How to decide outresolving?

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Lou Jost
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Post by Lou Jost »

I have an empirical test which I think would show that a lens is outresolving the sensor. I look for a target with linear features of high contrast (like the edges of light-colored butterfly scales against black scales). I line up the specimen so that the lines are parallel to the sensor edge. Of course the target won't be aligned perfectly with the boundaries of the pixels, but if you search around, it should be possible to find a point on an edge that coincides with a pixel boundary. If you can find a point on the boundary where a bright pixel sits next to a dark pixel with no intermediate gray pixel, then the lens is outresolving the sensor.

Justwalking
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Re: How to decide outresolving?

Post by Justwalking »

enricosavazzi wrote:
Justwalking wrote:This is a great article about

https://www2.uned.es/personal/rosuna/re ... esolve.pdf
Exactly to what in the article are you referring to?
About understanding joint work of both lens and sensor in terms of their resolution ability.

JH
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Post by JH »

Lou Jost wrote:Jorgen, in the post that you linked to, what do the magnifications (like "480x") mean?
Hi Lou Jost

Sorry for contributing to the x factor mist.

If I recall correctly this was the enlargement number I used on screen (the % value under Adobe PS ”Navigator”.) before I used Windows screen snipping tool. In practice the obvious meaning is that I had to enlarge the picture taken with the 150 mm tube lens more than the picture taken with the 360 tube lens to have the same size on screen.

Best regards
Jörgen Hellberg
Jörgen Hellberg, my webbsite www.hellberg.photo

rjlittlefield
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Re: How to decide outresolving?

Post by rjlittlefield »

mjkzz wrote:
rjlittlefield wrote: The 5X Mitty has NA = 0.14 . You can't set that combination into the microscopyu calculator or find it in their table.

However, their underlying formulas are pretty simple:

[light wavelength in microns] lambda = 0.55
[effective aperture at sensor] feff = m/(2*NA)
[cutoff frequency] nu_0 = 1/(lambda*feff)
[pixel size] = (1/2) * (1/nu_0)
From the above, they are all theoretical, I do not see the resolving power of 2um, specified by Mitutoyo, has any effect at all. Does this mean we can ignore that 2um spec? If so, it does not make sense. Say we have a mediocre 5x 0.14NA, but built with lesser glasses, so it has resolving power of 4um. With above theoretical analysis, it seems it does not matter if an objective has 2um or 4um resolving power.

Maybe I am missing something.
As Enrico said, the formulas assume that the lens resolution is limited only by diffraction. This is typical of microscope objectives in the center of their field. Additional abberations make the MTF curve sag compared to just diffraction, but it would take a very bad or damaged objective to have a lower cutoff than the one implied by diffraction alone.

If you have a lens spec like 4 um on subject, then you can combine that with magnification and Nyquist (2 pixels per resolution element) like this:

[pixel size] = (1/2) * magnification * [specified lens resolution]

So the Mitutoyo, with a specification of 2 um resolution, would calculate this way as pixel size = (1/2)*5*2 = 5 microns. That's the same as Nikon's calculation of 4.9 microns, to within rounding error.

But if you had a 5X lens specified as 4 um resolution, you would calculate as pixel size = (1/2)*5*4 = 10 microns.

--Rik

mjkzz
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Re: How to decide outresolving?

Post by mjkzz »

rjlittlefield wrote:
If you have a lens spec like 4 um on subject, then you can combine that with magnification and Nyquist (2 pixels per resolution element) like this:

[pixel size] = (1/2) * magnification * [specified lens resolution]

So the Mitutoyo, with a specification of 2 um resolution, would calculate this way as pixel size = (1/2)*5*2 = 5 microns. That's the same as Nikon's calculation of 4.9 microns, to within rounding error.

But if you had a 5X lens specified as 4 um resolution, you would calculate as pixel size = (1/2)*5*4 = 10 microns.

--Rik
Thanks Rik, I think [pixel size] = (1/2) * magnification * [specified lens resolution] totally makes sense.

On the other hand, could we interpret that formula this way:

For a GIVEN real (vs idealized) lens with [specified lens resolution] on subject side, designated it as R_sub, and [actual magnification] M_real, in real application, the lens projects resolvable object onto the sensor resulting an image of R_sub*M_real size, then apply sampling theorem, we get maximum pixel size to be (R_sub*M_real) / 2, ie, you have to sample it at least twice, this is the same as yours, but looked at different way.

