bbobby wrote: ↑Tue May 28, 2024 12:54 pm

microscopyu.com shows resolution value for this objective 1.375 µm and it is capable of that in the center, Group 8 Element 4 is clearly resolved on the USAF target (1.38 µm) and with 4 shots pixel shift used to compensate for the Bayer filter I can see Element 5, which is 1.23 µm... why I am able to resolve more - no idea...

I think you've fallen prey to a common misinterpretation of the numbers, conflating µm

*per cycle* with µm

*per line width*.

Here's the way I work the numbers, using the formulas discussed at

viewtopic.php?p=124831#124831 .

Nikon's 1.375 µm corresponds to the bandwidth limit of NA 0.20 for 550nm light. That number means µm

*per cycle*. It's the closest distance that two bright spots can be, and still have the lens see any darker space between them.

But according to the specs

HERE (at the Technical Information tab), USAF 1951 Group 8 Element 4 is 362 line pairs per mm. That calculates to be 1.38 µm per line

*width*, but it's 2.76 µm per line

*pair*, which also means 2.76 µm

*per cycle*. 2.76 µm is a lot bigger than 1.375 µm, so what you're seeing is well within the range of the objective.

Working the numbers, NA 0.20 should have no trouble resolving anything in Group 8. Even Group 9 element 3 is within reach, though barely.

So then the question becomes why your images don't show that, and the answer is "sensor resolution". Group 8 Element 6, which your images do resolve but just barely, is 456 line pairs per mm. With 4X magnification that becomes 114 cycles per mm = 8.77 µm per cycle, or 4.39 µm per sample at the Nyquist limit. Your camera has pixel size 3.76 µm, which is a little smaller than the Nyquist limit, but not small enough to give a high quality capture. So, your captured image is limited by sensor resolution.

Another way of reaching the same conclusion is to consider that 4X NA 0.20 is running at effective f/10. (That formula is Feff=magnification/(2*NA).) Under standard assumptions of 550 nm light, f/10 has a limiting resolution on sensor of 5.5 µm per cycle. Even at Nyquist limit, that would require 2.75 µm per sample, much smaller than your pixel size.

Edited to add: For one more confirmation, go to

https://www.microscopyu.com/tutorials/m ... resolution . Set up Nikon's calculator for 4X, NA 0.20, video coupler magnification 1.0, and you'll see that it says "Required Pixel Size 2.8 µm ".

Because your image is sensor limited, It would be interesting to stick a teleconverter on your camera and see how much more of that currently unresolved resolution you could pick up.

--Rik