (the frequency gets higher)." – Michael C Dec 12 '23 at 07:58
  • In this chart, for example, the MTF50 would be approximately 40 lp/mm. It's the point on the graph directly above 40 lp/mm on the scale across the bottom of the chart that is directly to the right of 0.50 (50%) contrast on the scale that goes up the side of the chart. Based on the same chart, the MTF30 (0.30 or 30% contrast) is approximately 52 lp/mm. – Michael C Dec 12 '23 at 08:12
  • @MichaelC, exactly... MTF 50 is however many lines can be resolved at 50% contrast. More resolution, smaller pixels, more l/mm, lower contrast... which is what I said in my first response. Your original statement was that MTF50 was measured at 50 l/mm; therefore it couldn't be a 40 l/mm result. And FWIW, l/mm on a manufacturer's MTF chart is the same thing as lp/mm... one counts the spaces between the black lines; and the other does not. – Steven Kersting Dec 12 '23 at 13:56
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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.

osullic
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  • 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. – vannira Nov 23 '23 at 21:48
  • 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. – vannira Nov 23 '23 at 21:50
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    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. – osullic Nov 24 '23 at 11:22
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    Nobody looks at a good photo and feels that what it lacks is a lens that can resolve 200LP/mm over 100LP/mm. – osullic Nov 24 '23 at 11:26
  • 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. – vannira Nov 24 '23 at 19:23