Resoloution and Light Wavelengths

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Stonius
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Resoloution and Light Wavelengths

#1 Post by Stonius » Mon Jul 19, 2021 7:19 am

Hey All,

I was just calibrating my microscope with a calibration slide and realised that at the highest magnification (2500 x) that one unit on the eyepiece graticule is equal to 0.5 um (or 500 nanometers).

Unless I've done my sums wrong, that is the wavelength of visible light somewhere between the blue and green part of the spectrum.

How is it possible that I could be resolving details at less than the wavelengths of visible light? I would have thought diffraction or maybe Nyquist might have something to say about that? Am I just magnifying a blurry diffraction limited image? If so, how do I figure out the diffraction limited power of the scope?

Assuming I haven't made a mistake, could I expect to get better details by using a blue, or even ultra-violet filter, for example? The scope comes with a green filter, but I'm not too sure what this is for. I figured maybe it was to lessen the effects of chromatic aberration for fine details when used with a monochrome camera?

Cheers

Markus
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Re: Resoloution and Light Wavelengths

#2 Post by MichaelG. » Mon Jul 19, 2021 8:58 am

Stonius wrote:
Mon Jul 19, 2021 7:19 am
Hey All,

I was just calibrating my microscope with a calibration slide and realised that at the highest magnification (2500 x) that one unit on the eyepiece graticule is equal to 0.5 um (or 500 nanometers).

Unless I've done my sums wrong, […]
I think you probably have ^^^

Could you please show us your workings, and preferably a photo ?

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Re: Resoloution and Light Wavelengths

#3 Post by Stonius » Mon Jul 19, 2021 9:49 am

Okay, in this example, the scope is maxed out. EP's at 12.5x, Objective at 100x and the Optovar in the middle is at 2x.

Altogether that's a total magnification of 12.5 * 2 * 100 = 2500

I'm not using oil, even though it's an oil objective.

The scale on the slide says that each division is .01mm

There are 19 graticule divisions in the eyepiece graticule per 1 division on the slide.

This picture is through the eyepiece, and not showing the full field of view (which is 0.063mm). My eyepieces are old and dirty and I should replace them, I know.

.01mm/19 means that each division is 0.0005mm, or 500 nanometers.

I know the graticule in the lens does not equal details resolved in the slide, but still, if I'm right, I'm looking at a distance that is equivalent to the wavelength of visual light, which seems incredible to me.

Markus
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Re: Resoloution and Light Wavelengths

#4 Post by apochronaut » Mon Jul 19, 2021 11:33 am

You have to remember that the divisions in the eyepiece are in the eyepiece and magnified only by the eyelens. They have no effect on what is being magnified. While it is theoretically possible to resolve down close to .2 microns or so with very excellent optics and illumination, even less using some modern illumination systems : that cannot take place when the magnification exceeds the resolution capability of the objective.

It you were to have an equivalent type of ruled graticule, only a stage version reduced in size so that the smallest divisions were equal to their real dimensions ; 500 nanometers across for instance, with the set up you have you would see nothing, just a blur.

In order to see two points .5 microns apart you don't particularly need high magnification , just an N.A. of a certain angle. By increasing the magnification with an accessory such as an optovar, or a high magnification eyepiece, your ability to see details sharply, reverses and becomes less as the magnification increases.

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Re: Resoloution and Light Wavelengths

#5 Post by Hobbyst46 » Mon Jul 19, 2021 2:23 pm

Assume that your microscope is a Zeiss Standard (?)

The width of the large image, the one that includes and shows most of the stage micrometer, is 1.27mm. Coast to coast. Because the micrometer ruler is 1mm long.
I assume it has not been cropped (?).
The eyepieces are described as 12.5x.


Tried to evaluate two possibilities. Regardless of the graticule and the expanded inset view.

((1))
The camera only caught about 2/3rds of the visual FOV. So the visual FOV was about 1.8mm.
This is possible if the eyepiece was 12.5x18 (although 12.5x12.5 are apparently more ubiquitous).
From the look of the stage micrometer it seems that the objective was 10x.
Then a 100x objective, with the same eyepieces, would visually cover 180um.
And the image width would be 120um.

((2))
The camera caught the full visual FOV, so the visual FOV was about 1.27mm.
This is possible if the eyepiece was 12.5x12.5.
Again, it seems that he objective was 10x.
Then a 100x objective, with the same eyepieces, would visually cover 127um.
And the image width would be 120um, as before.

So - I wonder how the 0.063mm (630um) obtains.

