on the why of NA and resolution

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iconoclastica
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on the why of NA and resolution

#1 Post by iconoclastica » Fri Mar 29, 2019 6:45 pm

Is there a verbal explanation why higher apertures result in better resolution? I mean, the maths is clear enough, but why can a wider cone of light resolve smaller details?

MicroBob
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Re: on the why of NA and resolution

#2 Post by MicroBob » Fri Mar 29, 2019 6:52 pm

This fact was determined by Ernst Abbe. He probably explained it at the time, around 1860. You might look for old texts of him.

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75RR
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Re: on the why of NA and resolution

#3 Post by 75RR » Fri Mar 29, 2019 7:28 pm

Have a look at this video:

Understanding the Light Microscope by Peter Evennett

https://www.youtube.com/watch?v=60_jgZtyR6U

The whole video at 1 hour and 18 minutes is well worth watching (should be a requirement for all amateur microscopists)

the section on Abbe's Diffraction Experiments starts at 21 minutes.
Last edited by 75RR on Sat Mar 30, 2019 9:48 am, edited 1 time in total.
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Hobbyst46
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Re: on the why of NA and resolution

#4 Post by Hobbyst46 » Fri Mar 29, 2019 7:34 pm

iconoclastica wrote:Is there a verbal explanation why higher apertures result in better resolution? I mean, the maths is clear enough, but why can a wider cone of light resolve smaller details?
Try the explanation here:

https://www.microscopyu.com/techniques/ ... microscopy

The text is exceptionally clear, in spite of the math :lol: . In fact, the starting point is that what determines resolution (for a single wavelength of light - say, very pure red or very pure blue light) is diffraction. Diffraction occurs because light rays are waves. Diffraction makes every physical dot visible in the form of a "wider" spot. Two nearby spots are to be resolved, not two nearby dots.
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Scarodactyl
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Re: on the why of NA and resolution

#5 Post by Scarodactyl » Fri Mar 29, 2019 8:16 pm

Not to piggyback too blatantly onto the topic, but I have been wondering what about the lens itself separates two given objectives of similar working distance and magnification but different resolution. Is it using the appropriate exotic glasses, precise placement of the lenses, physical shape of the lenses themselves? Discussions on NA help explain the link between working distance and resolution, as well as some of the harder limits imposed by the imaging medium and basic physics of light, but I've been kind of curious about the practical side of things once the larger-scale issues are in place.

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Re: on the why of NA and resolution

#6 Post by apochronaut » Fri Mar 29, 2019 9:42 pm

MicroBob wrote:This fact was determined by Ernst Abbe. He probably explained it at the time, around 1860. You might look for old texts of him.


Abbe's determination was incomplete and was further refined by Lord Rayleigh as the Rayleigh Criterion.

Resolution = 1.22 lambda over N.A. of the objective + N.A. of the condenser.

However, for a practical explanation. It really has to do with more points of information being included in a wider angle of acceptance. This lessens the negative effects of diffraction.


We are used to seeing objectives in rather standard defined increments of magnification and N.A.. 10x .25 , or .30; 40X .65 or .85 for instance and it is obvious that certain magnification/N.A. combinations are purpose built. It isn't necessarily the case that a 40X objective be .65 as a standard for instance. Resolution increase with magnification isn't a natural progression. It is a designed progression. One could easily make a 100X objective for instance that had an N.A. of .40 but it wouldn't be useful with any eyepiece over 4X. Bausch & Lomb on the other hand, with a wholly different perspective in mind in the design of a series of objectives, produced a series of at least 11 objectives for a specific application, from .8X magnification with an N.A. of .11 through to a 25X magnification with an N.A. of 1.4. The 10X fluorite in the series had an N.A. of .80., so N.A. and magnification, although somewhat linked, are not necessarily linked in the way we are used to seeing them.
Last edited by apochronaut on Fri Mar 29, 2019 11:37 pm, edited 2 times in total.

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Re: on the why of NA and resolution

#7 Post by MichaelG. » Fri Mar 29, 2019 10:40 pm

Nice accessible graphic of the Rayleigh Criterion, here:
http://hyperphysics.phy-astr.gsu.edu/hb ... aylei.html

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iconoclastica
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Re: on the why of NA and resolution

#8 Post by iconoclastica » Sat Mar 30, 2019 10:47 am

Thanks for al your replies. Part of it I understand, but still not the whole story. But you have given me a number of links that I will read thouroughly tonight. Hold on...

Wim

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iconoclastica
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Re: on the why of NA and resolution

#9 Post by iconoclastica » Sat Mar 30, 2019 10:07 pm

75RR wrote:Have a look at this video:

Understanding the Light Microscope by Peter Evennett

https://www.youtube.com/watch?v=60_jgZtyR6U

The whole video at 1 hour and 18 minutes is well worth watching (should be a requirement for all amateur microscopists)

the section on Abbe's Diffraction Experiments starts at 21 minutes.

An excellent video indeed. Thank you very much for this link. Peter Evennett is a gifted teacher and the demonstrations are great, even the ones of subjects I already understood.

So, I think the answer to my question comes down to this: The primary image is an interference pattern, resulting from interference of light beams from the spatially separated diffraction nodes in the back focal plain. The smaller the details/slits, the wider the diffraction nodes come apart and to resolve at least two of them are required.

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