Not enough pixels for 20/0.75?

[Pau]

At two recent threads (*) we were discussing about the advantages and possible disadvantages of a 20/0.75 Plan Apo objective against a 40X of comparable NA.
I was interested, apart from the theoretical aspects, because I was waiting a Nikon CFI Plan Apo 20X 0.75 inf/0.17 DIC objective to be shipped.

After receiving and testing it my initial evaluation is very positive.
It's a beauty: it covers APSC sensor without any corner degradation without any visible CA and it is very sharp and contrasty up to the corners, I guessed if it was outresolving my 18Mpx sensor...
As a bonus I can get nice DIC with my hybrid setup

Because my microscope is an old finite design I can't use it in a normal way with the trinocular head, I only tested it with a bellows with a Sigma LSA as tube lens with direct projection on sensor, so the actual magnification is 20X. I can put the Optovar (without Telan lenses) and get 40X but it induces vignette and chromatic aberration degrading the image. Would be nice to try a teleconverter but I haven't one.
So my comparison with my finite corrected objectives meant to be used with compensating eyepieces is kinda of apples to oranges

Results: Despite looking clearly sharper the image taken with the Nikon has less resolution that the one of the Leitz PL Fluotar 40 0.70 (64X on sensor). The Leitz resolves diatom dots like Pleurosigma that the Nikon doesn't.
I think that this is related with magnification: likely the objective is able to resolve them but both my sensor and eyes have not enough resolution to make them visible.

Playing with microscopyu.com tutorial** I can get the following comparison:

NOTE: Wrong data marked in red, see later in the thread




According to it I would need a 34Mpx camera to capture all details resolved by the Nikon 20/0.75 while my 18Mpx are enough to easily capture all 40/0.70 detail mainly due to higher magnification (64X)

Some numbers can be wrong: at the same site, at the table, I can read 3.7micron pixel size while the tutorial shows 1.9micron, and at Kurt's Microscopy Blog*** table shows 29.7Mpx


* https://www.photomacrography.net/forum/ ... 647#243647
* https://www.photomacrography.net/forum/ ... 386#243386
** https://www.microscopyu.com/tutorials/m ... resolution
*** https://nic.ucsf.edu/blog/2013/11/how-m ... -transmit/

Comments welcome!

[JohnyM]

You used different "video magnification couplers", hence error in calculations. For sure, you dont have enough pixels to get all the resolution of 20x/0.75 with 18mpx aps-c.

[rjlittlefield]

Some numbers can be wrong: at the same site, at the table, I can read 3.7micron pixel size while the tutorial shows 1.9micron, and at Kurt's Microscopy Blog*** table shows 29.7Mpx

The differences are due to a combination of factors.

Nikon's calculator is based on placing 2 pixels per cycle at the diffraction-limited cutoff frequency for lambda = 550 nm. This just barely meets the minimum Nyquist sampling requirement at a spatial frequency where the MTF drops to zero anyway. But it puts 4 pixels per cycle at the frequency where diffraction-limited MTF is about 40%. Not a bad tradeoff. Unfortunately the calculator is hard to use for APS-C and larger sensors because their controls don't allow you to specify such a large sensor directly.

As mentioned by JohnnyM, some of your numbers are strange because of video coupler magnification.

Kurt's Microscopy Blog uses a different value for lambda (500 nm versus 550 for Nikon, so more stringent), but he uses a "resolution" number based on the Rayleigh criterion (less stringent), and his MP count is what's needed to exactly fill the circular field of view, not an inscribed or circumscribed rectangle (just different, and a bit weird).

Anyway, for Nikon's approach the governing equations are:

lambda = wavelength = 0.55 micron
effective f#, Feff = m/(2*NA)
cutoff frequency, nu_0 = 1/(lambda*Feff)
pixel spacing = 2 pixels per cycle at nu_0

20X NA 0.75 gives Feff = 13.3333, nu_0 = 0.136364 cycles/micron = 7.33333 microns/cycle, so pixel spacing = 3.66666 microns or smaller.

Nikon rounds this to 3.7 micron pixel size.

On a 22.3 mm x 14.9 mm sensor, this gives 24.7 megapixels minimum. Any fewer pixels are guaranteed to not be enough; more may be required for shorter wavelength and/or losses to antialiasing filter, Bayer filter, etc.