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Re: Resoloution and Light Wavelengths

#6 Post by Stonius » Mon Jul 19, 2021 4:52 pm

The larger image has been cropped, and the inset is just a picture taken using my smartphone at the eyepiece to capture the EP graticule so you can see it overlaid on the slide graticule. But IIRC, the FoV in the eyepiece was larger than the camera.

I didnt think the cropping would matter as I'm trying to find out how many microns the EP graticule represents at different magnifications.

Is it not correct to look at one division on the slide, which we know is 0.01mm, and divide by the number of EP divisions that fit within? In this case, 0.01mm /19 = 0.0005263158.

Oh, and yes, it's a zeiss standard 1 (2nd edition) with the optovar at 2 x in this case. Combi ed with 100x objective and 12.5x EPs that gives 2,500 x magnification (in theory only, I'm sure).

Cheers, Markus
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Re: Resoloution and Light Wavelengths

#7 Post by MichaelG. » Mon Jul 19, 2021 5:15 pm

Markus,

It may be better to go ‘back to basics’ … Take a photograph of the slide and count the pixels that represent some chosen length on the scale : Then check your camera specification, which should tell you the ‘pixel pitch’ and do your sums.

All other numbers in the system can happily be ignored until you have got that relationship sorted.

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Re: Resoloution and Light Wavelengths

#8 Post by hans » Mon Jul 19, 2021 5:47 pm

Stonius wrote:
Mon Jul 19, 2021 4:52 pm
Is it not correct to look at one division on the slide, which we know is 0.01mm, and divide by the number of EP divisions that fit within? In this case, 0.01mm /19 = 0.0005263158.
I don't see any problem with this, the projected size of the graduations in the object plane depends only on the magnification of the objective+optovar. Eyepiece magnification, FOV, pixel pitch, etc. don't affect the result. Do you know what the actual size of the graduations on the reticle glass is? If so that distance divided by 200 should agree with the ~500 nm number measured using the calibration slide.

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Re: Resoloution and Light Wavelengths

#9 Post by MichaelG. » Mon Jul 19, 2021 5:55 pm

hans wrote:
Mon Jul 19, 2021 5:47 pm
pixel pitch, etc. don't affect the result.
Just to be clear ... I suggested using pixel pitch as a measuring scale, because all the other factors are 'nominal' values.

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Re: Resoloution and Light Wavelengths

#10 Post by crb5 » Mon Jul 19, 2021 8:15 pm

I am surprised you get such a good image with a dry 100x lens designed for use with immersion oil, although there is noticeable chromatic aberration at the extremities of the image. The Abbe resolution limit for the dry (n=1) objective, i.e. = wavelength/(2n * NA), would suggest a resolution of 0.5 /(2*1.25/1.52) = 0.3 um with 500 nm light. So, if the edges of the black lines on your graticule slide were spaced 0.3 um apart, you would not be able to separate them. A scan of your magnified graticule image (attached) shows the edges are not abrupt, but slope with a width of about 0.5 um, which is due to the diffraction limit. Magnification with an optivar and eyepiece does not overcome this limit, since they magnify the graticule separation and blur in proportion.

Blue filters are provided to minimize chromatic aberration and maximize resolution with a monochrome camera, but green filters do almost as good a job and offer better sensitivity for visual inspection of an image. Uv filters would give slightly better resolution, but many highly-corrected objective lenses transmit poorly in the uv.
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Re: Resoloution and Light Wavelengths

#11 Post by hans » Mon Jul 19, 2021 9:58 pm

MichaelG. wrote:
Mon Jul 19, 2021 5:55 pm
... I suggested using pixel pitch as a measuring scale, because all the other factors are 'nominal' values.
Maybe I misunderstand what you are suggesting, but Markus is measuring directly in relation to the calibration slide so no "nominal" values other than the specification of the slide itself are involved? Agree sensor pixel pitch is likely be a more accurate absolute length reference than a cheap calibration slide if there is a precise specification available for it, but then calculated sizes of features in the object plane based on pixel pitch depend on the nominal specifications of all the optics between the sensor and object...
crb5 wrote:
Mon Jul 19, 2021 8:15 pm
The Abbe resolution limit for the dry (n=1) objective, i.e. = wavelength/(2n * NA), would suggest a resolution of 0.5 /(2*1.25/1.52) = 0.3 um with 500 nm light.
Why do the original NA and refractive index of the immersion medium matter? I still find some aspects of these NA calculations confusing, but thought effective NA of an immersion objective used dry is slightly less than 1 independent of the original design parameters?

