Why are numerical aperture and color correction related?

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farnsy
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Why are numerical aperture and color correction related?

#1 Post by farnsy » Thu Apr 29, 2021 12:43 am

At a fixed magnification, there is a positive relation between the degree of color correction in an objective and its numerical aperture. A 40X achromat may have an NA of .65, while the 40X fluor has .75 and the 40X apo has .95. I'm not clear on why this relation exists. My understanding is the NA is determined by the angle of light the objective captures and color correction is achieved via other lenses in the system that undo the breaking of the light into its component colors by the magnifying lens. It's not clear that they two specifications need to be related. In other words could they easily make a lens with high NA but no color correction (perhaps for use with monochromatic light)? Or could there be lenses with excellent color correction but low numerical aperture for their magnification?

I can think of a few possibilities:
  • High numerical aperture and color correction are both expensive, so expensive lenses tend to have both, despite the two being independently achieved
  • There is no point in having high NA if the additional detail is being blurred out by chromatic aberrations (and no point in great color correction if you have low detail)
  • The additional lenses involved in color correction somehow also make it possible to have higher NA
  • At low numerical aperture, it's somehow difficult to achieve good color correction
  • When you have good color correction, it's somehow easier to have a higher numerical aperture.
Can you help me understand if it is one of the above situations (or a combination), or perhaps something I have not thought of? What's the theory behind this?

PeteM
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Re: Why are numerical aperture and color correction related?

#2 Post by PeteM » Thu Apr 29, 2021 1:17 am

You might look up "Airy disc." Here's ar rough explanation.

Diffraction limits the ability to distinguish / resolve any two closely-spaced points on a specimen when magnified in a microscope. Two very closely spaced points that we're trying to see as distinct, can be represented as Airy discs that that either overlap or are seen as separated.

Higher NA objectives, with their higher light-gathering ability, will have smaller Airy discs and thus higher resolution.

Better corrected objectives will also have smaller Airy discs - there's not so much a muddle of colors magnified differently.

So the sensible thing in designing any objective is to aim for the best possible resolution possible at any magnification at any given price point and with any given immersion medium.

Plan achromats end up limited by what might be considered color smudging - various aberrations.

Plan fluorite glass costs more, but can be better color corrected (and thus have those smaller Airy discs).

Plan apos have additional lens elements to do even better color correction, but thos typically cosst a lot more.

To add: there aren't always huge differences in NA at the high end. For example, Olympus has made 100x oil achromats with 1.25 and 1.3 NA, semi-fluorite to plan fluorite with 1.25 to 1.4 NA, and plan apos (if memory serves) from 1.35 to 1.4 NA.
Last edited by PeteM on Thu Apr 29, 2021 1:21 am, edited 2 times in total.

Matador
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Re: Why are numerical aperture and color correction related?

#3 Post by Matador » Thu Apr 29, 2021 1:18 am

I think it's the resolution that is better when the NA is higher.
There are formulas where you can see that resolution depends on NA: https://www.microscopyu.com/tutorials/i ... ion-airyna

Matador

Matador
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Re: Why are numerical aperture and color correction related?

#4 Post by Matador » Thu Apr 29, 2021 1:21 am

Also, since resolution also depends on light wavelengs, you get better resolution for the same objective if you use blue light (shorter wavelenght) than if you use red light (higher wavelength).

Matador

farnsy
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Re: Why are numerical aperture and color correction related?

#5 Post by farnsy » Thu Apr 29, 2021 2:04 am

Interesting stuff. So is the following a reasonable restatement of what y'all are saying?

Both (poor) color correction and (low) numerical aperture limit the resolution of the image, so objective makers choose a degree of color correction and an NA that pretty much both bind at the same time. That way, potential resolution gains by one of those specifications are not wasted due to limitations in the other.

That sounds like the two properties can by changed independently, but they aren't because of the generality of the expected use cases. Therefore, it would be possible to have a very high NA objective with no color correction that might be useful for specialized uses where monochromatic light is used to determine an object's shape, but its color is not of interest.

MichaelG.
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Re: Why are numerical aperture and color correction related?

#6 Post by MichaelG. » Thu Apr 29, 2021 8:22 am

farnsy wrote:
Thu Apr 29, 2021 2:04 am
That sounds like the two properties can by changed independently, but they aren't because of the generality of the expected use cases. Therefore, it would be possible to have a very high NA objective with no color correction that might be useful for specialized uses where monochromatic light is used to determine an object's shape, but its color is not of interest.
.