--Rik

[Pau]

You used different "video magnification couplers", hence error in calculations...

I did it intentionally to match the FOV to my setups as much as possible, of course it can't be exact. I did it based in the Field Number and adjusting the sensor rectangle to it and I think that it's a good approximation.
Doing so, at the calculation what matters is not pixel size but the total pixel count for a given FOV to capture all resolution of the objective.
Thanks for your comment.

[Pau]

Rik, thanks for clarification and calculations.

As you know I'm not good with Maths. If we take 4 pix/cycle as you say, are my results a reasonable approximation?

[JohnyM]

You used different "video magnification couplers", hence error in calculations...

I did it intentionally to match the FOV to my setups as much as possible, of course it can't be exact. I did it based in the Field Number and adjusting the sensor rectangle to it and I think that it's a good approximation.
Doing so, at the calculation what matters is not pixel size but the total pixel count for a given FOV to capture all resolution of the objective.
Thanks for your comment.

That's not how it works, at all. You've exagerated 20x way more than you did with 40x. Also FOV have NOTHING to do with resolving power. With that calc you are running with 10x on sensor and ~33x on sensor, which makes no sense, how is that matching anything? How are you getting 10x with 20x/0.75 and 200mm tube lens?
That would be exercising for my english to explain it, but im sure Rik will do that anyway.

[Pau]

Johny,
I see you've edited your last post, Mpx count and pixel size are related: you will get the same image with different sensor sizes with the same Mpx count if you change the secondary magnification to match them to the same FOV, of course pixel size will be smaller with the smaller sensor.

That's not how it works, at all.

I disagree, this is just how it works.
Actual objective resolution doesn't depend of FOV (neither of the pixel count or size), of course, but the ability of the sensor to capture it does.

Please let me explain what I did with the online app:
Actually I am projecting the image of the 20X with a 200mm tube lens on sensor, so actual magnification on sensor is 20X. The calculator doesn't have APSC sensor size, the maximum is 1", this is why I need to push the magnification video coupler down to 0.5X to make an image bigger than the 26mm FN circle approximately matching the field I capture with the APSC sensor. The secondary magnification at the app must be half the actual one because my sensor is about twice its size.
With the 40X I use the microscope as intended, with FN 18 eyepieces and 1.6X secondary magnification. Again the image I'm capturing matches well the rectangle, of course because of the different sensor size the secondary magnification at the app must be smaller, about half the actual one.

You've exagerated 20x way more than you did with 40x

Nope, just 1.6X at secondary magnification The other 2X comes from the actual difference of the objectives magnification

[rjlittlefield]

Rik, thanks for clarification and calculations.

As you know I'm not good with Maths.

Sorry, I can never remember who is, who isn't. Some days I can't even decide about myself!

If we take 4 pix/cycle as you say, are my results a reasonable approximation?

As I understand it now, you're comparing 20X NA 0.75 against 40*1.6X NA 0.70 .

By my calculations (based on Nikon's approach, 4 pixels/cycle at 39.1% MTF, on a 22.3x14.9mm sensor), that would require at least 24.7 MP for 20X NA 0.75, versus only 2.1 MP for 40*1.6X NA 0.70.

So yes, I agree that you have not quite enough pixels to resolve one, and plenty of pixels to resolve the other.

--Rik

[JohnyM]

Johny,
I see you've edited your last post,

And i dont see it, like any other user on this forum. Because i've edited it before it could influence any response. So what exactly is your point behind bringing it up?

Mpx count and pixel size are related: you will get the same image with different sensor sizes with the same Mpx count if you change the secondary magnification to match them to the same FOV, of course pixel size will be smaller with the smaller sensor.

That is correct.

That's not how it works, at all.

I disagree, this is just how it works.
Actual objective resolution doesn't depend of FOV (neither of the pixel count or size), of course, but the ability of the sensor to capture it does.

That is also correct,
EDIT (just so you know)
It actually aint.
Actual (what is actual?) objective resolution doesnt depend on FOV - true.
Also sensor ability to capture the detail still doenst depent on FOV.

