Better resolution with curved prisms? (1 Viewer)

Hello Gentlemen,

Here is a question that has come to my mind and I hope those of you with a good background in theoretical optics help clarify.

Background:
The errecting prism system (be it porro or roof) is normally placed in the light path of the objective lens before its focus plane. The errecting system is equivalent to a thick flat glass plate when it comes to its effect on image aberrations. A flat glass plate does not introduce any aberrations if placed in collimated (parrallel) beam but in a focused beam it introduces several aberrations including spherical aberration.

Idea:
If we shape the front and back surfaces of the errecting prisms so that they look like spheres with center at the focus point, then the "unfolded" (i.e. equivalent) prism will act like a zero-power miniscus lens in the focused beam. As a result, it will not introduce any aberations on the optical axis.

Question:
The above idae will eliminate aberrations caused by the prism on the part of the image on or close to the optical axis. It might cause increased aberrations in oblique beams that create the off-axis parts of the image. Is this a trade of worth considering? Any comments or experinces on this??

Omid,
I don't have any experience with it, so don't have a feel for the magnitude of the problem, but that sounds to me like a good idea, theoretically. Your are right that flat glass in the path of a converging beam introduces a monochromatic aberration which is very close to spherical. It isn't clear to me that it is purely spherical, but close enough I think. I have read, for example, in old optics books, that one reason the Kellner eyepiece was common in binoculars was its spherical aberration, which happens to cancel that introduced by the prisms and fast objectives. I have also read of early Zeiss Apo scopes where the objective and star diagonal (90 deg bending prism) came in "matched sets" to cancel spherical aberration. Your idea would optimize for the use of perfect eyepieces and perfect objectives, which would be an advantage for "binocular telescope", with interchangeable eyepieces intended for astronomy. Of course every intermediate gap in the prism, not just the first and last surfaces, would require the spherizing treatment.

I think the idea has practical downsides though, mainly the expense of shaping prism surfaces into spheres, which would then require better alignment, and also the possible introduction of ghost images by close convex and concave surfaces having the same curvature, internal to a 2-piece prism. The latter is an annoying problem in old uncoated telescope lenses, mostly solved with antireflection coatings. But before coatings were developed, the best design was often compromised to make facing curves not quite match, to avoid these ghosts. Provided the instrument has built-in eyepieces, and the designer is skilled, it is probably cheaper to simply make flat prism surfaces, and while designing the optical train, just go ahead and put the necessary canceling spherical aberration into the objectives and eyepieces. This might be a little harder to design, but would pay off in manufacturing costs.

In addition, I think there might be also a color aberration introduced by prisms. Dispersal of a converging beam at the entering boundary is not completely undone at the exiting boundary. Colored rays are indeed restored to their original directions on emergence, but their locations have been mixed up, ie., the point has been spread. Your idea would solve that problem too, if indeed it occurs (comments appreciated I may be crazy on this one), on axis.

Thanks for sharing this very interesting idea!
Ron

Omid,
Let's imagine the first of a pair of Porro prisms to be represented, without the complication of reflection, by a chunk of glass that is convex on the front, and concave on the back. The radii of these surfaces has been chosen to match the focal ratio of the objective, so that on-axis light meets the entrance and exit surfaces normal, at all points it strikes, hence passes through the prism without refraction or dispersal.

Now consider light from an off-axis direction. It meets the first surface more obliquely than if that surface was flat, and that is a bad thing. It meets the second surface less obliquely than if it was flat, a good thing. So, unfortunately, I haven't a clue whether the off axis performance would be bettered, or worsened, by the curved prisms!
Ron

ronh said:

Omid,
The radii of these surfaces has been chosen to match the focal ratio of the objective, so that on-axis light meets the entrance and exit surfaces normal, at all points it strikes, hence passes through the prism without refraction or dispersal.

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Yeah, that is exactly what i meant: to make the beam strike the prism glass surfaces at normal angle hence removing all the aberrations. Unfortunately, this only works for the center point of the field of view.

As you explained, it is not clear if the off-axis image aberrations will be increased or decreased by this technique. Furthermore, again as you correctly pointed out, the designer might be able to cancel out the aberrations introduced by the errecting prisms by designing the objective/prism/eye-piece system as a total unit. But is it really that easy? May be if we give the designer this additional degree of fredom (i.e. spherical prism surfaces) he might be able to use them to his advantage?

The major thing to consider is manufacturing tolerances.

Not only how to you make these high precision objects but how you install and align them. Both prism would have to be aligned precisely in 3 dimensions (they have to be centered ... regular porro prisms don't or rather if they aren't they don't suffer very much) and with correct tilt along three directions too.

One of the nice thing about the porro prism errector is it doesn't require high precision components or high precision alignment either. The current porro prisms right angle has a tolerance of 60 seconds or so. SP prisms need a tolerance of a few seconds and a sharp roof edge.

I suspect even ignoring potential other off-axis issues actually building bins with these would be prohibitively expensive. And the current top bins show you that it's not really needed.

I'm pretty sure good bin designs are correcting for those aberrations in the ocular design. And it's easy to do in that assembly.

Production engineering often kills off all sorts of potentially interesting designs.

Kevin Purcell said:

Production engineering often kills off all sorts of potentially interesting designs.

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Yes. But there is hope too! There is always a small market for the very best device, no matter how expensive it is. Amateure astronomers pay thousadnds of dollars and wait in line for months to get the best refracting telescopes.

Anyway, I agree that a curved porro prism would be more costly to make and align but this doesn't make it more complicated to make than a roof prism with all the tight tolerances needed, does it?

The main issue with my idea, as you and Ronh pointed, is the possibility that the gain obtained in aberration reduction might be very small or nonexistant. I am not an experinced lens designer so I can't be sure if this is true or not.

Binocular objectives have always been designed to work properly only when prisms are included in the light path. It's quite amazing how bad the image is if you place a binocular objective and its eyepiece at opposite ends of a hollow tube without the prisms in between. I think if a curved surface were useful at the prism entrance it would be cheaper and easier to simply cement a plano-convex lens to the prism rather than try to make the prism itself convex.

Henry,
If I read you right, binocular eyepieces and or objectives are typically made with aberrations to cancel those from the prisms.

So, how do binocular telescopes, that accept "perfect" eyepieces intended for astronomy, do it? It seems like this would be a worse problem at their higher magnifications. Is all the compensation built into the objectives?
Ron

Ron,

I think it's more like the objective and prisms are made to work together for lower (not cancelled) chromatic and spherical aberrations. I don't think the eyepiece plays much of a role in reducing axial aberrations. My slight understanding of this is that the prisms cause overcorrection of SA and bring red to closer focus with green while at the same time sending blue farther out of focus compared to green. The overcorrection of the prism acts to partially correct the undercorrection of SA in the fast objective and the color correction of the objective design is shifted toward blue at the expense of red to compensate for the extra blue CA coming from the prism.

Henry

Henry,
Thanks for that explanation.
Ron

henry link said:

It's quite amazing how bad the image is if you place a binocular objective and its eyepiece at opposite ends of a hollow tube without the prisms in between.

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Very interesting! Have you actually observed this yourself? I have taken a few chinese-made binoculars apart but havn't done such a test yet. I'll try it!