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avogra

Joined: 31 Oct 2017
Posts: 6
Location: Munich / Germany

rjlittlefield

Joined: 01 Aug 2006
Posts: 19245
Location: Richland, Washington State, USA

 Posted: Tue Oct 31, 2017 4:03 pm    Post subject: avogra, welcome aboard! 1. The absolute limit is actually 2 details per wavelength, not one-half detail per wavelength. Think one per peak of a standing wave. But when imaging with a lens, the smallest resolvable detail is determined both by the wavelength of light and the width of the lens aperture. Your friend's rule is correct for say a 10X microscope objective with NA = 0.25 (NA = Numerical Aperture). That is because cutoff frequency is (2*NA)/wavelength, so NA=0.25 gives 1/2 cycle per wavelength. As an example, Mitutoyo rates their 10X NA 0.28 objective at a "Resolving Power" of 1.0 micron. Higher magnification objectives with wider apertures can resolve finer detail, in proportion to the NA. In addition, you need at least 2 pixels per resolvable detail element (Nyquist sampling limit). 3-4 pixels is better, as shown & discussed at http://www.photomacrography.net/forum/viewtopic.php?t=2439 . With that 10X NA 0.28 objective, 1.0 microns on subject becomes 10 microns on sensor, so your 4 micron pixels give only about 2.5 pixels per detail element. That's barely adequate. At higher magnifications, the magnification grows faster than the resolution does, so things get better for your sensor. Using the Mitutoyo 50X NA 0.55, rated at 0.5 microns, each detail element becomes 25 microns on sensor which is a little over 6 pixels per detail element. That's more than you need, so indeed the sensor is out-resolving the lens by a factor of 2 or so. 2. The Componon-S 50/2.8 is an excellent lens. In general, the only reliable way to determine best f-stop is by experiment, shooting at a range of apertures. Even so, the result that you get may only be correct for that one lens, due to manufacturing and history differences between lenses. (Example: some Canon MP-E 65 lenses are clearly best wide open at f/2.8; others are clearly best one stop down at f/4.) The sharpest aperture also varies from one magnification to another; typically larger magnifications require wider apertures to reduce diffraction blurring. If you don't have time to run a test with your own equipment, then using the data reported at coinimaging.com is generally a pretty good way to go. However, in this case I notice that the lens was tested at m=1.3, which is significantly different from your m=3 and is also not near the magnification that lens was designed for. I have not run an aperture test series for my sample of that lens, but I would probably choose f/4 at 3:1. That would give f/16 effective, which corresponds pretty well with the cutoff resolution for 4 micron pixels. By the way, be sure that you reverse the Componon, so that the side designed to face the film when enlarging, faces the subject when shooting. Failing to reverse the lens will give a lower quality image due to aberrations introduced by the not-as-designed focus arrangement. BTW, the bold-face recommended settings in the zerenesystems.com tables assume perfect lenses. (I constructed those tables, so I am quite sure on this point.) As with all DOF tables and formulas, you would have to run a test for yourself if it is important to know for sure. But I generally use the step size values straight out of the table, rounded down if necessary to some convenient value, after first choosing my aperture based on either personal testing or published data as discussed above. 3. Almost everything that you list is promising. The Componar 75/4 is an exception. It is a simpler design from the other lenses, optimized for cost rather than quality. --Rik
Chris S.

Joined: 05 Apr 2009
Posts: 3040
Location: Ohio, USA

Posted: Tue Oct 31, 2017 9:47 pm    Post subject:

Avogra, welcome to the forum!

 rjlittlefield wrote: Using the Mitutoyo 50X NA 0.55, rated at 0.5 microns, each detail element becomes 25 microns on sensor which is a little over 6 pixels per detail element. That's more than you need, so indeed the sensor is out-resolving the lens by a factor of 2 or so.

For a demonstration of this lens near its resolution limit on a sensor very like yours (my Nikon D7100), look at the fourth image here. The scale bar is 1/2 micron square. To my eye, details one-half the width of the scale bar are convincingly rendered. If so, Mitutoyo's specification is conservative by a factor of 2 or so--nicely matching the resolution of the sensor!

--Chris S.
avogra

Joined: 31 Oct 2017
Posts: 6
Location: Munich / Germany

 Posted: Wed Nov 01, 2017 6:10 am    Post subject: Hi Rik, Thank you for this wealth of information! So the mystery of resolution is solved :-D The componon is reversed, so no issue here. I think my next steps will then be some tests of the componon at different magnifications and apertures. I remember a thread with some laser printed sheets as target at 200%, that seems to be a quick and easy method. After that I will do the same with the tamron with achromat and extensions. For when i try the stacked lenses, this is what I picked up: some stop down the combo with black cardboard between the lenses instead of using the lenses' stop. Put the lenses as close together as possible. Set focus of both lenses to infinity. AnThing else to take care of? Oh, and I have to post some pictures of my rig and especially the stacking rail :-) - Alex
cube-tube

Joined: 10 Oct 2017
Posts: 67
Location: Durham, NC

 Posted: Wed Nov 01, 2017 7:13 pm    Post subject: About maximum resolving power... I think that you also need to consider that no lens is anywhere near optically perfect. So even if technically you're in a situation where the maximum resolving power will match perfectly to each individual pixel, which would be well below 50x, you can still resolve finer detail with higher magnification because the objective/tube lens combo will scatter some light.
avogra

Joined: 31 Oct 2017
Posts: 6
Location: Munich / Germany

Posted: Thu Nov 02, 2017 12:47 am    Post subject:

Chris, I missed your post. Great take! It's exciting to approach physical limits especially if it's at home and not in a super fancy laboratory.

