Numerical Aperture

A forum to ask questions, post setups, and generally discuss anything having to do with photomacrography and photomicroscopy.

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Frez
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Numerical Aperture

Post by Frez »

Does anyone know what units of measurement describe NA? For example my computer screen has a diagonal measurement of 17 inches. My 10x objective has a numerical aperture of .25 ???. It's not important. I've just never been able to find an answer.

Thanks
Frez

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discomorphella
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Post by discomorphella »

Hi Frez--

NA is effectively a dimensionless number like f/# for a camera lens. In fact, 1/(2*NA) = f/#. Its effectively the sine of the collection half-angle of a lens, so you can think of it as the ratio of the lens radius to is focal length, which is effectively dimensionless (but not meaningless...). So in a sense, the higher the NA, the greater the collection angle, and the more information the lens can take in from the object its imaging.
Hope this helps. You can also look at the microscopy u website, they have lots of cool java demo applets too.

--David

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Post by rjlittlefield »

Frez,

NA (Numerical Aperture) has no units. It involves only the ratios of measurements, so it is just a number.

Basically, NA bundles together two factors. One factor is how wide a cone of light your lens will accept. The wider the cone, the larger the NA. The other factor is the refractive index of the medium between the lens and your subject. The exact formula is NA = n * sin(a) , where n is the refractive index and a is half the angle of the cone.

See http://www.microscopyu.com/articles/for ... lasna.html .

The main significance of NA is that it tells how much fine detail can be resolved. NA is directly proportional to maximum resolution before you hit the diffraction limit.

You may wonder why the refractive index of the medium is bundled into NA.

As far as I can tell, this is done specifically so that NA does track maximum resolution. Physically, what happens is that when light passes through a medium with refractive index > 1, it slows down. Slowing down causes it to have a shorter wavelength (in that medium!), and the shorter wavelength permits higher resolution at the same cone angle. From the standpoint of resolution, using blue light with immersion oil is like using ultraviolet in air.

Googling things like numerical aperture microscope objective will get you lots more good info. Also, I strongly recommend spending some time at the MicroscopyU site.

If you are familiar with f-number from conventional photography, you may notice some similarity between f-number and NA. This is discussed in more detail in a different forum post.

Hope this helps!

--Rik

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Ken Ramos
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Post by Ken Ramos »

Gentlemen, isn't this a bit advanced stuff for a beginner? :-k :lol:
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Post by rjlittlefield »

Ken Ramos wrote:Gentlemen, isn't this a bit advanced stuff for a beginner? :-k :lol:
David, I think Frez and Ken were testing us. Apparently we failed... :( :wink:

--Rik

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Post by Ken Ramos »

Hey Rik! :D Glad you guys dropped by the new forum. All of you really threw me a ringer there. :lol: Of course your comments to help our beginners or novices is indeed welcomed and encouraged, however probably a good deal of them have no idea what...
The exact formula is NA = n * sin(a) , where n is the refractive index and a is half the angle of the cone.
is all about. Me included! :lol:
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Post by rjlittlefield »

Well, gee, it's hard to know what an appropriate level of response is.

Of course if Ken had asked the question, I would have dumbed down the answer. :lol: :wink:

But Frez, see, has a profile that says he's a Live Audio Engineer with interests in both Microscopy and Astronomy, and I remember that he's posted some pretty arcane stuff of his own, like this little beauty:
...The FK has less field curvature than my Nikon projection lens and less CA than an HR series relay from Diagnostic Instrument. To determine spacing I simply find the correct distance from the CCD by matching FOV to that in the binocular eyepieces. When I do this with the Nikon lens, there is too much curvature. (relative to the FK) The Nikon is a larger diameter lens though and may be a bit better with DF and other low light applications. (requires more study)

The FK is about 27mm from my DP10's chip. Of course chip size would change that parameter. After trying many different ways to project the image onto the chip, the FK 3.3x is best. The Nikon "TV Relay lens 1x/16" is a close second with the FK 5x in third place. I get the impression that the FK 3.3x is a wee bit sharper than the others.
So for him, I figured it'd be best to throw a gob of info and see what stuck!

Personally, I was surprised to find Frez posting a question in the Beginner's Forum in the first place. :D

Hey Frez, what's the story?

--Rik

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Post by Ken Ramos »

Rik wrote:
Of course if Ken had asked the question, I would have dumbed down the answer.
You might just have to go a little deeper down than that. :lol: That's why I am moderating the beginners forum. :wink:

Yeah Frez, what's up. Ya old epi fluorescence shooting, groupie chasing microscopist? :lol:
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Post by discomorphella »

Hi Rik--

You're correct, its my terminally pedantic nature...I should have read a bit more carefully...what ARE the two of us doing explaining NA to a guy who is posting beautiful autofluorescence images as of yesterday? Frez, if you really want to understand the link between image information content, collection efficiency of a lens and the diffraction limit for partially coherent imaging, I can give you LOTS of references. But since I fully expect to see you posting confocal 2-photon images next, I'll suggest that if you'd like a good text, find a copy of
"The New Fourier Optics Notebook: Tutorials in Fourier Optics" which is an SPIE publication by Reynolds et. al., c 1989, ISBN 0-8194-0130-7
which I needlessly add, is intended for people with some experience....(as opposed to those complete neophytes who do epifluorescence imaging... :D )

further, since you seem to like fluorescence microscopy and botanical specimens, you should check out Steven Ruzin's excellent book (which also has lots of stuff on NA as well)

"Plant Microtechnique and Microscopy", Oxford Univ Press, c. 1999, ISBN 0-19-508956-1

Happy Fluorescing....also, post your ex/im wavelengths in case others want to try as well...