For example, if a lens with specified resolving power (on subject side) of 4um is used as 5x lens, the maximum pixel size is 4*5/2= 10um.

So if we interpret this way, we really do not need those theoretical calculation, the real (vs idealized) pixel size requirement is ultimately determined by the real resolving power of the lens.

I think one coincidental factor is that most objective manufacturers specify their objectives with a resolving power VERY close to theoretical value, leading us (at least me) always think in theoretical way, but when it comes to real world, we can not use those formulas anymore. I have mentioned this (puzzling fact) in another thread, now, it ([pixel size] = (1/2) * magnification * [specified lens resolution]) is pretty clear.

Do not want to deviate Omar's thread into, yet another, discussion of finding optimal "matching" sensor for a given lens, so I PROBABLY will start another thread for that, I say probably because we had enough of similar discussion already :D

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Re: How to decide outresolving?

Post by rjlittlefield »

mjkzz wrote:this is the same as yours, but looked at different way
I confess I don't see the difference. The thought sequence that you describe sounds like what was going on inside my head when I wrote the formula. But if you're more comfortable now, I'm delighted.
discussion of finding optimal "matching" sensor for a given lens, so I PROBABLY will start another thread for that, I say probably because we had enough of similar discussion already :D
Emotionally I agree about the last part. But technologically I'm not sure. I cannot resist pointing out here that the Mitty 5X will be operating at effective f/17.9 on the sensor side, so its Airy disk diameter will be 2.44 * 0.55 * 17.9 = 24 um. At 5 um recommended pixel size, that calculates out to 24 / 5 = 4.8 pixels per Airy disk diameter. I'm hoping you do not have in mind resuming a position that 2 pixels per Airy disk diameter is all that's needed.

--Rik

lonepal
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Post by lonepal »

Dear all;

Thanks for the very useful informations.
I am more clear now.
Regards.
Omer

lonepal
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Re: How to decide outresolving?

Post by lonepal »

rjlittlefield wrote:
lonepal wrote:I am still not clear about how to decide if the lens outresolves the sensor or vice versa.
...
Can I get a simple explanation about calculating resolving powers and deciding outresolving?
The first thing to realize is that there's no clear dividing line. As you move toward wider apertures, diffraction is less of an issue and the lens can clearly outresolve the sensor. As you move toward narrower apertures, diffraction is more of an issue and the sensor can clearly outresolve the lens. But there's a big murky area in the middle where image quality is affected significantly by both diffraction and pixel size.

Nikon's calculation at https://www.microscopyu.com/tutorials/m ... resolution gives exactly 2 pixels per cycle at the cutoff frequency of the lens. In other words, it barely meets the Nyquist sampling criterion, at the level of detail where MTF drops to zero anyway. On the other hand, this means that it puts 4 pixels per cycle at the level of detail where an aberration-free lens will have about 39% MTF due to diffraction. This pixel size puts Nikon's recommended pixel size smack in the middle of the murky zone. Using smaller pixels would improve the image, and so would using a wider aperture.
I have a 5X Mitty+Sigma LSA and Canon EOS 100D+Olympus OMD M10 MKII.
The 5X Mitty has NA = 0.14 . You can't set that combination into the microscopyu calculator or find it in their table.

However, their underlying formulas are pretty simple:

[light wavelength in microns] lambda = 0.55
[effective aperture at sensor] feff = m/(2*NA)
[cutoff frequency] nu_0 = 1/(lambda*feff)
[pixel size] = (1/2) * (1/nu_0)

Plugging your Mitty's numbers into those formulas gives pixel size = 4.9 microns, as Nikon's recommendation for "matching". Your Canon EOS 100D has a pixel size of 4.29 microns, so it's a hair better than Nikon's recommendation. Your Olympus OMD M10 MKII has a pixel size of 3.74 microns, so it's a hair better yet in terms of pixel size, but at the cost of covering only 68% as much of the field area.

