Telecentric optics, third round.

[rjlittlefield]

In previous threads (here and here), I've talked about telecentric optics and why they're attractive for making big images using a stack-and-stitch approach. But those threads have used some lens setups that could charitably be described as "special purpose". In this thread I'll discuss a telecentric lens design that might be more practical, particularly as a modification of some existing device like a microscope.

Recall that one of the definitions of a telecentric lens system is "the entrance pupil (apparent position of the aperture) is at infinity".

In my earlier postings, I made that happen primary by adding an auxiliary diaphram, so that the limiting aperture fell at the rear focal point of existing lens elements.

In this post, I take the alternative approach of adding a lens element between the existing lens and the subject. With proper strength and position, the added lens causes the existing aperture to appear at infinity.

Here's the concept.



The thing called "Normal Lens" is the existing lens. I've diagrammed it here as a thin lens, with its aperture at its center. In reality, the Normal Lens would be thick, with lots of glass between the aperture and the subject. It really doesn't matter where the aperture physically is, just where it appears to be. Those converging rays point to where it appears to be.

The added lens has focal length f_added, and it's positioned exactly that far away from the previous entrance pupil position. If you look upward through the added lens with a telescope, the aperture will focus at infinity.

The choice of f_added is not critical, though there are some constraints. It has to be short enough that you can fit the added lens between the normal lens and the subject, while the system as a whole is refocused on the farthest depth. And it needs to be long enough that it can have decent diameter and still not introduce aberrations. Ignoring illumination, the best added lens would be the longest possible, fitting right against the subject at deepest focus. Illumination considered, some shorter length may be a better choice.

I prototyped several variations of this scheme today, and I'll show you the best one. The first few were done with fancy lenses, and while illustrative they weren't exactly compelling. Then I happened to remember the little box of lenses that I bought ages ago for the kids to play with. Lo and behold, in one envelope there was a partially delaminated achromat of just the right size to work with. Sometimes you get lucky...

The lens system that I'm going to make telecentric is a closeup rig consisting of an 80 mm lens on just enough bellows to reach 1:1. That puts the subject around 160 mm in front of the lens (and the sensor 160 mm behind it).

The added lens is a basic achromat with focal length around 140 mm, and a diameter of 37 mm. That length puts it just barely in front in the focus plane when it's positioned to give perfect telecentricity, and the diameter is more than enough to surround my entire 22.7x15.1mm field.

It turns out, of course, that perfect telecentricity may not be needed. In the grand scheme of stack-and-stitch, the computer can give us perfectly parallax-free geometry simply by refusing to scale images to compensate for differences between focus planes. It's OK if the optics produce a slight change in magnification with distance -- that change just has to be small enough that there's no significant lateral movement of image features from the depth that they start to come into focus, until the depth they go out.

So in addition to testing at the perfect position, I also tested with the added lens at progressively more approximate positions.

Here are the test configurations. The slanted bar at the bottom is the mm scale of a vernier caliper, seen edge-on.



The left column is the system with no added lens. These optics are very far from telecentric -- the entrance pupil is smack in the middle of the lens. The second column has the added lens in its perfect telecentric position. Subsequent columns move the added lens into positions that are less and less telecentric.

And the results... (drum roll, please)



All columns are using Helicon Focus, autoadjustment turned off. What's shown here are actual pixels of the upper left corner of the full frame (rotated 90 degrees to line up with the configuration photos). Focus step 0.020 in, f/11 on the aperture ring.

As you can see, the left column is completely unacceptable. The optical system has so much magnification change within the DOF slab that stacking without scale adjustment produces terrible "echoing". In contrast, the perfectly telecentric system shows no echos and is quite clear. The third column seems completely acceptable as well. At roughly 10% off from perfectly telecentric, it's providing a 10X reduction in magnification change within the DOF slab. We don't start to see noticeable degradation until the fourth and fifth columns, which at 20% and 30% off from perfectly telecentric, are providing only 5X and 3X reduction in magnification change.

A couple of points worth noting. First, the added lens makes only a modest change in total system magnification, particularly when it's close to the subject. Second, the added lens does not need to be very high quality, again, particularly when it's very close to the subject so that the ray cones are only going through a small part of the added lens. It is important that the added lens be an achromat. A simple lens acts like a prism toward the edges of the field, and you get severe color fringing.

It's late, and I don't know what to add at this point.

Questions, comments?

--Rik
Edit: corrected typo about column numbering.

[phero66]

Rik,

What differences are there (if any) between using the above acromat lens and an enlarging lens w/o the glass (iris only)? Seems to be a bunch of cheap ones on eBay, I just don't know how to remove the glass without perhaps smashing it to bits...

Also, is there any potential pitfalls using a 50mm setup instead of 80mm for telecentric?

Thanks

-John

[rjlittlefield]

John,

Based on very limited experience, I'd say the added lens will work better over a wide range of conditions.

