Eugene,
On a quick review of your numbers, I think I disagree with your analysis that the sensor is not limiting. Let me tell the story in a different way and see if you agree.
Start by assuming that you're getting 1.55 µm per pixel at the subject. Then because of the Nyquist limit, you could not possibly resolve more than one cycle every 3.1 µm, no matter how sharp your lens is. So, your estimate of one cycle every 3.3 µm suggests that the lens is
at least NA 0.1, but it could be arbitrarily wider & sharper than that and you would never know given the sensor at hand.
Looking again at your images, I find that I am confused by your phrase "image scale of 1.55um/pixel". In the first image posted, I measure 554 pixels in 0.6 mm. Dividing out, that gives 1.08 µm per pixel in the image as displayed. Is the image a 100% crop? If so, then the resolution would be 1.08 µm per pixel on subject. Or is the image reduced to 50% of an original 1280 x 960? If so, then the resolution on subject would be twice as good, 0.54 µm per pixel. Either way, it's substantially better than 1.55 µm per pixel on subject. Hence my confusion. When you write "image scale of 1.55um/pixel", what does that mean and how was the number obtained?
Popping up a level, let me caution that it's notoriously difficult to measure NA by looking at image resolution. Consider for example the dramatically different results obtained from three different 10X NA 0.25 objectives
HERE,
HERE, and
HERE. The first two are quite sharp, the third is fuzzy. If one were to estimate NA based on the third lens's resolution, I think the calculation would come out far below the manufacturer's rating, which is most likely pretty accurate because it would have been based on geometry.
Speaking of geometry, I notice that the FOV shown in your first image is only 0.69 mm. If that's the total field of view, then it's in the range of what's typically covered by a 20X microscope objective, whose NA's are typically 0.4 or higher. If you need more resolution than what you're getting, it won't be hard to come by.
Popping up even another level, I'm curious what you're really trying to determine, and why.
If you really care about NA, it's not terribly difficult to determine from geometry. With many lenses you can measure pupil sizes and focal length, and compute from there. Where that doesn't work (for example because the pupils cannot be measured), you can measure the cone angle directly by setting up an experiment like shown
HERE.
Alternatively, NA can also be estimated pretty well by comparing image brightness for the unknown lens and for a known lens set up at the same magnification. The typical approach is to match histograms by changing the exposure time. This presumes, of course, that you're using a camera where the exposure time can be accurately controlled. The scheme also depends on having a "known lens" whose behavior really
is known. That can be harder than it sounds, because due to
pupil factor many lenses have smaller or larger effective apertures than would be suggested from their rated f-numbers alone.
In any case, I'm having trouble figuring out why you'd be interested in NA for a lens that you have in hand. If it's all you have to work with, then NA is useful as some indicator of how sharp a lens may be, and certainly what DOF it will have. But lenses commonly do not resolve as well as their NA would suggest, and for most applications it's ultimately resolution that matters. So why not just concentrate on resolution in the first place?
I see I haven't answered one question you asked. That was "Does my assumption that two lines dividing the 10um tics sound reasonable?". It does, and that's easy to demonstrate by experiment. Simply pull the image into Photoshop, copy/paste the image to form 3 layers, set the layer opacities to top=33% and middle=50%, shift the top two layers to evenly distribute the tick marks, and observe that 3 times as many lines can be seen. Here is the demonstration, scaled by 200% from what you posted.
Bottom line, I have no trouble with the idea that your lens and sensor are resolving at least 3.3 µm per cycle. After that, I'm not so sure.
Sorry for the long posting. It's a personal curse that I spend so much time thinking about things like this. I hope you find my comments and questions helpful.
Best regards,
--Rik
