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timeruinsbelief
01-15-2006, 12:15 PM
ok, call me dense... but what is a zone plate?

earlj
01-15-2006, 01:22 PM
Here's a good start:

http://ca.geocities.com/penate@rogers.com/zoneplate.html

A google search will scare up many more.

timeruinsbelief
01-15-2006, 03:04 PM
wow, reading that i felt like a grade-schooler who wandered into a college physics lecture!
very interesting and sounds like very over my head.

staft
01-15-2006, 04:35 PM
hey, trb- we are pinholers, not competent, normal people! if we can do this, anybody can. the only thing more complicated than a pinhole is that you need to match the focal length of zp to camera, and the f-stop will be larger (around f64?) and exposures faster. and you've gotta embrace the tao of fuzzy...

ImageMaker
01-15-2006, 05:08 PM
Say, reading Penate's description of the fuzziness being caused by undiffracted light gives me an idea. Could one mount a second, negative ZP behind the primary one, positioned to block the bulk of the unrefracted light, but pass (and possibly even refocus) the light that's been bent by diffraction? Distance would be somewhat critical, in order to have the clear and opaque zones exactly offset, and one might need the second plate to be concave toward the first to get a perfect match, but I expect you'd see improved sharpness even with a simple contact "print" in perfect register, separated by the thickness of a single film base. As a bonus, the maximum film density requirement would be relaxed...

Andrew
01-15-2006, 05:11 PM
also look up "pinhole sieves"... very very C_O_O_L ;)

gneissgirl
01-15-2006, 07:49 PM
...and check out some of Daryl's pinhole seive shots on this forum (if I remember correctly).
Way cool.

earlj
01-15-2006, 09:47 PM
ImageMaker:


positioned to block the bulk of the unrefracted light, but pass (and possibly even refocus) the light that's been bent by diffraction

Can you come up with the math to support this post? Or can you come up with the image to prove the point? I am exremely intrigued by your proposition, but I can't make my reality to mathematics abstraction machine come up with the mental algorithm. Please send assistance right away; my cooling circuits are overloading . . . . .

ImageMaker
01-16-2006, 01:08 AM
Math? I damned near flunked calculus in college 27 years ago (took three tries to get through the first of 3 semesters, then it clicked and the rest was no big deal -- but I quit before Differential Equations), and haven't used any math more advanced than algebra (and darned little of that) since leaving college in 1982.

I can visualize what's happening -- parallel light strikes the zone plate rings as plane waves; diffraction more or less breaks that light into three populations; some is focused and becomes the image, some diverged (as if through a negative lens) to become flare/fog, and some unaffected, to produce the blur by letting the entire plate act as a very oversize pinhole. If a second plate, with dark zones exchanged for light (except the center left open and the outside left opaque), is positioned directly behind the first, the unaffected light will be blocked or, if off axis, still attenuated somewhat.

The diffraction effects of the second plate are less clear -- ISTM, on visualization, that it will have much the same effect as the original; that is, light that strikes it is either converged (giving half the focal length for the combined array), unaffected (focusing at the original focal point for a single plate with the same zone dimensions), or diverged (back to parallel). However, the same is happening with the diverged light -- some of which will be converged back to parallel.

So, it seems what would *actually* happen with a pos/neg pair of zone plates is that you'd get a weakened "pinhole" image, or halo, but a double focus that would add back some strength with a different distribution -- that is, you'd get a *different* halo, but not eliminate it or even significantly weaken it -- and you would lose some light from the "main" image, into the "second focus" halo. Worse (from a standpoint of having any idea what to expect), the two effects would mix differently on axis than off; the "direct pinhole" image would be attenuated most in the center of the image, while the other effects would be strongest there; further off axis would see a gradation to a simple shorter focal length, but otherwise "conventional" zone plate image, as if two lenses were stacked one in front of the other (though building the camera for that shorter focal distance might give an intriguing sort of image that's sharper in the corners than in the center).

Bottom line, I now doubt it would gain anything. Howver, if you have a film zone plate, it would be relatively easy to test; just make a contact copy of the plate onto ortho lith film, develop for high contrast, and mount the two together, emulsion sides facing the same direction. In this simple test configuration you'd lose a lot of light because the center hole would be blocked; in addition, you might find you need additional distance between the planes of the two plates, which would translate to this working better with longer (or shorter, if the film thickness is thicker than optimal) focal length zone plates.

Of course, the analogy between a zone plate and lens may not hold up at the level of stacking them -- I can easily see an alternate outcome (by visualizing individual spherical wavefronts emanating from each transparent point in the zone plate) in which the second plate would have no desirable effects at all, but simply form an image of the first plate, and high school physics was too long ago to let me decide which way the real world would fall...

Josh
01-16-2006, 05:38 AM
This is an intersting theory. The zone plate would be curved much like a lens, yes, and give a different distribution of light , I could not imagine what the resulting image would look like, the image getting less defined towards the limits of the image circle or evenly. From what I understand you propose a slovak style zoneplate with all of the even zones covered instead of the odd as the secondary element concave to the first zp if you will?

