Making scale bars with no calculations (OT-->diffraction)

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Graham Stabler
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Post by Graham Stabler »

Thanks Graham that puts it more clearly than I did, I did rather go off on one talking about angular spectrum.

Graham

rjlittlefield
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Post by rjlittlefield »

gpmatthews, that is surely the best explanation I have ever seen in so few words. Many thanks.

--Rik

Epidic
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Post by Epidic »

I am not sure that description is clear as one person is talking about resolution at the object plane and the other the resolution at the image plane. A high NA objective does not necessarily have a high resolving power at the image plane as magnification is always a factor, although resolving power at the object plane is high.

The concepts are not different in that the angular size of the aperture is a determining factor to its corresponding plane - the entrance pupil determines object resolution, exit pupil determines image resolution. If you are talking about the image, then the NA by itself is not going to give you information about the "sharpness" of the image.

Images exist because of diffraction - a brightfield image is caused by destructive interference of the deviated and undeviated light passing the specimen. Some of that light passes through the object, some is diffracted. This diffraction can be seen in the plane behind the objective. If you use a simple grating, you can see a bright point in the center with is simply an image of the optical system's aperture. This is the undeviated light and is called the 0th order diffraction. On each side of that can be seen images of the aperture. This is the diffracted light called 1st order, 2nd order, 3rd order, etc. diffraction spectra. The more of these orders you can see, the greater the resolution of the specimen (if all the diffraction orders are not visible leaving only the 0th order, the specimen is not resolved). The greater the NA, the greater number of diffraction orders are captured. However, the finer the detail of the specimen, the fewer orders of diffraction can be seen. So higher NA aperture objective have higher resolution at the subject plane, but as the specimen changes size, most people change objectives to show finer detail. So while my 40x objective has a higher NA than my 10x objective, my images do not look sharper or more detailed because I use them at different magnifications for different specimen sizes (or object plane resolutions).

So when you are talking about resolving power, which plane makes a difference. Yes, high NA objectives do have greater resolving power at the object plane, but it may not have higher resolving power at the image plane. On my scope, my 10x objective gives the sharpest looking images even though my higher power objectives have high NAs and can show finer detail.

So, there is no spatial filtering. It is all diffraction. Without diffraction, there are no images. The aperture and specimen size (object plane resolution) determine the number of orders of diffraction that are captured. The greater the number of diffraction orders, the more resolution.[/u]
Will

gpmatthews
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Post by gpmatthews »

Yes, indeed, thanks Will.

I wanted to keep it simple, but maybe I should have gone on to say that the resolved detail possible in the image depends upon the amount of information available in the light diffracted by the object and that in turn is limited by the fineness of structures in the object relative to the wavelength of the illumination... but I thought I ran the risk of becoming long winded and confusing.

Simple explanations of complex phenomena are rarely comprehensive!
Graham

Though we lean upon the same balustrade, the colours of the mountain are different.

Epidic
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Post by Epidic »

Graham, it is a confusing thing (But not as confusing as two members called Graham.). You are right in the sense that the usual way microscopist think about this is resolving power at the subject plane and your description is very clear. Photographers are brought up thinking of resolving power at the image plane, which I think Graham S. was talking about. But the relationship between the two is not that clear.
Will

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Post by rjlittlefield »

I cannot resist the pun that "diffraction is a fuzzy subject". :roll: :D
--Rik

puzzledpaul
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Post by puzzledpaul »

Dunno about the content being confusing ... the thread title could well make a modelmaker indulge in more head scratching than normal :)

pp

Epidic
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Post by Epidic »

rjlittlefield wrote:I cannot resist the pun that "diffraction is a fuzzy subject". :roll: :D
--Rik
I hate to interfere, but is that constructive? (But it is a sine we are on the same wavelength. Or is it just a phase you are going through?)