Please let me explain what I did with the online app:
Actually I am projecting the image of the 20X with a 200mm tube lens on sensor, so actual magnification on sensor is 20X. The calculator doesn't have APSC sensor size, the maximum is 1", this is why I need to push the magnification video coupler down to 0.5X to make an image bigger than the 26mm FN circle approximately matching the field I capture with the APSC sensor. The secondary magnification at the app must be half the actual one because my sensor is about twice its size.
With the 40X I use the microscope as intended, with FN 18 eyepieces and 1.6X secondary magnification. Again the image I'm capturing matches well the rectangle, of course because of the different sensor size the secondary magnification at the app must be smaller, about half the actual one.

You've exagerated 20x way more than you did with 40x

Nope, just 1.6X at secondary magnification The other 2X comes from the actual difference of the objectives magnification

This is very convoluted and makes little sense to me.
This calc doesnt care at about FN so i dont understand why you bring it up at all.

It's quite simple in fact.
20/0.75 on 200mm tube being an EF~13,3 lens and need a pixel size of 3,7 um to satisfy nyquist cryterium of 2 pixels / blur.
If you introduce secondary magnification, this number will change when divided by it.
Sensor size have nothing to do with it.
If your calculation, come to same conclusion as above statement, then it is correct. I have no strenght to solve that gordian knot you've presented.
Yet, if it indeed is, then I find the way the way it's presented is very confusing.

[Greenfields]

On Feb 8th. Rik Littlefield Wrote:

On a 22.3 mm x 14.9 mm sensor, this gives 24.7 megapixels minimum. Any fewer pixels are guaranteed to not be enough; more may be required for shorter wavelength and/or losses to antialiasing filter, Bayer filter, etc.

When the first HD [1920 x 1080p] video cameras were introduced, some were produced in two versions: one with a single sensor which used a Bayer colour filter array and demosaiking, and another with a beamsplitter and three seperate sensors each of which captured a 1920 x 1080 colour channel with no demosaicing.

At that time practical measurements of the linear resolution of the single sensor cameras with a colour CFA were 30% less than the resolution achieved by cameras with three sensors.

If Bayer sampling and reconstructions cost 30% in linear resolution, this means that the 24.2 megapixel count would have to be doubled to off-set the impact of demosaiking on resolution. [If linear resolution reduced to 70% this means the pixel count of length and width would each have to be increased by a factor of 1.427 to off-set the effect.]

There is still the additional effect due to the antialiasing filter.

Henry

[rjlittlefield]

There is still the additional effect due to the antialiasing filter.

I have been reminded of the discussion & data at http://www.photomacrography.net/forum/v ... php?t=2439 . That's pretty old data at this point (over 11 years!), but I think it's still relevant. The tests were shot with a Canon DSLR having both Bayer and anti-aliasing filters. Summary was that the whole workflow ended up resolving pretty well at 3 pixels per cycle but hardly at all at 2 pixels per cycle. That's consistent with Nikon's calculated pixel density working pretty well down to about 20% MTF on the diffraction curve, but nonetheless having to about double the megapixel count to capture the whole tail clear out to 0% MTF.

That would be exercising for my english to explain it, but im sure Rik will do that anyway.

To be honest, I struggle with explaining to myself how to use that calculator outside the range limits that are built into it. Life would be so much simpler if the calculator would let us specify APS and full frame sensors directly. But let's see what I can do.


As I understand it, Pau's goal was to compare the demands of (A) 20X NA 0.75 and direct projection onto an APS sensor, against (B) 40X NA 0.70 and a 1.6X afocal setup giving total 64X projection, also onto an APS sensor.

Unfortunately the calculator does not have an APS sensor. So to use the calculator, we have to either ignore a bunch of its outputs, or fudge its inputs so the outputs will be more or less right.

Pau took the second approach, adjusting the video coupler magnification so as to make a 1" CCD inside the calculator have about the same FOV that his APS sensor would have in the real world.

I could quibble about the exact numbers. By my calculations, direct projection onto Canon APS is about the same as 0.59X onto 1" video, and 1.6X onto APS is about the same as 0.95X onto 1" video. Pau used slightly smaller numbers: 0.5X and 0.83X. Those would make the calculator's MP numbers about 40% higher than I would get. But Pau's ratio between the two setups is 1:3.32, while mine would be 1:3.2, so there's only a small discrepancy in terms of comparing 20X NA 0.75 against 64X NA 0.70.

