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Optimal sensor pixel density for Mitu 10x
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rjlittlefield
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PostPosted: Sun Oct 25, 2015 12:03 am    Post subject: Reply with quote

Quote:
Though it is sometimes hard to be sure all the implicit and explicit assumptions in a derivation have been satisfied.

As ChrisR said, these issues have been discussed extensively. I have no interest in doing it again from scratch.

This post from 2009 might be a good place to start reading:

http://www.photomacrography.net/forum/viewtopic.php?t=8763

An earlier thread addressing many of the same issues is here:

http://www.photomacrography.net/forum/viewtopic.php?t=4108

Quote:
I actually do believe in mathematics!

Though it is sometimes hard to be sure all the implicit and explicit assumptions in a derivation have been satisfied.

I believe in mathematics too -- but only to the extent that the math matches reality and helps to either predict or understand it.

A lot of the work behind those threads was to ferret out what the problematic assumptions were, and then resolve what otherwise appeared to be conflicts.

The results discussed in the above threads have been subjected to the test of matching reality, and they're held up quite nicely so far. If you think they don't, in some experiment of your own, then the onus will probably fall on you to clearly demonstrate the effect, find the flaws in the earlier analysis, and offer some resolution of them.

I apologize if this sounds a bit grouchy -- I'm under some stress at the moment -- but perhaps it's not such a bad thing to be clear, either.

--Rik
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rjlittlefield
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PostPosted: Sun Oct 25, 2015 1:55 am    Post subject: Reply with quote

Now, getting back to the issue of how many pixels are needed, and looking at some of those implicit and explicit assumptions...

As Charles Krebs noted, by using a 90 mm tube lens, you've pushed the 10X objective down to 4.5X .

On the camera side, at 4.5X the optics will be working at an effective f-number of 4.5/(2*0.28 ) = f/8.

Going back to those formulas I mentioned earlier, this gives a cutoff frequency around 226 cycles/mm at 550 nm, requiring Nyquist minimum sampling of 452 pixels/mm but more realistically 1.5-2 times higher to avoid excessive contrast loss due to issues with pixel alignment, anti-aliasing filters, and such. Call it 2*452 = 904 to catch everything. Your results at 840 pixels/mm, 648 pixels/mm, and 181 pixels/mm seem pretty consistent with theory.

They are also consistent with other experiment. I am thinking specifically of the thread titled Pixels for use at 4-5X on an APS-sized sensor, where at http://www.photomacrography.net/forum/viewtopic.php?p=101164#101164 there is a direct visual demonstration followed by a simple calculation to end up with the result that at f/11 a reasonable number is 47 megapixels needed. Scale that by a factor of 2 to account for the difference between f/8 and f/11, to get a number of 94 megapixels, and this seems pretty similar to your statement that "An APS-C sensor should have 120 megapixels, not 10 or 20."

That number, say 120 megapixels, will apply whenever using the same objective (NA 0.28 ) to view the same size subject area. It's in that latter issue that things get a little sticky.

Quote:
If you have an object that's 3 mm across, you can spread it across 5000 pixels on the bridge camera sensor using just 2x optics. Or you can spread it across 5000 pixels on an APS-C sensor, but you'll need 8x optics.

True, but in both cases you'll be needing the same NA on the subject side.

Quote:
The price difference between these two options is very large. It may be useful to be aware of this cheap easy alternative.

Perhaps, but I'm not convinced about exactly how large "very" is. When I look at prices, I'm seeing the Sony Cyber-shot DSC-HX400V at 20.4MP for about $430. Meanwhile a Canon T5 at Adorama, with 18-55 mm kit lens, is $399. To make that work with the Mitutoyo objective at rated 10X magnification would require something like a 200 mm telephoto; I'm thinking the Canon EF-S 55-250 would work OK, add $179 for that. Or maybe even the body + 18-55 + 55-300, currently offered at http://www.adorama.com/ICAT5K1A.html for $499.

This doesn't strike me as a huge difference, particularly since we've implicitly assumed that there's a Mitutoyo 10X NA 0.28 sitting out front -- list price $885 for that.

I don't intend any of this to argue that a bridge camera is a bad idea. However, given the historical problem of vignetting with zooms at much less than max focal length, combined with your observation that "There was also vignetting at middle and lower focal lengths.", I think some caution is called for.

I have no problem believing that using a bridge camera is a quick and easy way of capturing the center of the Mitutoyo's field -- much quicker and easier than sticking a long zoom on APS-C. But for capturing the whole field, or even as much of the field as would be typically captured by an APS-C setup, I'm still very concerned about the vignetting issue.

Comparative images at same field width would be very helpful for addressing that concern.

--Rik
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Lou Jost



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PostPosted: Sun Oct 25, 2015 5:41 am    Post subject: Reply with quote

Rik, thanks for your comments. Not my intention to make you grouchy, quite the contrary!

Quote:
"The results discussed in the above threads have been subjected to the test of matching reality, and they're held up quite nicely so far. If you think they don't, in some experiment of your own, then the onus will probably fall on you to clearly demonstrate the effect, find the flaws in the earlier analysis, and offer some resolution of them."


My experiment agrees with those calculations (and not with some others on the forum which made claims that more pixels don't help).

Yes, agreed, I overestimated the price difference. It isn't big if you go with that combo you mentioned.

What impressed me about the bridge camera was its ability to get nice detailed pictures of tinier subjects than one can easily get on a Mitu + 200mm + APS camera. You'd need extra stuff to put a comparable number of pixels beneath the same subject on that APS sensor. A 400mm lens, or a not-so-expensive teleconverter, or perhaps a long-focal-length achromat like the Canon 500D.

