Comparing macro lenses using MTF - part II

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ray_parkhurst
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Post by ray_parkhurst »

elimoss wrote:
ray_parkhurst wrote: In general how well do short tube lenses (75-80mm) work in this stacked arrangement? Would I see significant vignetting?
I tried the SK 50 f2.8 reversed on the Rokinon 135 f2 without vignetting on APS-C. I tried same on an old 50mm lens and there was too much vignetting.
Didn't try anything between.

I also wonder whether we should try focus distances on the 'tube' lens other than infinity. We are using the SK 50 (or your favorite enlarger) as a diopter or close up filter; I don't think we should necessarily expect infinity focus to have the best IQ. But clearly it works alright.
I would expect somewhat off infinity focus to be best since for sure enlarger lenses were not designed for operating at infinity.

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Post by rjlittlefield »

elimoss wrote:I also wonder whether we should try focus distances on the 'tube' lens other than infinity. We are using the SK 50 (or your favorite enlarger) as a diopter or close up filter; I don't think we should necessarily expect infinity focus to have the best IQ. But clearly it works alright.
ray_parkhurst wrote:I would expect somewhat off infinity focus to be best since for sure enlarger lenses were not designed for operating at infinity.
"Thinking out loud" here...

If, say, the enlarger lens is 50 mm and optimized for 10:1, then its ideal situation would be to produce output rays that are converging around 0.5 meter behind the lens.

To get that part exactly right would require a tube lens that is focused about 2 diopter "beyond infinity", and I'm guessing that's not near the design point for any tube lens either.

So, finding the absolute best sweet spot seems to be a matter of balancing empirical tradeoffs. Having the region between the lenses be infinity space might be viewed as a first shot at doing that, by making both lenses be "equally unhappy" with their share of the work.

--Rik

elimoss
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Post by elimoss »

rjlittlefield wrote:
To get that part exactly right would require a tube lens that is focused about 2 diopter "beyond infinity", and I'm guessing that's not near the design point for any tube lens either.
Good thoughts. I think that is a good rationale for infinity being a reasonable starting point, particularly if the tube lens performs well at infinity.

It does make sense to me that if the tube lens would be focused to rays at the design point of the reversed enlarger then those rays would be converging beyond infinity. However, I am not sure how to intuitively understand 1/2 meter -> 1/(1/2) diopters -> 2 diopters beyond infinity nor how to actually focus a tube lens to that. Kind of like when a kid says, "infinity + 1" as a superlative, but in this case, infinity + 2 diopters. :lol:

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Post by rjlittlefield »

elimoss wrote:However, I am not sure how to intuitively understand 1/2 meter -> 1/(1/2) diopters -> 2 diopters beyond infinity
"Beyond infinity" just means that the incoming rays from each point on the subject are already converging toward the lens. This contrasts with focusing "at infinity" which means that the incoming rays from each point on the subject are parallel, or focusing on a subject "closer than infinity" where the incoming rays from each point are diverging toward the lens.

"2 diopters beyond infinity" means that the incoming rays are converging to a point 1/2 meter behind the lens, if the lens were not there.
nor how to actually focus a tube lens to that.
If you happen to have a +2 diopter closeup lens handy, then just stick that close in front of the tube lens and adjust the combo to focus at infinity.

More generally, you could focus at infinity, then reduce the extension by a distance equal to FL-(1000/(1000/FL+2)) , where FL is the focal length in mm of the tube lens.

For example using a 100 mm tube lens, the reduction would be 100-(1000/(1000/100+2)) = 16.67 mm.

You can confirm this calculation by observing that the combo of a 500 mm lens plus a 100 mm lens is equivalent to a lens of FL = 1/(1/500+1/100) = 83.33 mm = 100 - 16.67 mm.

Unfortunately, these (relatively) simple calculations assume "thin lenses" with no separation. With real thick lenses in barrels, they're only approximations, and not necessarily very good ones.

As a matter of practice, I'm afraid that results will end up having the form "This is what I did, and these images show how well the combo worked". I don't expect theory to provide much insight for this problem, beyond what's already been discussed.