And thank you both for the warm welcome!

 Quote: For when i try the stacked lenses, this is what I picked up: some stop down the combo with black cardboard between the lenses instead of using the lenses' stop. Put the lenses as close together as possible. Set focus of both lenses to infinity. AnThing else to take care of?

Any advice on the stacked lenses?

-Alex
rjlittlefield

Joined: 01 Aug 2006
Posts: 19245
Location: Richland, Washington State, USA

Posted: Thu Nov 02, 2017 10:10 am    Post subject:

Alex & Chris,

To clarify about the resolution issue...

The limiting resolution of 1 micron for 10X NA 0.28 and 0.5 micron for 50X NA 0.55 is for a full cycle of information, essentially one complete dark/light line pair.

An alternative interpretation is that it's the minimum distance between two bright points that will be rendered with a darker division between them.

In Chris's images at http://www.photomacrography.net/forum/userpix/679_Mitty50xlensesPMaxstackscomparedsingleflatwingscalecroppedforhalfmicronbiggererer_1.gif, it's clear that we can see individual features such as dark bars or bright spots that each are smaller then 0.5 microns.

But that's completely consistent with what the formulas predict, when they are correctly interpreted. Mitutoyo's spec is not conservative.

Earlier, I wrote "In addition, you need at least 2 pixels per resolvable detail element (Nyquist sampling limit). 3-4 pixels is better, as shown & discussed at http://www.photomacrography.net/forum/viewtopic.php?t=2439 ." That phrase "resolvable detail element" was not as clear as it should have been. It means a full cycle, a line pair if you will, and it's that full cycle that requires 2 pixels at the Nyquist limit, or better 3-4 pixels per cycle. Even more is better still, but at 6 pixels per cycle at 50X NA 0.55, the sensor is indeed out-resolving the lens.

 Quote: It's exciting to approach physical limits especially if it's at home and not in a super fancy laboratory.

Agreed, and this is commonly the case when working with high mag optics. Light waves are just painfully long compared to lots of the features of our subjects. It's like trying to make an accurate picture of a marina by interpreting the waves that bounce off the boats and pilings.

--Rik
avogra

Joined: 31 Oct 2017
Posts: 6
Location: Munich / Germany

 Posted: Wed Nov 08, 2017 12:27 pm    Post subject: Recently I stumbled across a thread where a simple formula was posted for calculation of the (effective?) aperture for stacked lenses when both are set to infinity focus and an aperture is inserted between the lenses. I have been searching the thread for an hour now but can't find it anymore. I think it was something like EA = "diameter of aperture"/"focal length of rear lens". Can someone confirm that? Is this something worth mentioning in https://www.photomacrography.net/forum/viewtopic.php?t=8336 ?
rjlittlefield

Joined: 01 Aug 2006
Posts: 19245
Location: Richland, Washington State, USA

 Posted: Wed Nov 08, 2017 7:10 pm    Post subject: The valid version of that formula would be the other way up: EA = "focal length of rear lens"/"diameter of aperture". But that leads to the next question: what is "diameter of aperture"? The answer is that "diameter of aperture" is the smaller of rearFocalLength/rearFNumber and frontFocalLength/frontFNumber. Physically, each lens has an aperture diameter that is determined by its own focal length and f#, and it's the smaller of those two apertures that limits the pencils of light that get through the combo. At least that's the simple model. It works OK when the two apertures are different enough that only one of them is limiting. As an example, if you reverse 50 mm f/2.8 in front of 200 mm f/5.6, then the 50 has its aperture diameter 50/2.8 and the 200 has its aperture diameter 200/5.6. The smaller of those is 50/2.8 = 17.857, and then 200/17.857 = 11.2, so the answer is effective f/11.2 for the combo. An equivalent approach that avoids the intermediate calculation is that the effective f# of the combo is either the f# of the rear lens, or the f# of the front lens multiplied by rearFocalLength/frontFocalLength, whichever is larger. The larger of those is 2.8*(200/50), again = 11.2, so f/11.2 . --Rik
avogra

Joined: 31 Oct 2017
Posts: 6
Location: Munich / Germany

 Posted: Thu Nov 09, 2017 9:47 am    Post subject: Thanks Rik! One piece is stll missing for me: I guess that if a lens is focused to infinity, and I put a diaphragm in front of the lens, then i can use the diameter of the diaphragm as aperture size? To stay in your example I would guess, that a diaphragm with a hole of 20mm between the lenses has no effect at all, as the aperture is still limited by the 50/2,8 lens. When I put a paperstop with a hole of 10mm between the lenses, then effective aperture would be f/ (200mm/10mm) -> f/20. Did I get that right? -Alex
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