:lol: :lol: :lol: :lol: :lol: :lol: :lol: :lol: :lol:
Will

Graham Stabler
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Post by Graham Stabler »

Will,

The objective has a certain NA and hence a certain resolving power and you are correct that this is not necessarily the resolution you will get at the image plane, the resolution at the image plane comes down to the system NA.

Typically you may have a high NA objective and a low NA tube lens forming the image, however the effective NA of the second lens is higher because of the magnification, basically because the objective tends to collimate the light the angles into the tube lens are much lower so it should not reduce resolution.

That is a specific set up but in general resolution comes down to the angles at the object plane and then keeping that information when the light is collected, closing the aperture removes some of the light from the higher angles and hence reduces resolution. The angles in the illumination matter as well of course.

Graham S
Last edited by Graham Stabler on Sun Jan 13, 2008 12:50 pm, edited 1 time in total.

Graham Stabler
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Post by Graham Stabler »

Oh and I still maintain that it is spatial filtering:

The aperture may not be at the proper fourier plane but it has the same effect. Cutting out diffracted orders is filtering and it is done in space not time hence spatial filtering.

To say it is caused by diffraction in the way you do is the same as saying it is caused by light propagation.

Graham

rjlittlefield
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Post by rjlittlefield »

puzzledpaul wrote:Dunno about the content being confusing ... the thread title could well make a modelmaker indulge in more head scratching than normal :)
pp, I don't understand. No doubt the discussion (soon to be a bar fight?) has drifted off the original subject of scale bars into exactly what's meant by this word "diffraction". But is there something else going on that I've missed? I've tried creative misinterpretation on the thread title, but I can't come up with anything that would prompt head scratching. Is there perhaps some clever way to parse it to create nonsense?

--Rik

Graham Stabler
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Post by Graham Stabler »

modelmaker = moderator??

Sorry to go OT, I'll leave it now.

puzzledpaul
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Post by puzzledpaul »

<< pp, I don't understand. >>

Sorry, Rik ... weird soh here (so better half is always saying) :)

Am a lapsed aero / boat modeller ... and just had a vision of a modelmaker being asked to make some scale models of bars (maybe as they were working for a shop-fitting Co?) ... but without being allowed to use / do any calcs :)


Will find suitable rock to crawl under now ...

pp

rjlittlefield
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Post by rjlittlefield »

pp - Ah, got it! I didn't think of that one. It is an amusing image! :lol:

Graham, not to worry, threads drift off topic all the time. I have found this discussion to be interesting and helpful.

I realize now that in photographic contexts I've always used "diffraction" as a convenient one-word shorthand for any effects that depend on the wave nature of light and would not be predicted by ray theory.

It's easy for people to understand that you get more DOF by stopping down (ray theory; geometric blur), and not so easy to understand that the images get fuzzy when you stop down too far (wave nature; "diffraction" blur).

If they go looking for more information, they'll find a lot more relevant stuff by searching Google on DOF diffraction than they will by searching on DOF "wave nature". That's good.

On the other hand, if they Google on define: diffraction, all the definitions that pop up have to do with the "bending" or "spreading" of waves around obstacles. That's not so good, since it's far from obvious what bending and spreading might have to do with how come the images get fuzzy.

No doubt I'll think about this the next time I have to reference the effect. At the moment, I suspect I'll write just "diffraction" if I want one word and a fuzzy one will do, but something like "the wave nature of light" if I'm willing to spend some more words.

Good discussion ... carry on ... no weapons please.

--Rik

Graham Stabler
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Post by Graham Stabler »

Reduction in resolution with decreasing aperture is predicted by ray theory if you understand that fine detail requires high angles into the object lens.

Imagine a simple imaging system consisting of two lenses, the high angle rays will hit the outer edges of the object lens before being collimated, if you put an aperture between the lenses you can block these high angles and hence reduce the resolution of the resulting image.

I really don't think you are moving into some special regime when you stop down, there will be some loss in resolution for any reduction in aperture.

Graham

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