In my setup, the added aperture works OK when the first-stage optics have 2:1 or higher magnification. But at lower magnifications, various forms of vignetting kick in. It can also be physically difficult to place the added aperture at the right place and hold it there. With my 38mm Olympus bellows lens, the right place is actually inside the rear barrel of the lens, though behind the last lens element. For some lenses, the right place could be completely inaccessible.

The one big advantage to the added aperture approach is that it's easier to play with if you don't have an appropriate added lens at hand. One of the test runs that I didn't post used an added aperture made of black paper using a hole punch! (That was with the 38mm Olympus.)

Regarding the enlarging lens, I have disassembled only the one. All of its glass came out easily by removing retaining rings on front and back, and the diaphragm was left firmly fastened into the mount. I have no idea how other lenses are fastened together.

That's a good question you ask, about 50mm vs 80mm. Thinking this through, I guess one general rule is that "longer is better". Consider, for example, using both systems at 1:1. The subject-to-lens distance will be around 100mm in one case, 160mm in the other. If you're taking the added lens approach, the first case requires a correspondingly shorter (higher power) added lens. Since the added lens needs to be at least as wide as your telecentric field, using a shorter added lens may do bad things like limit the field size or crank up the cost. At 1:1, using my Canon 300D, full frame means a field diameter of about 28mm. It's a lot easier to get an achromat whose diameter is 30-35mm at FL=140 than at FL=80 (leaving 20mm for working distance -- and all these numbers are theoretical!). But using the 50mm is certainly not out of the question. For example I see one surplus outfit is currently offering a 65mm FL, 34mm dia achromat for $18. No doubt there are also tradeoffs in optical quality, since a shorter added lens will have stronger curves at the same field diameter.

This reply turned out to be longer than I had anticipated. (They usually do.) Sorry I don't have enough experience to offer simple answers. I hope that talking through the issues is of some help.

--Rik

[phero66]

Rik,

I'm still working on theory myself (most of the equipment is in the mail!). After doing a bit of drawing I immediately saw the problem you mentioned when working with the 50mm and not having enough room - between the added lens and subject due to 100mm working distance. For me it gets worse because I have a 5D w/ 36mm sensor size. From the site you mention it looks like my only option is in the longer FL range.

One more question though, I'm new to this whole macro world and need to ask you a VERY stupid question If I reverse the 50mm will it give me more FL to work with (or was that already figured into the 100mm distance)?

Thanks,

John

[rjlittlefield]

[phero66]

Rik,

Well shoot, looks like i will have to do some experimenting, but I have a feeling its going to be too difficult to manuever, especially since I want more then 1:1.

In the mean time I have a spherical pano-head coming (Nodal Ninja), and if I calculate the weight of my gear right, it should hold my camera with the 50mm reversed on a Pringles can. Chips anyone?

http://www.photocritic.org/2005/macro-photography-on-a-budget/

[rjlittlefield]

50mm reversed on a Pringles can, mounted in a Nodal Ninja -- now there's an image that makes even my head hurt! I shall eagerly await a test report. I could never figure out how to properly control focus with a rig like that.

A couple more thoughts that come to mind...

First, I just realized that you said you're new to macro. I'd recommend to get comfortable with ordinary macro techniques first, before moving up to stacking for increased DOF at high resolution. Then get comfortable with stacking before moving up to stack-and-stitch. The whole purpose of stack-and-stitch is to get high resolution and large DOF over a large field. And the whole purpose of telecentric optics is to simplify stack-and-stitch at lower magnifications where the optics' intrinsic DOF vs change in scale with distance would otherwise cause smearing or echoing if the computer tries to enforce parallax-free geometry while processing the stack.

It should be clear that these "telecentric" threads of mine are really pretty arcane. Most likely they're not the best places to start if you're new to macro.

Second (since we're here in this arcane thread ), the situation with reversed 50mm on a Pringles can may not be as hard as you're thinking. There are two reasons. First, at high magnifications the optics' intrinsic DOF gets a lot shallower. At larger apertures, which you'll want for best sharpness anyway, the DOF per frame may be so shallow that you can just ignore scale change. That seems to be the way that Steve Valley has been doing his excellent stack-and-stitch work, and it's definitely the way that I did mine for the Autographa moth wings. Second, at magnifications above 1:1, you would be dealing with a smaller field, e.g. only 18x12mm (22mm dia) at 2:1, 9x6mm (11mm dia) at 4:1, so that reduces the diameter of added lens you'd need.

I just now set up a 4:1 system with a 55mm f/1.8 on bellows (150mm extension to the reversing ring). It gives 50mm clear working distance. The entrance pupil for that lens is about 20mm behind the front lens element when reversed, so a 50mm FL added lens would give perfect telecentricity and a fair amount of working distance (20mm minus roughly half the thickness of the added lens). It's simple enough to get a 50mm FL achromat to cover a 9x6mm field, at 4:1. At 2:1, the working distance is around 70mm, and while FL=70mm, dia>22mm is more challenging, it's still doable.