Bridge cameras are definitely not good if your desired subject area is relatively large. They do vignette badly at short focal lengths.
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ChrisR
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PostPosted: Sun Oct 25, 2015 8:06 am    Post subject: Reply with quote

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Yes, agreed, I overestimated the price difference. It isn't big if you go with that combo you mentioned.
If you used the Nikon 10x BE though at about $90, the case for a smaller/cheaper camera is stronger.
I did try one, it worked, using CHDK to step-focus the compact for a stack in-field, but I didn't take it far.
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Lou Jost



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PostPosted: Sun Oct 25, 2015 2:24 pm    Post subject: Reply with quote

The difference is especially important when one wants to get lots of pixels under a very small subject. With a bridge camera I can work at 5x or 10x on the sensor, whereas getting the same number of pixels under the same object on an APS sensor requires more like 20x.
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rjlittlefield
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PostPosted: Sun Oct 25, 2015 3:43 pm    Post subject: Reply with quote

This is a bit of a side note, but perhaps it will help to tie things together.

At microscopyu.edu, Home > Interactive Tutorials > Java Tutorials > Matching Camera to Microscope Resolution, there is a calculator described as "Digital Camera Resolution Requirements for Optical Microscopy". That calculator represents Nikon's sort-of-official standard guidance for how many pixels to use for microscopy.

As far as I can tell by running some examples, what the calculator does is to put exactly 2 pixels per cycle at the spatial cutoff frequency for lambda = 0.55 micron. This corresponds to the Nyquist minimum sampling rate at the spatial frequency where optical MTF=0. In other words, the sensor and the optics reach rock bottom at the same time. That might seem a little under-spec'd, but on the other hand the same calculation puts 4 pixels per cycle at the frequency where MTF is about 40%. So, their number is "optimum" in the sense of degrading the image about equally badly due to diffraction and sensor limitations.

In terms of those 10X objectives that we've been talking about, the calculator's result matches pretty closely to current APS-C sensors with ~20 megapixels, when used at the objectives' rated magnification.

What we're accomplishing by using the bridge camera, or by using a longer tube lens on the APS-C, is to cram the same number of pixels into a smaller area. That gets us a higher quality capture of that part of the optical image, at the cost of cropping away what would otherwise be useful image area. If we're evaluating the lens, or we only care about the area inside the crop, or we're prepared to do some stitching, then it's a helpful technique.

Note that, as always, there's no free lunch. Putting 4 pixels per cycle at the cutoff frequency will guarantee that you capture everything that's in the optical image, but that comes at the cost of also guaranteeing that the captured image will not look as "sharp" in terms of pixel to pixel variation. There's more discussion of that idea at my musings "On the resolution and sharpness of digital images..."

I notice that in my own work I often go the other direction, pushing down the magnification of the objective at constant NA so as to get a sharper image over a larger field. In doing that I know that I'm failing to capture lots of detail that is hiding unobserved in the optical image, but I don't care about that because what I want is the best image I can get of the larger field, using the resources currently at my disposal. Tradeoffs, tradeoffs...

Quote:
What impressed me about the bridge camera was its ability to get nice detailed pictures of tinier subjects than one can easily get on a Mitu + 200mm + APS camera.

That makes sense. You have a particular objective, and a particular subject that is smaller than that objective is normally used for, so use the bridge camera to fill the sensor with the subject. Faced with the same situation, and a larger set of objectives, and an APS-C rig, other people would choose to swap out the 10X NA 0.28 for a 20X NA 0.42 or 50X NA 0.55, and capture even more detail on the same subject, but at a higher cost.

--Rik
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Lou Jost



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PostPosted: Sun Oct 25, 2015 5:22 pm    Post subject: Reply with quote

Rik, that last paragraph is a good summary.

I read the resolution/sharpness article you linked to. Your photo of the aerial image led me to wonder about photographing the aerial image of my Mitu 10x + 200mm tube, using say a 2x or 3x lens on an APS sensor. That's another interesting way to get more resolution or magnification out of the Mitu....why don't more people do that?
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rjlittlefield
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PostPosted: Mon Oct 26, 2015 10:36 am    Post subject: Reply with quote

Lou Jost wrote:
...photographing the aerial image of my Mitu 10x + 200mm tube, using say a 2x or 3x lens on an APS sensor. That's another interesting way to get more resolution or magnification out of the Mitu....why don't more people do that?

I could only guess why other people don't do it. The reasons that I don't do it -- except for experiments & demos like you've mentioned -- are that my multi-stage setups are fiddly to assemble and use, and their main value is to definitively capture the smallest details offered by any particular lens. For investigating optics that technique works great for me; for real photography, not so much. I have other simpler and better ways to get the images that I want of real subjects.

--Rik
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Pau
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PostPosted: Mon Oct 26, 2015 11:44 am    Post subject: Reply with quote

Quote:
...why don't more people do that?


Well, in fact many people do it...when the objective is mounted in a microscope.
In most cases the final magnification on sensor is realised in two steps: objective and relay optics (the equivelent of the eyepiece, in some cases including true eyepieces).

What an eyepiece or relay optics does is to amplifly the objective aerial image.

The typical magnification on sensor is usually higher than the nominal objective magnification when using big sensor cameras, for exemple 2.5X for FF and 1.6X for APSC. I most cases the goal is to capture a rectangle inscribed inside the round visual field
Many microscopes can increase the magnification by means of magnification changers or switching between different relay optics.

Microscopists do not follow this approach much further: usually is better to switch to a higher magnification objective and with high magnification ones you risk to easily get empty magnification.
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