I wrote about my "poor man's Repro-Nikkor" here.

http://www.photomacrography.net/forum/v ... highlight=

It is made of two 50mm Olympus Four-thirds macro lenses stacked front-to-front. It acts as if it were an f/1.0 lens with fixed magnification of 1x.

I figured I could move it up from 1x to a bit higher m by bringing the subject closer and adding extension, like any other lens. To my surprise, when I added 26mm of extension and refocused the lens on the subject (which had to be brought much closer to the lens), the size of the image stayed about the same size! In fact it shrunk slightly, by approx by 2%. What on earth is going on?

Edit: Ah, that's what a "Measuring objective" does. Perhaps by varying the spacing between the two lenses, or putting my paper aperture exactly in the middle instead of 2mm higher, I could turn my "Repro-Nikkor" into a perfect double-telecentric lens????

## Bizarre: Image size stays constant as lens is extended

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- rjlittlefield
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### Re: Bizarre: Image size stays constant as lens is extended

Lou, welcome to yet another of the often unexpected behaviors of lens combos!

The relevant formula is given at https://en.wikipedia.org/wiki/Lens_(optics)#Compound_lenses :

When d = f1+f2, it reduces to 1/f = 0, which implies that f, the effective focal length of the combined system, is infinite! Probably confusingly, this combination that has infinite focal length is nonetheless capable of focusing at finite conjugates with no problem.

The catch is that the combined system still obeys the extension formula that

AddedMagnification = AddedExtension / EffectiveFocalLength ,

and with EffectiveFocalLength = infinity, that formula correctly predicts zero change in magnification as you change extension!

The particular combo that you're testing apparently has d > f1 + f2. That drives the effective focal length of the combined system into the negative range, which in turn implies that as you add extension you get less magnification. The change is small because the focal length has large magnitude, because d is not

Personally I find it quite counterintuitive that a lens combination with negative effective focal length can nonetheless focus with finite conjugates, but yep, that's the way it works. Interestingly, the ray tracing diagrams don't seem confusing at all. The problem is only that I'm so used to the simplified formulas that ignore lens spacing. Those simplified formulas become increasingly inappropriate as the spacings get large, and in cases like you have here, they make wildly crazy predictions.

However, it's worrisome that your image size shrank slightly as you added extension. That indicates you need to slightly reduce the separation between the lenses, and I can imagine that might be mechanically challenging to accomplish.

--Rik

The relevant formula is given at https://en.wikipedia.org/wiki/Lens_(optics)#Compound_lenses :

When d = 0, this reduces to the classic thin-lenses-with-no-separation formula that 1/f = 1/f1 + 1/f2.If two thin lenses are separated in air by some distance d, the focal length for the combined system is given by

1/f = 1/f1 + 1/f2 - d/(f1*f2)

When d = f1+f2, it reduces to 1/f = 0, which implies that f, the effective focal length of the combined system, is infinite! Probably confusingly, this combination that has infinite focal length is nonetheless capable of focusing at finite conjugates with no problem.

The catch is that the combined system still obeys the extension formula that

AddedMagnification = AddedExtension / EffectiveFocalLength ,

and with EffectiveFocalLength = infinity, that formula correctly predicts zero change in magnification as you change extension!

The particular combo that you're testing apparently has d > f1 + f2. That drives the effective focal length of the combined system into the negative range, which in turn implies that as you add extension you get less magnification. The change is small because the focal length has large magnitude, because d is not

*much*greater than f1 + f2.Personally I find it quite counterintuitive that a lens combination with negative effective focal length can nonetheless focus with finite conjugates, but yep, that's the way it works. Interestingly, the ray tracing diagrams don't seem confusing at all. The problem is only that I'm so used to the simplified formulas that ignore lens spacing. Those simplified formulas become increasingly inappropriate as the spacings get large, and in cases like you have here, they make wildly crazy predictions.

Perhaps. What's needed is to have lenses be exactly the correct distance apart, and to have the central aperture be located at the focus point of each lens individually. When you do that, you will have completely fixed the magnification as the ratio of focal lengths, and the combination will be telecentric on both sides.Lou Jost wrote:Perhaps by varying the spacing between the two lenses, or putting my paper aperture exactly in the middle instead of 2mm higher, I could turn my "Repro-Nikkor" into a perfect double-telecentric lens????

However, it's worrisome that your image size shrank slightly as you added extension. That indicates you need to slightly reduce the separation between the lenses, and I can imagine that might be mechanically challenging to accomplish.

--Rik

The male-male ring I used to join them was an especially fat one. Maybe I can find a thinner one and hit that special spot.

I wonder if the real Repro-Nikkor has similar behavior.

- rjlittlefield
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My male-male ring has a three-millimeter spacer between the threads. I could sand down the lenses' front threads a bit, or destroy the ring and mount the threads on the outside of a 50mm cylinder with epoxy....

Could I find that distance, and the proper place to put the aperture, by finding the front focal plane of each lens when the rear element is aimed at the sun, and making sure that the two planes overlap?

If so, then just about any pair of stacked lenses that don't have deeply recessed front elements can be made telecentric on image and object sides. That could be useful.

Is there some cost in IQ? We usually find that large distances between lenses causes aberrations.

- rjlittlefield
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Right. That will give you magnification 1.4 or 1/1.4, depending on which lens is in front.Lou Jost wrote:I see there is nothing special about the lenses having the same focal length. I can replace one of the 50mm lenses by my 70mm lens (also excellent) and then I only need to add a bit of distance, not shave it off.

Yes, that sounds correct.Could I find that distance, and the proper place to put the aperture, by finding the front focal plane of each lens when the rear element is aimed at the sun, and making sure that the two planes overlap?

Probably. But as always with lens combos, the devil is in the details. It's impossible to know from published specifications how well the IQ will hold up. What you find experimentally with a particular pair of lenses can reasonably be expected to apply with other samples of the same lenses. But it won't apply to other models of lenses, even from the same line.Is there some cost in IQ?

--Rik