All of this casually assumes that lambda = 0.55 micron (green) is the appropriate value to use. If your subject is strongly blue, then the lenses will resolve finer detail while the sensors resolve less because the Bayer filter only uses one photosite out of every 2x2 for blue. Those two effects, working together, mean that just switching subjects from green to blue can change your system from being a little on one side of "matched" to being strongly on the other side.

--Rik
Thanks for the great explanation Rik.

Do you think which sensor size is better for macro? APSC or m4/3?

I understood that m4/3 sensor resolves finer detail but field coverage is worse. Which one is important for you coverage or resolving power?

I also got one more question. The f numbers on the lenses means the same light amount for all sensor types?

For example we have a nifty-fifty f/1.8 that has a FF coverage.

For FF it is 50mm f/1.8
For APSC it is 80mm f/2,88
For m4/3 it is 100mm f/3,6

Should we multiply it with the crop factor according to the sensor size? Because I think when the sensor gets smaller, it takes in less light.

But if the lens is designed for related sensor size for example a 25mm f/1,2 m4/3 lens, it is f/1,2 for m4/3 sensor.

Is it right?
Regards.
Omer

mjkzz
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Re: How to decide outresolving?

Post by mjkzz »

rjlittlefield wrote:
mjkzz wrote:this is the same as yours, but looked at different way
I confess I don't see the difference. The thought sequence that you describe sounds like what was going on inside my head when I wrote the formula. But if you're more comfortable now, I'm delighted.
discussion of finding optimal "matching" sensor for a given lens, so I PROBABLY will start another thread for that, I say probably because we had enough of similar discussion already :D
Emotionally I agree about the last part. But technologically I'm not sure. I cannot resist pointing out here that the Mitty 5X will be operating at effective f/17.9 on the sensor side, so its Airy disk diameter will be 2.44 * 0.55 * 17.9 = 24 um. At 5 um recommended pixel size, that calculates out to 24 / 5 = 4.8 pixels per Airy disk diameter. I'm hoping you do not have in mind resuming a position that 2 pixels per Airy disk diameter is all that's needed.

--Rik
OK, I was only trying to interpret your formula from a different angle, good thing it coincides with your derivation process.

As for the 2 pixels for airy disc, I think that was in the context of Cambridge In Color discussion where CIC uses 2.5 pixels as CoC (vs my 2 pixels). This does not mean the pixel size can not go lower, it only means for a given lens/obj, at this pixel size, the resultant MFT would not be zero. Or interpreted another way, it is the point where pixels start to go bad. Sure that path (pixel going bad) is probably gradual, but we have to draw a line somewhere (to define an acceptable MFT)

There are still a lot of things remain unclear for me and I need to do some experiment or read some reliable articles. For example, for a normal lens, magnification is very, very low, that formula suggests very very small pixel size. Another thing is, what happens to a measurement target filled with line pairs with exactly same width (each line, not pair) as resolving power, then look through that optical device? A complete gray card?

Anyways, I will find answer for those unclear things when I have time. But thanks for all the things, very educational.

Justwalking
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Re: How to decide outresolving?

Post by Justwalking »

Can i put a spoon of tar, please?

The general rule for an optimal sampling is 2 pixels per Airy disk diameter in monochrome sensors, which match the Nyquist rate of 2 pixels per line pair.
To resolve pairs of lines (one black, one white), and in order to do so you need two pixels, one for each line. This is true only if the lines and the pixels are perfectly aligned, this is, if signal and sampling are in phase. But we cannot expect it, so the number of pixels per line pair should be higher than two. Usual photographic subjects aren’t pairs of high contrast black and white lines on a plane.
In Bayer type sensors the sampling unit is not the pixel, but the 2x2 matrix formed by 2 green, 1 red and 1 blue pixels. Then, in order to avoid chromatic aliasing the sampling must be doubled, this is, 4 pixels per Airy disk diameter.

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Re: How to decide outresolving?

Post by Pau »

lonepal wrote:Do you think which sensor size is better for macro? APSC or m4/3?
It depends of the lenses you use
I understood that m4/3 sensor resolves finer detail but field coverage is worse. Which one is important for you coverage or resolving power?
It can do it only if it has smaller pixels.
I also got one more question. The f numbers on the lenses means the same light amount for all sensor types?

For example we have a nifty-fifty f/1.8 that has a FF coverage.