You've exagerated 20x way more than you did with 40x. Also FOV have NOTHING to do with resolving power. With that calc you are running with 10x on sensor and ~33x on sensor, which makes no sense, how is that matching anything?

I beg to differ. Perhaps JohnyM overlooked the 1.6X afocal setup used with the 40X, as I initially did. Taking that into account, the ratio of actual magnifications is 1:3.2, and as Pau has set up the calculator, the ratio of calculated magnifications is 1:3.32. That seems pretty well matched to me.

Does this explanation help?

--Rik

[Pau]

Rik, thanks for the clarifications.
I've revised my calculations and I've detected a mistake due to taking a wrong value of the Canon sensor diagonal (I can't recall why). Although the conclusions are basically the same -and they match the experimental evidence- my numbers weren't.
So I've edited the original post to red mark the wrong parts (would be clearer just editing them, but that could affect the following posts)

Here I present the new calculator screen captures making the right proportional conversion between 1" and Canon APSC sensor diagonals (0.6X)
The yellow rectangle matches well the image captured in both cases, in the second one it matches the vision with 18FN eyepieces of my microscope
1. 20/0.75 direct projection on sensor at 20X

2. 40/0.70 projected on sensor at 64X with afocal setup


Now for the 20/0.75 the required pixel size is 3.33micron and about 25.4Mpx
while for the 40/0.70 at 64X they are 12.5micron and 2.2Mpx. Clearly in the fist case the objective outresolves the camera while in the second case the camera outresolves the microscope by much. The numbers do not pretend to be exact but they match well Rik's calculations.

[Pau]

Johny, thanks for commenting

Johny,
I see you've edited your last post,

And i dont see it, like any other user on this forum. Because i've edited it before it could influence any response. So what exactly is your point behind bringing it up?

Well, I already was writing my response when I saw that it was edited and I wasn't able to quote the first sentences. If it disturbs you in any form I will delete it.

I can admit that my post was not enough clearly expressed but I don't see the difficulty to understand it by an experienced microscopist like you.

Disagreements, critiques, corrections and discussions are welcome although I dislike the harsh style when doing so.

[rjlittlefield]

Just adding some notes to the permanent record...

I took a look at the guts of Nikon's calculator. The computations are done by a piece of JavaScript which is located at https://nikon.magnet.fsu.edu/html5/tuto ... culator.js .

The relevant computations are done by these lines:

Code: Select all

            optResPre = 0.55 / (2 * numAperture),
            optResVal = roundSignificant&#40;optResPre, &#40;optResPre < 1 ? 2 &#58; 1&#41;&#41;,
            reqPxSizeVal = roundSignificant&#40;optResVal * objMagVal * 0.5 * vcMagSldrVal, 1&#41;,
            optCCDArrSizeFirst = 1000 * _ccd&#91;ccdIndex&#93;.width / reqPxSizeVal,
            optCCDArrSizeSecond = 1000 * _ccd&#91;ccdIndex&#93;.height / reqPxSizeVal,

Paraphrasing:

• optResPre is the MTF=0 spatial cutoff for diffraction, in microns per cycle, at illumination wavelength 0.55 microns (550 nm green).
• optResVal is a rounded version of OptResPre, used for display and subsequent calculations.
• reqPxSizVal is the required pixel size, in microns at the sensor. It corresponds to 2 pixels per cycle at cutoff, after magnification, rounded for display and subsequent calculations.
• optCCDArrSize{First,Second} are pixel counts for the selected sensor size, given the required pixel size.

Earlier, I wrote

Anyway, for Nikon's approach the governing equations are:

lambda = wavelength = 0.55 micron
effective f#, Feff = m/(2*NA)
cutoff frequency, nu_0 = 1/(lambda*Feff)
pixel spacing = 2 pixels per cycle at nu_0

These formulas are rooted in the same theory and produce the same pixel spacing as Nikon's code. They differ in that Nikon computes cutoff at the subject and then scales up by magnification to get pixel size at the sensor, where my formulas convert from NA to Feff based on magnification, then compute cutoff at the sensor based on Feff. Just slightly different paths to the same result.

--Rik

[JohnyM]

Perhaps JohnyM overlooked the 1.6X afocal setup used with the 40X, as I initially did.

Indeed i have.
Also i would sworn my post was written differently than it looks now. Until i figure why my mind is playing tricks on me, i'll refrain from further discussion.