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Re: Resoloution and Light Wavelengths

#12 Post by MichaelG. » Tue Jul 20, 2021 6:07 am

hans wrote:
Mon Jul 19, 2021 9:58 pm
MichaelG. wrote:
Mon Jul 19, 2021 5:55 pm
... I suggested using pixel pitch as a measuring scale, because all the other factors are 'nominal' values.
… but then calculated sizes of features in the object plane based on pixel pitch depend on the nominal specifications of all the optics between the sensor and object...
Yes, Hans; that ^^^ was exactly my point
I was suggesting that Markus should determine his overall magnification by directly comparing the object and image sizes and ignoring the stack of nominal values with which the optics are labelled. [i.e. I am suggesting that he should measure the magnification, not calculate it].

I am inevitably assuming that the ‘stage micrometer’ is to specification in the first place, and that the pixel pitch of the sensor is known.

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Re: Resoloution and Light Wavelengths

#13 Post by 75RR » Tue Jul 20, 2021 7:21 am

.
I believe I have the same stage micrometer. The scale is 1mm square. Divided by 100 divisions that equals 10µm per division.

So 10µm/19 = 0.52µm per division

If we ignore the optovar magnification (i.e. 2x) then we get 10µm/9.5 = 1.05µm per division which is about right for the 100x objective using a graticule 10mm long divided into 100 parts.

My eyepieces are old and dirty and I should replace them, I know.
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Re: Resoloution and Light Wavelengths

#14 Post by Stonius » Tue Jul 20, 2021 8:04 am

I think what I'm trying to do is to be able to estimate sizes by eyeballing the EP graticule, because the scale on the slide won't be there when looking at specimens, and it will be quicker than photographing and measuring in photoshop. So if I can use a scale of known dimensions to define the length of a division in the EP graticule, then I think that's probably the information I want. Unless I screwed up somewhere.

But anyway, I figured out the calculations you suggested. The camera sensor has 6144 pixels horizontal resolution, across a chip that is 23.1mm wide. I believe this gives a pitch close enough to 3.7um. At the highest magnification, (supposedly 2,500x) the field of view is 0.077mm

I guess that means that each individual pixel captures an area 12.5nm across? Is that right? I know at that level it's massively oversampling detail that aint there. Are these the sort of sums you're talking about?

Oh,BTW, I have cleaned my EP's comprehensively, many times. That's as good as they get. But in stereo it's not too bad.

Cheers

Markus
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Re: Resoloution and Light Wavelengths

#15 Post by Hobbyst46 » Tue Jul 20, 2021 8:19 am

Stonius wrote:
Tue Jul 20, 2021 8:04 am
At the highest magnification, (supposedly 2,500x) the field of view is 0.077mm
Irrespective of the graticule and ruler and calculations above, may I suggest that x2500 magnification by means of a 100x objective, 2x Optovar and 12.5x eyepiece means "empty magnification" - namely, useless. Because the NA of the objective is (say) 1.3, 1000x1.3 = 1300, any magnification above 1300 does not contribute to resolution. For a 100x objective, and a 12.5x eyepiece, the Optovar should be set to 1.

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Re: Resoloution and Light Wavelengths

#16 Post by hans » Tue Jul 20, 2021 8:37 am

Stonius wrote:
Tue Jul 20, 2021 8:04 am
So if I can use a scale of known dimensions to define the length of a division in the EP graticule, then I think that's probably the information I want. Unless I screwed up somewhere.
No screw-up, ~500 nm from your first, second, and third posts in the thread is correct.
Stonius wrote:
Mon Jul 19, 2021 7:19 am
...that is the wavelength of visible light somewhere between the blue and green part of the spectrum.
In air, however if the specimen is in media with higher refractive index the wavelength scales inversely, so for example at 1.5 green is 370 nm and 500 nm is near-IR.

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Re: Resoloution and Light Wavelengths

#17 Post by 75RR » Tue Jul 20, 2021 8:37 am

So if I can use a scale of known dimensions to define the length of a division in the EP graticule, then I think that's probably the information I want.
You need to calculate the value of a graticule division for each objective.

http://www.ruf.rice.edu/~bioslabs/metho ... uring.html
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Re: Resoloution and Light Wavelengths

#18 Post by MichaelG. » Tue Jul 20, 2021 9:33 am

75RR wrote:
Tue Jul 20, 2021 7:21 am
.
I believe I have the same stage micrometer. The scale is 1mm square. Divided by 100 divisions that equals 10µm per division.