For FF it is 50mm f/1.8
For APSC it is 80mm f/2,88
For m4/3 it is 100mm f/3,6

Should we multiply it with the crop factor according to the sensor size? Because I think when the sensor gets smaller, it takes in less light.

But if the lens is designed for related sensor size for example a 25mm f/1,2 m4/3 lens, it is f/1,2 for m4/3 sensor.

Is it right?
No, it isn't

If a lens is 50mm f1.8 it is the same with FF, APSc or 3/4. You're cropping more or less the lens image circle. Is much better to think about crop factor than in the in some cases useful but misleading focal length equivalence

Yes, an smaller sensor will capture less light just because the image is cropped.

Rik would explain all this much better, of course.
Pau

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Re: How to decide outresolving?

Post by rjlittlefield »

lonepal wrote:Do you think which sensor size is better for macro? APSC or m4/3?

I understood that m4/3 sensor resolves finer detail but field coverage is worse. Which one is important for you coverage or resolving power?
They both work well. I would decide on the basis of other features of the cameras. Some of the new m4/3 are very good at shooting focus stacks automatically, excellent for field work. For studio work I would probably go with APSC because it's a little better match for microscope objectives.
I also got one more question. The f numbers on the lenses means the same light amount for all sensor types?

For example we have a nifty-fifty f/1.8 that has a FF coverage.

For FF it is 50mm f/1.8
For APSC it is 80mm f/2,88
For m4/3 it is 100mm f/3,6

Should we multiply it with the crop factor according to the sensor size? Because I think when the sensor gets smaller, it takes in less light.

But if the lens is designed for related sensor size for example a 25mm f/1,2 m4/3 lens, it is f/1,2 for m4/3 sensor.

Is it right?
No, not right. The nifty fifty f/1.8 lens is f/1.8 for all sensor sizes. As Pau explained, the lens is also 50mm for all sensor sizes; smaller sensors just crop smaller. Because of the crop, sometimes people say that 50 mm on m4/3 is "just like" 100 mm on FF. That is a useful equivalence when shooting at long distance, like landscapes or even portraits. But for macro work it breaks down. Better to just think that it's a 50 mm f/1.8 lens being used with a crop factor sensor.

As for "less light", I don't know what you mean by that. If say f/8, ISO 400, 1/125 second is the proper exposure on FF, then the very same combination (f/8, ISO 400, 1/125 second) will also be proper exposure on APSC and m4/3. If you have more questions about this aspect, please ask again in more detail.

--Rik

Justwalking
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Re: How to decide outresolving?

Post by Justwalking »

lonepal wrote:
But if the lens is designed for related sensor size for example a 25mm f/1,2 m4/3 lens, it is f/1,2 for m4/3 sensor.

Is it right?
In order to make relevant comparisons among formats, a common point of reference must be adopted.
For a smaller format to resolve the same detail in absolute terms than a bigger format (the same detail in a A3 print, for instance), it must resolve more detail per millimeter on the sensor (or negative). Then, lenses and sensors of smaller formats must have higher resolving power for approaching the detail captured by larger formats.

The point here is that you cannot directly compare the MTF curves of a lens designed for 35mm format, and a lens designed for APS-C or Four Thirds format. Even if you use a lens designed for 35mm format on a cropped sensor, the relative performance of that lens is difficult to measure.
The 40lp/mm resolution curves for 35mm format are equivalent to 60lp/mm resolution curves in APS-C format (x1.5 crop factor), to 80lp/mm curves in a 4/3 format(x2 crop factor).

Lou Jost
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Post by Lou Jost »

I'm playing with a crazy m=5 photolithography lens right now. It greatly outresolves any sensor I can put under it, and it is easy to see this just by pixel-peeping at the image. I'll post some examples in the next few days. It will show you what to look for when checking a real-world lens. Diffraction-based calculations assume perfect lenses, as mentioned above, and no lens is perfect, so it is worth checking empirically, especially if the lens is not a microscope objective.

Justwalking
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Post by Justwalking »

Lou Jost wrote:I'm playing with a crazy m=5 photolithography lens right now. It greatly outresolves any sensor I can put under it, and it is easy to see this just by pixel-peeping at the image. I'll post some examples in the next few days. It will show you what to look for when checking a real-world lens.
Lou, what is the resolution limit of this lens?

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