I am guessing here but would an aperture behind the fresnel lens refocus the light or give better image definiton, how would this effect the light reaching the zones and the resultant image? I would be inclined to try a single convex zp with an aperture mounted behind, better still if someone can mod a lens barrel you can view the focus through an slr. Then if a slovak was mounted concave? at the bottom I don't think it need necessarily match the size and odd /even distribution as the fresnel zp it would simply need to be centered.

I don't know if this does stack up at all.

ImageMaker
01-16-2006, 02:16 PM
This is an intersting theory. The zone plate would be curved much like a lens, yes, and give a different distribution of light , I could not imagine what the resulting image would look like, the image getting less defined towards the limits of the image circle or evenly. From what I understand you propose a slovak style zoneplate with all of the even zones covered instead of the odd as the secondary element concave to the first zp if you will?

That's about what I was thinking, yes. Honestly, after attempting to visualize it at a wave level, I wonder if you'd get any image at all, but it would be cheap enough to test the first approximation with a flat contact print copy of the common odd-zone plate.


I am guessing here but would an aperture behind the fresnel lens refocus the light or give better image definiton, how would this effect the light reaching the zones and the resultant image? I would be inclined to try a single convex zp with an aperture mounted behind, better still if someone can mod a lens barrel you can view the focus through an slr. Then if a slovak was mounted concave? at the bottom I don't think it need necessarily match the size and odd /even distribution as the fresnel zp it would simply need to be centered.

I'm pretty certain a pinhole behind a zone plate would just form an image of the ZP; an aperture similar in size to the ZP might have some effect in reducing halo but would probably just vignette if it were far enough from the ZP to do anything other than limit the number of contributing zones. As for non-matching Slovak plates, you're completely on your own -- as I mentioned previously, because the focusing effect is all due to diffraction, it's very possible that none of the common rules that govern multi-element lens systems would apply to zone plate optics, and I'm not enough of a wave physicist to be able to say one way or the other. Nor do I have a ZP or lith film around to perform the test. Mounting the plates in a body cap or extension tube to fit a 35 mm SLR, however, would give a nice way to do a few quick tests and potentially get the exposure right the first time, so cut down the bracketing and time requirements.

murrayatuptowngallery
01-17-2006, 12:39 AM
Well, last week I found out this whole pinhole thing is a lot messier mathematically than Rayleigh's optimal formula. I wanted to know where was the rest of his math to justify a Nobel Prize.

I probably can't regurgitate the summary, but something to the effect that the Airy disk diffraction pattern is the 2-dimensional Fourier Transform of the aperture. It falls under the topic of Fourier Optics.
The Zone Plate mimics the Airy diffraction pattern...a circle surrounded by concentric rings, but I don't know how closely they are tied together.

Some of the Zone Plate generator software (pinhole.cz?) describes what happens when you have odd and even numbers of rings in a Zone Plate. Dig further and there is 'in the literature' discussion of what kinds of patterns the internal reflections in multi-element lenses are seen as...not only the number of iris leaves but whether the number is odd or even. This all comes back to which terms in the Fourier Transform are being 'messed with'.

I am taking a mathematical physics class after 13 years out of math classes (so you aren't going to hear much from me for the next few months!) and have to do an extra-curricular paper on any math topic not covered in class, and this qualified. I don't know if it'll kill me to do this, but it's a lofty goal. I want to explore the connections behind the various pinhole optimization constants.

As you probably know, the shape of a pinhole has artifacts also, for the same physical reasons.

So, my guess is you'd be challenged to align a pair of Zone Plates in a manner that approaches optimal...I think it would be a whole new beast.

For what that's worth... in the time it took me to type all this e-Blah, the experiment could already have been done and developed in Acetaminophenal/odinal.

ImageMaker
01-17-2006, 12:07 PM
For what that's worth... in the time it took me to type all this e-Blah, the experiment could already have been done and developed in Acetaminophenal/odinal.

Yep. If I had a zone plate and some lith film, I could have done the whole experiment over the weekend, at the worst -- copy the plate, mount the negative copy, and test the resulting image.

Josh
01-18-2006, 04:20 AM
I'm willing to mutilate a lensbarrel, I ordered a second canon fd 50mm 1.8, I wondered if anyone knows whether it will be a bother to remove all of the elements and simply replace with zp. That's if I can unscrew the screws, I tried the ol' WD-40 but they just won't budge for toffee. I also have a zenit with a helios 44M 50mm that looks simple enough to convert (though I'm quite fond of it for some reason. )

ImageMaker
01-18-2006, 01:41 PM
It's probably a lot simpler (likely cheaper, too) to convert a macro extension tube and/or body cap. No annoying glass optics to remove. The downside is that you need your zone plate(s) focal length to match the length of the tube -- and you'll likely need more than one focal length of zone plate for the pos/neg plate experiment, because of the uncertainty about whether a second plate will refocus the light already affected by a first (though with extension tubes behind a body cap you might be able to get away with one long focus plate and shortening the tube set to test shorter distances with the double plate in place).