So 10µm/19 = 0.52µm per division
Very happy with that … but I think Markus has made a ‘leap of faith’ in assuming that he therefore has 0.52µm resolution
I see nothing in the posted photo to demonstrate resolution of two points separated by half a micron.
[ and nor would I expect to ]

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Re: Resoloution and Light Wavelengths

#19 Post by Hobbyst46 » Tue Jul 20, 2021 9:57 am

MichaelG. wrote:
Tue Jul 20, 2021 9:33 am
I see nothing in the posted photo to demonstrate resolution of two points separated by half a micron.
Agreed, moreover the apparent resolution from that photo alone is 10 um... with the 100x objective as well as with the lower mag objective used for the whole ruler image...

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Re: Resoloution and Light Wavelengths

#20 Post by Stonius » Tue Jul 20, 2021 12:12 pm

MichaelG. wrote:
Tue Jul 20, 2021 9:33 am
Very happy with that … but I think Markus has made a ‘leap of faith’ in assuming that he therefore has 0.52µm resolution
I see nothing in the posted photo to demonstrate resolution of two points separated by half a micron.
[ and nor would I expect to ]

MichaelG.
Sorry, maybe I wasn't clear. I come from a background in Astronomy, and believe me, telescopes suffer from the same 'empty magnification' when pushed beyond useful limits. it's a concept I'm very familiar with. I never meant to imply I was actually seeing details at that level. It just blows my mind that the end of visible light microscopy is that... obvious and final - that the blur you see is because you're approaching the size of the visible wavelengths of light. *That's* what I find cool, not the level of detail (or *not* detail as the case may be). I'd always thought the wavelengths of light were unapproachably small. I never thought I'd be able to get a sense of their scale through my little microscope. it blows my mind is all. The universe is an amazing place.

Thanks for all your help guys, I appreciate it.

Markus
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Re: Resoloution and Light Wavelengths

#21 Post by hans » Tue Jul 20, 2021 8:51 pm

MichaelG. wrote:
Tue Jul 20, 2021 9:33 am
I see nothing in the posted photo to demonstrate resolution of two points separated by half a micron.
What's wrong with the plot crb5 posted showing ~500 nm transitions at the edges of the lines on the calibration slide?

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Re: Resoloution and Light Wavelengths

#22 Post by MichaelG. » Wed Jul 21, 2021 12:06 am

hans wrote:
Tue Jul 20, 2021 8:51 pm
MichaelG. wrote:
Tue Jul 20, 2021 9:33 am
I see nothing in the posted photo to demonstrate resolution of two points separated by half a micron.
What's wrong with the plot crb5 posted showing ~500 nm transitions at the edges of the lines on the calibration slide?
That doesn’t fit my definition of resolution

Figure 6(d) here does : http://zeiss-campus.magnet.fsu.edu/arti ... ation.html

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Re: Resoloution and Light Wavelengths

#23 Post by hans » Wed Jul 21, 2021 1:36 am

MichaelG. wrote:
Wed Jul 21, 2021 12:06 am
That doesn’t fit my definition of resolution

Figure 6(d) here does : http://zeiss-campus.magnet.fsu.edu/arti ... ation.html
Two pages discussing the relationship among PSF (as in Zeiss fig. 6(d)). LSF, and edge response with some nice illustrations:
https://www.strollswithmydog.com/the-sl ... ge-method/
https://www.dspguide.com/ch25/1.htm

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Re: Resoloution and Light Wavelengths

#24 Post by 75RR » Wed Jul 21, 2021 3:58 am

hans wrote:
Wed Jul 21, 2021 1:36 am
MichaelG. wrote:
Wed Jul 21, 2021 12:06 am
That doesn’t fit my definition of resolution

Figure 6(d) here does : http://zeiss-campus.magnet.fsu.edu/arti ... ation.html
Two pages discussing the relationship among PSF (as in Zeiss fig. 6(d)). LSF, and edge response with some nice illustrations:
https://www.strollswithmydog.com/the-sl ... ge-method/
https://www.dspguide.com/ch25/1.htm
or you can go old fashioned and resolve the stria of a Amphipleura pellucida diatom
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Re: Resoloution and Light Wavelengths

#25 Post by hans » Wed Jul 21, 2021 4:39 am

75RR wrote:
Wed Jul 21, 2021 3:58 am
or you can go old fashioned and resolve the stria of a Amphipleura pellucida diatom
Yeah I like how even in recent, highly-technical papers on optics/microscopy there are sometimes still shots of diatoms. The ultimate test to earn credibility among microscopists, no integral transforms necessary...

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Re: Resoloution and Light Wavelengths

#26 Post by Hobbyst46 » Wed Jul 21, 2021 7:50 am

hans wrote:
Tue Jul 20, 2021 8:51 pm
MichaelG. wrote:
Tue Jul 20, 2021 9:33 am
I see nothing in the posted photo to demonstrate resolution of two points separated by half a micron.
What's wrong with the plot crb5 posted showing ~500 nm transitions at the edges of the lines on the calibration slide?
There is nothing wrong with the plot, except that it does not indicate resolution in the classic sense (defined according to the Abbe or Raleigh criteria).