Thanks for the questions. They make me think, and that's always good.

--Rik

[phero66]

Well I would hate to disappoint you but I might have to forgo any Pringles can excursions if I can pull off the level of detail and accuracy of your moth wing image! I will have to do some testing to see how wide open I can get my lens before it loses sharpness.

Is there a general aperture cutoff before parallax becomes an issue? Did you notice any parallax problems when stitching the moth?

As for the 55mm setup you mention, 4:1 @ 50mm working distance doesn't give you much room for lighting right?

-John

[rjlittlefield]

John,

> Is there a general aperture cutoff before parallax becomes an issue?

No simple one.

It depends on the magnification, the FL (actually entrance pupil location) of the lens that's being used, the nature of the subject, and the parameter values used in the software. In the example I posted at the top of this thread, it seems that starting from 1:1 at f/11 with an 80mm lens, we need about 10X reduction in DOF and/or scale change with distance to avoid echos & smearing. The moth wings were at about 2:1 at f/4 and a 38mm lens, only about a factor of 5 better (by a rough mental calculation).

I just now tried reprocessing one of the moth wing stacks. Using Helicon Focus, it renders clean with default R=8, S=4 and no auto-adjustment, but at R=4, S=2 there is just a bit of echo/smearing on particularly susceptible edges.

So, as a ballpark reference point, I'd say the moth wings are near the edge of what can be done without worrying about parallax and/or telecentricity. (I'm using "parallax" here to mean seeing two features in different relationships depending on viewpoint, and "telecentricity" to mean change in scale with distance. Again, you can always eliminate parallax as an issue by just not doing scale adjustments in the software. But then telecentricity becomes important.)

> 4:1 @ 50mm working distance doesn't give you much room for lighting right?

That case is no problem. The lens occludes a cone of lighting that's only about 30 degrees off axis. That leaves 60 degrees of space to get light around the lens, plenty for most subjects.

Where things start to get really sticky is using higher power microscope objectives, whose ratio of width to working distance is much less friendly. My 20X objective (as for the jumping spider foot, 2nd picture) has a working distance of 3.3 mm, which allows only about 30 degrees of space to get light around the lens. That's markedly more difficult.

--Rik

[PaulFurman]

This is a reply from the rear aperture method telecentric thread

The only suitable 'achromat' (if I understand the term) that I have is a +2 diopter closeup lens, 77mm Canon 500D, a nice 2-element piece. Am I remembering correctly that my optometrist said it was about 200mm?

[rjlittlefield]

No, a +2 would be 500 mm (focal length in meters = 1/diopters).

--Rik

[PaulFurman]

I did try it and it sort of worked with a 75mm lens. The pupil went a foot or so behind the lens when viewing from the front and the view through the lens is significantly telecentric. It makes a very awkward rig though, I'd need to mount it on a 9-inch long 3-inch diameter pipe attached to the front of the lens for 0.5x magnification. Possibly useful for hand held stacks except it's a big threatening thing that comes an inch away from the subject so not that good for bugs. It would be nice though since the problem I have with those hand held stacks is my position wavers around so they don't match up well at all, especially bug legs & wings. Telecentricity would solve those problems.

[kds315*]

very interesting concept Rik! I know telecentric lenses from industrial imaging systems and was wondering why it was used only there. Food for thought, so I guess I will start experimenting myself! Thanks for that great push forward!
_________________
Klaus

http://www.macrolenses.de for macro and special lens info
http://www.pbase.com/kds315/uv_photos for UV Images and lens/filter info
http://photographyoftheinvisibleworld.blogspot.com/ my UV diary

[Harold Gough]

[fourchambers]

Great info on the telecentrics!

Now the big burning question I have here...

Any recommendations on telecentric lens or combinations that would yield a higher magnification (beyond 1x and up to 10X)...and also work for a DSLR sensor setup?

The closest I've found is the Edmund / Mitutoyo...but it isn't clear what sensor size they are designed for...guessing a 2/3".
http://www.edmundoptics.com/onlinecatalog/displayproduct.cfm?productID=2481

We've been working on different ways of correcting for parallax, but this is really an ideal method...if we can find the equipment to do it.

So...we need the telecentrics because we are also doing stitching of stacked photos and the less parallax, the more accurate our images and stitches. We go up into the gigapixel range of the final resolution of the image, so we're talking many images and parallax errors add up fast. Examples... http://www.smallworldexplorations.com/

The other factor is that we are trying to keep the equipment as affordable as possible but also reproducible...so that the entire system we are working on is as affordable as possible with the goal of putting it in the hands of not research labs but schools and hobbyists too.

Any ideas?

Thanks!
Gene