--Rik

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Post by mjkzz »

Thanks for the explanation, Rik, I got the 0.5m (or is it 0.55m, not to nitpicking) part, but stumbled upon "+2 diopters "beyond infinity"", too.

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Post by mjkzz »

Rik wrote: You can confirm this calculation by observing that the combo of a 500 mm lens plus a 100 mm lens is equivalent to a lens of FL = 1/(1/500+1/100) = 83.33 mm = 100 - 16.67 mm.

Unfortunately, these (relatively) simple calculations assume "thin lenses" with no separation. With real thick lenses in barrels, they're only approximations, and not necessarily very good ones.
With thick lens, if we know the structure of it or finding an equivalent thin lens, we can still model it even though the tube lens is not close enough to this equivalent lens, we can think of them as cascaded lens.

Of course, the formula 1/f = 1/f1 + 1/f2 will be invalid because of separation (between tube lens and equivalent thin lens), but if we know the separation distance, which can be measured, then we can calculate it stage by stage in cascading manner.

Edit: by finding equivalent thin lens, lets take one example, say a Canon EF 100mm lens, if after some experiments or calculation based on its structure, the equivalent thin lens is a 100mm lens located some where in the middle of the barrel. In this case, the tube lens and this equivalent lens will have a gap that will make 1/f = 1/f1 + 1/f2 invalid. Thus we need to model the assembly as two lenses cascaded together.

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Post by rjlittlefield »

mjkzz wrote:With thick lens, ... we can still model it
Yes, of course. In that case the relevant equations come from "thick lens" theory. "Thick lens" is a technical term, which you can use to search for many articles.

To do the analysis, you will need to know the locations of the principal planes for both lenses, so that you can determine the effective separation between them.

If you're very lucky, those locations might be listed in technical literature for the lenses. In that case, the only challenge is to be sure that you've identified the correct principal plane, because they're often reversed from what you might expect.

If the locations of the principal planes are not listed in the literature, then you would have to measure them.

I've done that task a couple of times, mainly in search of insight that I did eventually find. ("Oh, that's why adding extension didn't give me as much additional magnification as I expected!".

But despite the eventual satisfaction in those cases, I also found the measurements and calculations to be tedious and easy to mess up.

For the task of optimizing a lens combo, I personally would skip detailed calculations and go straight to empirical testing.
is it 0.55m
Yes, 0.55 would be the exact calculated number. That's measured behind the appropriate principal plane of the reversed enlarging lens, and assuming that the focal length really is exactly 50 mm. Given those complications, and considering that the peak of the optimum is probably broad, I decided that "around 0.5m" would be a helpful simplification. Maybe I should have gone with the exact number to avoid unnecessary confusion.

--Rik

mjkzz
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Post by mjkzz »

Thanks Rik, now, because of my mis-use of the term "thick lens", now I think I know how to model a thick lens :D

I was thinking about a lens with multiple groups and elements, like Nikkor EL-50 and I thought that can be thought of as "thick lens". I thought that each element in a lens could be thought as thin lens, and knowing its parameters, we can model the whole lens easily. Now I know how to model a real thick lens, it is even better, probably more accurate if we treat each element in a composite lens, ie, like Nikkor EL-50, as thick lens instead.

Adding tube lens or relay lens to an existing lens can also be modeled -- simply add that additional lens to the model with its parameters and separation between them.
Rik wrote: But despite the eventual satisfaction in those cases, I also found the measurements and calculations to be tedious and easy to mess up.
So true, I messed up a few times with a simple two lenses setup!!! And that is only 2 lenses. It is the sign of parameters I keep messing up. But for proficient optical engineer, it is probably piece of cake.

Miljenko
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Post by Miljenko »

Thank you guys for this inspiring discussion which coincides with my intuitive contemplation. Every time I was adjusting tube lens for infinite focus, I was thinking about the lens on test that was actually NOT designed to project at infinity. I was tempted to try other focusing plane distances but the whole project was already so time consuming that I've left this experiment for some other ocassion. I might pick those magnification group winners in a near future and retest while adjusting tube lens.
Miljenko
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