The classic Abbe resolution criterion is the ability to distinguish between two nearby objects in a given image.
The relevant image in our case is the original photo of the enlarged space between two scale marks of the stage micrometer, taken at 100x and posted above by the OP.
Two dark vertical bars are visible, in my opinion, with nothing in between. So the resolution is 10 um if one refers to the centers of the bars or 5.6 um if one refers to the bright space between the inner edges of the two bars.

The classic Rayleigh criterion- citation from Wikipedia:
"two point sources are regarded as just resolved when the principal diffraction maximum of the Airy disk of one image coincides with the first minimum of the Airy disk of the other".

The plot crb5 posted shows, IMHO, that the distance between maxima and minima in the picture is ~5 um.
Moreover, the width of the bar edge, even when judged from the plot, is IMHO at least several um.

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Re: Resoloution and Light Wavelengths

#27 Post by Stonius » Wed Jul 21, 2021 8:58 am

I don't know if this helps. This is an uncropped, but scaled image of the entire frame with measurements (again, 100x objective, 2x optivar and 12.5x EP - only using OIL this time). The objective is a Neofluar PH3 130 Oel 160/-

The insert image is at 100% and unscaled.

So the blue line represents the width of the frame in pixels. The other red lines just indicate the stage micrometer measurements. The entire field then, is about 0.062mm across. Each pixel at this resolution represents about 0.00001mm

The insert at 100% shows a line separated from the edge of the black division marker by about 50 pixels, or 0.0005mm. I take it this line is an effect of diffraction and represents the point beyond which no further detail can be resolved, even if all else were perfect?

Best,

Markus
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Re: Resoloution and Light Wavelengths

#28 Post by Hobbyst46 » Wed Jul 21, 2021 10:03 am

Stonius wrote:
Wed Jul 21, 2021 8:58 am
So the blue line represents the width of the frame in pixels. The other red lines just indicate the stage micrometer measurements. The entire field then, is about 0.062mm across. Each pixel at this resolution represents about 0.00001mm.
The insert at 100% shows a line separated from the edge of the black division marker by about 50 pixels, or 0.0005mm. I take it this line is an effect of diffraction and epresents the point beyond which no further detail can be resolved, even if all else were perfect?
I would look differently at this image. Consider only the larger image, not the insert.

First, obviously, the presence of oil has sharpened the object, as expected.

I displayed the image on my computer monitor such that the bright-color spacing between two adjacent black scale marks on the monitor is 32mm.
From the stage micrometer dimensions, regardless of the microscope and monitor, the same spacing is ~5.6 um (NOT 10um as depicted by the red line).
The thin line around the scale mark, which is probably an artifact (besides diffraction, there is chromatic aberrations), is nevertheless a distinguishable object in the image, So I treat it as if it were a real object.
Its distance from the scale mark visible border on my monitor is ~2mm. Hence, its true distance in the image created by the microscope is 5.6*2/32 = 0.35 um.
This 0.35 um is a reasonable resolution for white light and a 100x1.3 objective. In practice, resolution is often worse than expected from the simple formulae.
Since the thin line is so thin, likely even better resolution is possible, but to prove that, one needs narrower spaces between distinct objects. Indeed, the stage micrometer is not the appropriate indicator of microscope resolution (even for low-mag objectives).

Pixel-wise calculation : the image width is 6144 pixels, and there are six spaces between scale marks, and considering the width of the marks themselves, it comes that each space on the average is 620 pixels. if the thin line distance from the black bar is 50 pixels, the resolution is 5.6*50/620 = 0.45 um. Roughly the same as above.

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Re: Resoloution and Light Wavelengths

#29 Post by Stonius » Wed Jul 21, 2021 1:54 pm

Hobbyst46 wrote:
Wed Jul 21, 2021 10:03 am
Since the thin line is so thin, likely even better resolution is possible, but to prove that, one needs narrower spaces between distinct objects. Indeed, the stage micrometer is not the appropriate indicator of microscope resolution (even for low-mag objectives).
So I guess the appropriate method would be to obtain some diatom slides?

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Re: Resoloution and Light Wavelengths

#30 Post by 75RR » Wed Jul 21, 2021 2:06 pm

.
A Kemp 8 Form Test slide or similar is what you want. See below

Note that Period/stria is within a range as diatom size varies.
.
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