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