In a word ... Yes

... and you might like to include planarity in the mix of options: If you can accept a part-spherical image plane, then it allows the lens designer much more freedom to optimise other aspects.
Ref. https://en.wikipedia.org/wiki/Petzval_field_curvature

MichaelG.
Too many 'projects'

Hobbyst46
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Re: Why are numerical aperture and color correction related?

#7 Post by Hobbyst46 » Thu Apr 29, 2021 11:08 am

Note, that there are other important features of the objective, such as working distance, depth of focus, number of glass elements, correction for coverslip thickness, which are taken into consideration.

apochronaut
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Re: Why are numerical aperture and color correction related?

#8 Post by apochronaut » Thu Apr 29, 2021 3:00 pm

Colour correction and resolution are quite independent factors in an objective but reduced levels of either or both interacts with the other, potentially overlapping and obscuring one another.
An acceptable but not perfect analogy is the effect on the image of a coin in the bottom of a pool. The airy disc separation mentioned above is like dropping two stones in the water creating interacting ripples, representing diffraction. The chromatic aberration and spherical aberration are represented by the displacement of the image of the coin, relative to it's actual position as you view it from above. The ripples( diffraction) can obscure the image of the coin. The displacement will distort it's image, even if the stones were not dropped. The two together is a disaster.
If we were to replace the water with some sort of clear syrup, then the ripples would be much less or non existent and they would not obscure the image of the coin as much. This represents an increase in N.A. However , the dispersion of the light distorting and displacing the position of the image of the coin, would only be reduced if the refractive index of the syrup was closer to that of air, than water is.

In lens systems that critical component , the magic syrup in the above analogy, has traditionally been low dispersion fluorite glass. More recently, some companies are using proprietary synthetic fluorite and probably/possibly others . Fluorite, being low dispersion, causes less splitting of the component wavelengths of the light and less spherical aberration. This allows for superior colour correction with fewer lens elements than would be required in an equivalently corrected objective using conventional glasses . For even better colour correction, add those lens elements back in with some more fluorite and you have an apochromat
What this means is that in a lens system, where a glass lens of standard dispersion of a particular magnification would need such and such a correction after the light passes through it, a low dispersion lens would need less correction. This gives the lens designer more flexibility in design possibilities with fewer elements to produce a compound lens with lower chromatic aberration. An offshoot of that is that because increased angles of incidence to a lens( higher N.A.) produce greater dispersion, a higher N.A. lens can be made with lower ca, when low dispersion glass is employed. The situation is more severe the higher in N.A. one goes and the higher in magnification too, the latter because the lens curvatures are more severe.o
So, essentially a higher N.A. and better colour correction go together because of the use of low dispersion glass but they are solutions to somewhat different technical problems created as the light passes through the glass.

Fluorite glass can hide in objective lenses and not be revealed by the manufacturer. There seems to be a certain design ethic or maybe also performance level that an objective that qualifies as fluorite must have. Apochromatic objectives utilize many design tools, including low dispersion glass, so are not usually referenced as fluorite. Terms such as Plan Fl.apo, Plan semi-Apo, Super Apo or Advanced Achromat might belie the fact that the mfg. has varied somewhat from their previous practices in the lens formulas and included more or less low dispersion glass in the formula.
There is nothing to stop a mfg. from making a higher N.A. than normal achromat or a lower than normal N.A. fluorite or apochromat and examples of such exist. There is a 40X .65 Lomo apochromat out there, which would be a joy to use with variable thickness cover slip samples. I own and sometimes use a very odd 60X 1.25 oil immersion Spencer objective from the 1940's. There is nothing to indicate that it is anything but an achromat but in performance it does lean slightly towards the fluorite class. Objectives that are not described as fluorite but have a higher than normal N.A. , usually have one or more elements of low dispersion glass in order to assist in the design goal of a higher N.A. , which will almost always additionally allow for better colour correction, a performance characteristic that higher N.A. objectives almost always possess.

Matador
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Re: Why are numerical aperture and color correction related?

#9 Post by Matador » Fri Apr 30, 2021 12:45 am

Cool video I stumbled on a few years back... Imaging a hidden world (it's a classic):
https://www.youtube.com/watch?v=tPBH0cMf_8s

Better image quality version here: https://www.dailymotion.com/video/x31jvmu

Enjoy

Matador

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