--David

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Post by Frez »

Well I kind of figured NA was related to some archaic mathematical formula that was going to be difficult for me to grasp. The beginners forum seemed like the ideal place to get a dumbed down answer. :) Now that the truth is out, my buddy and I, Jethro Bodine, are glad to know that it all relates to NOTS. You see 2 NOTS + 2 NOTS = 0 NOTS. So those little numbers on a condenser that span the travel distance of the aperture diaphragm are actually NOTS. No matter what NOT you are using, it's still just a NOT. I know this is a little heavy for you guys and it's a good thing it was moved to this forum. NOTS are all about advanced mathematics. In fact it's so confusing that major scope manufacturers are all mixed up. My Olympus condenser's NOT scale ranges from 01 > 1.4 while my Nikon's NOT scale is 1 > 33. AO gave up completely and doesn't even have NOT scales. To summarize, my 10x objective has a NA of .25 NOTS. Thanks for clearing all of this up. 8)

Now if anybody wants to know how to establish phase relationships between 2 curvilinear line array clusters to enhance stereophonic perception based on microphone placement within a 70 piece orchestra, then I'm your man. This is even over Jethro's head. :shock:

Oh...whoever sited coherence between fluorescence microscopy and intelligence has my unending gratitude.

Truth be told, it would be a simple matter to write a lengthy book based on what I don't know about photography. I understand the use, function and importance of NA well enough, but never knew how the figure was arrived at. I thank you fine gentlemen for giving me your best shot, but I'll just continue to move that lever thingy until the bugs look good. :D

As for what filters were used for the fluorescence images...I really don't recall. The AO model 2070 vertical EPI illuminator does not have cubes and allows the mixing of 4 exciters, 3 dichroic beamsplitters and 3 barrier filters. In the future I'll take notes and include them with images. The rig still needs some work as a couple of the beamsplitters are giving off some serious reflections that "ghost" the specimen.

Thanks
Frez (going to the kitchen for some possum stew)

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Post by rjlittlefield »

Hhmm...

I have a friend who tells this great story about his kid, to whom he's trying to teach arithmetic.

At one point, the kid says, "One and one is two, two and two is four, four and four is eight,..."

And the guy thinks "Wow, this is great!"

Until the kid pauses, then asks "Daddy, what's a 'two'?"

This NA thing strikes me as kinda similar.

At one level (practice), it's easy to understand that bigger NA means you get more resolution but less depth of field and more brightness, at least at the same magnification. Also that bigger NA costs more $$'s.

At another level (theory), it's easy to parrot exactly how NA is calculated, but I'm not clear who would care. At yet another level (more theory!), we can talk about why that's a reasonable calculation, given the wave nature of light, yada, yada, and maybe we can eventually get some useful insight. Or maybe not. It's hard to know.

But... It kinda seems like there must be some other level, maybe between the first two, that would satisfy Frez's curiosity without making his eyes glaze over like mine do when confronted by audio.

The problem is, I don't have a very good idea what that would be.

This "inability to explain" happens fairly often to me, and I always find it frustrating. When it happens in a classroom, we can usually get past it by dialog, and if that doesn't work, some other student will usually bail me out by saying something that makes sense.

Handling the same problem in an Internet discussion group is likely to be a bit more challenging.

Frez, please accept my apologies if I said anything offensive while attempting to be humorous. It may be reassuring to know that I only publicly insult people that I like and respect! :)

I gotta say, too, that "moving that lever thingy until the bugs look good" worked just fine for me for a long time. Now that I finally learned exactly what NA is all about, it provides me great personal satisfaction to understand what's going on, while I continue to move that lever thingy until the bugs look good. There's a time and place for everything.

I appreciate everyone's thoughts about this issue, whatever it is.

--Rik

PS. Dang, there's no possum stew left. I'm jealous...

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Post by S. Alden »

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Post by Frez »

Hi Rik

I was absolutely in no way insulted and I genuinely hope that nobody thinks that. I will absorb as much of what was said as possible and put it away for future reference. Every bit of knowledge, no matter how mundane, obtuse, or, for some of us, incomprehensible, will at some point, even for the briefest of moments, be useful. Hopefully somebody just learned how to use commas. :)

The definition that lies between theory and practice would be easier to explain in a classroom environment where hands and a blackboard can be used. It would involve physical models from "practice" and just enough math from "theory" to convey useful information that would provoke thought and not frustrate the listeners. I frequently have opportunities to explain the workings of a 52 channel audio console to people that have enough knowledge to setup their home stereo. Over the years I've learned to do it in a way that will not make them think, "Okay...time for me to go sit down", but instead open their minds to the realization that things aren't as complcated as they appear to be at first glance.

Frez

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Post by Frez »

Nice link Sue. I'll not attempt to comprehend Snell's law, but other parts of the page are extremely useful. At first glance I now have just enough knowledge to get in trouble as I go in search of a diamond cover slip. :D

Thanks
Frez

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Post by S. Alden »

I like pictures (illustrations)... :lol:
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