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Inferring lens design from behaviour

 
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Beatsy



Joined: 05 Jul 2013
Posts: 1390
Location: Malvern, UK

PostPosted: Wed May 09, 2018 6:26 pm    Post subject: Inferring lens design from behaviour Reply with quote

I'm still having more success with the Linoscan 1800 lenses by treating them as infinity corrected and mounting them reversed on tube lenses.

However, I want to understand the parameters for direct projection too. I did a quick test "off the rig" as working distance and extensions make things a bit too big to fit. I simply taped a receipt to a flat panel lamp then moved each lens between the lamp and the desk (projecting an image of the receipt onto a piece of white paper on the desk). These lenses seem to have two focal points! That is, with the lens closer to the lamp, I get a large, in-focus image of the receipt projected. But as I move the lens closer to the desk (keeping everything else the same distance apart) the receipt image starts to shrink and go out of focus as expected. But as the lens gets closer to the desk, the projected image suddenly comes back into focus again, but this time at (roughly) quarter the size!?!?

Does this imply anything about the lens design that might be useful to know?
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rjlittlefield
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Joined: 01 Aug 2006
Posts: 19318
Location: Richland, Washington State, USA

PostPosted: Wed May 09, 2018 6:38 pm    Post subject: Reply with quote

This is completely ordinary behavior. The lens is focused when 1/f = 1/i + 1/o. Just exchange i and o, and you get the reciprocal magnification in the same subject-to-sensor distance.

Some lenses do exhibit more interesting variations on this effect. Canon's MP-E 65, for example, can focus certain distances at two different magnification settings, but the magnifications are not reciprocal.

--Rik
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Beatsy



Joined: 05 Jul 2013
Posts: 1390
Location: Malvern, UK

PostPosted: Wed May 09, 2018 6:46 pm    Post subject: Reply with quote

Thanks Rik. Obvious when you think about it but I have *never* in my life seen that happen. Ever. I just checked with a loupe and a couple of other simple lenses, and it does exactly that. It just never occurred to me to try it...

Y'know, sometimes I can be really, really, really, thick!! Shocked
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rjlittlefield
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Joined: 01 Aug 2006
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Location: Richland, Washington State, USA

PostPosted: Wed May 09, 2018 7:20 pm    Post subject: Reply with quote

Yeah, right, "obvious when you think about it".

I am reminded of the story about the mathematician who was giving a lecture to his students. At one point in a proof he said, "Now it's obvious that...", and paused. Looked at the blackboard, rubbed his chin, scratched his head, finally left the classroom. Came back 15 minutes later, said "Yes, that's correct, it is obvious", and went on with his lecture.

If you'd like some really counterintuitive behavior, try adjusting the subject-to-sensor distance so that you get perfect focus at 1:1, then move the lens and watch the image. The dang image changes size a lot, but changes focus hardly at all.

Of course that's "obvious" too, once you've worked through the details of 1/f = 1/o + 1/i, but calculus helps, and I predict more than 15 minutes before all becomes clear. I think it's about 50 years for me, and I'm still expecting complete clarity any day now.

By the way, the behavior of the MP-E 65 does tell something about its design. The MP-E is nominally 65 mm focal length , but internally it's really a shorter lens in front with a fixed teleconverter group behind it. The two focus points for same subject-to-sensor distance happen at reciprocal magnifications for the front lens alone. If you set the MP-E 65 at 1X, move a subject to focus, then turn the magnification ring, you'll find that the subject goes out of focus and then comes back in focus at a magnification slightly above 2X. By inference, the teleconverter group must be around 1.4X (harmonic mean of the two focus magnifications).

If you play around to find the minimum focus distance, that will happen at a focus ring setting also around 1.4X, when the front lens is at 1:1. But it's hard to tell quite where that happens, because as noted above that's the point where magnification can be changed a lot without changing focus much at all. Trying to focus-stack "by ring" is a really bad idea in this area.

I just now confirmed this behavior with some quick eyeball tests. Much more care would be needed to get precise measurements.

--Rik
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Beatsy



Joined: 05 Jul 2013
Posts: 1390
Location: Malvern, UK

PostPosted: Thu May 10, 2018 12:45 am    Post subject: Reply with quote

rjlittlefield wrote:
Yeah, right, "obvious when you think about it".

Haha, yes, I meant "thinking about" the formula you supplied (which I'd never come across before). Flippin' obvious, given that.

Quote:

...I think it's about 50 years for me, and I'm still expecting complete clarity any day now.

Similar time scale (and expectation) here! I guess, being positive, I could say I independently discovered a fundamental property of lenses Very Happy
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