How to decide outresolving?

[lonepal]

Hi;

May be this matter discussed many time but I am still not clear about how to decide if the lens outresolves the sensor or vice versa.

I have a 5X Mitty+Sigma LSA and Canon EOS 100D+Olympus OMD M10 MKII.

Can I get a simple explanation about calculating resolving powers and deciding outresolving?

Thanks!

[mjkzz]

If the pixel size of your sensor is smaller than the resolving power of your lens, your sensor is out resolving the lens.

To get resolving power of your lens, usually you have to read the specs for your lens.

I have read some specs for some line scan lenses, some of them do not indicate resolving power, but recommend a pixel size for the sensor, the actual resolving power is smaller than that.

Your 5X Mitty has resolving power of 2um (https://www.edmundoptics.com/p/5x-mitut ... tive/6621/) and your sensor size is 4.3um, so your lens is out resolving your sensor.

[Lou Jost]

Resolving power in the context of that objective probably means resolving power on the subject, not on the sensor.

[mjkzz]

thanks Lou, I was thinking about 1:1. In case of 5x, I am wrong there.

[enricosavazzi]

Strictly speaking, the only rigorous proof that a lens is outresolving the sensor is by proving that the lens achieves a higher resolution on a second sensor with smaller pixels. Conversely, rigorously proving that the sensor is outresolving the lens requires the sensor to give a higher resolution when used with a known-better lens. In practice, without better terms of comparison there can be no proof.

[Justwalking]

Microscopy calculation
https://www.microscopyu.com/tutorials/m ... resolution

[enricosavazzi]

Microscopy calculation
https://www.microscopyu.com/tutorials/m ... resolution

Assuming that the lens is diffraction limited and that its NA is known, the calculation is simple. A lens cannot be any better than this calculated value.

There is however a lot more that can go wrong, including several types of aberration that can make the lens worse than calculated on the basis of NA and diffraction alone.

[Justwalking]

This is a great article about

https://www2.uned.es/personal/rosuna/re ... esolve.pdf

[enricosavazzi]

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?

[rjlittlefield]

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

[JH]

Hi lonepal

If you have the possibility to test different tube lenses for example 300 mm and 100 mm with your objective you can se if there is any more detail resolved that you want/need in the picture.

For me, the stripes in butterfly scales is sometimes a structure I want to have in my pictures. Here is a post where you can see the difference between a 150 mm and one 360 mm tube lens both used with a 10x objective.

http://www.photomacrography.net/forum/v ... hp?t=35913

For 5x and less magnification -with my type of pictures - I usually think more about field of view than outresolved detail.

Hopes this helps

Best regards
Jörgen Hellberg

[mjkzz]

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.

[enricosavazzi]

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.

The above assumes that the lens is diffraction limited, i.e. that it works close enough to perfectly except for being affected by diffraction (or in other words, that whatever aberrations are present, their visible effect is lesser than the effect of diffraction, and therefore hidden by the latter).

This is a reasonable assumption for a Mitutoyo M Plan Apo in prime condition, based on our experience with these lenses. Of course this does not apply to Mitutoyo M Plan Apos that have been dropped or disassembled, or to lenses of lesser quality.

[Lou Jost]

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

[mjkzz]

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.

The above assumes that the lens is diffraction limited, i.e. that it works close enough to perfectly except for being affected by diffraction (or in other words, that whatever aberrations are present, their visible effect is lesser than the effect of diffraction, and therefore hidden by the latter).

This is a reasonable assumption for a Mitutoyo M Plan Apo in prime condition, based on our experience with these lenses. Of course this does not apply to Mitutoyo M Plan Apos that have been dropped or disassembled, or to lenses of lesser quality.

OK, but still your explanation does not explain if I have a lesser objective with resolving power of 4um due to its construction. Maybe I am missing something here.