How to shift an image optically? (1 Viewer)

I know there are some very bright minds here so I thought I would reach out to my Bird Forum friends regarding this problem I am thinking about.

Assume that we use an objective lens to form an image of a distant object. We then add an erector system consisting of two relay lenses to form an up-right image on a screen (see drawing below). The problem is finding an "optical" way to shift this image up and down by a couple millimeters.

A first way I thought was to shift one of the relay lenses up to shift the image by the same amount.

A second way is to add a tilted glass window or a pair of wedge prisms as shown in the figure. The problem with this solution is it is going to add coma and astigmatism to the image.

What are your thoughts? Thank you for your help!

Tilted glass would be the least disturbing, but it doesn't do much shifting unless it's pretty thick.

Your drawing has a problem: using lenses for image inversion always uses two achromats, not two
uncorrected lenses. True, two lenses can sort of color-correct, but at the inverting distance you have
a system with fairly miserable correction across the field. For the f/value of most binoculars,
you may aggrevate the spherical aberration. For telescopes, it's less challenging, or if you limit
field width.

Anyway:
You can tilt the objectives up front and put wedges after the "relay-inversion" set. That probably messes
things up less. Objectives alone are shifted in many binoculars. It doesn't disturb the field much if it's
cropped a little.

Hi Optic_Nut!

Thank you very much for your answer. The lens drawings in my diagram were symbolic. Of course, a realistic relay system needs doublet lenses. Now, I want to make sure that I understand the effect of shifting each element correctly:

1- Shifting the second relay lens (close to image) by "Delta", makes the image shift by "Delta"

2- Shifting the first relay lens (close to objective) by "Delta", makes the image shift by "Delta" X (Magnification of the relay system)

3- Shifting the objective by "Delta", makes the image shift by "Delta" X (Magnification of the relay system)

Am I right? Also, are the above statements valid when the relay lenses change position as in a zoom system?

Really appreciate your help (and other members in case they would like to help)

. I have in my hands now a beautiful miniature Broadhurst Clarkson relay lens from an 18 times telescope.
This certainly does not have achromatic doublets. Neither do tens of thousands or may be hundreds of thousands of other similar telescopes.
They have two sets of two widely spaced single elements and the one I'm holding is absolutely beautifully made with a sliding fit to perfection.
The field is narrow, but you certainly don't need doublets.
The only downside of the traditional system is that dust is in focus when it settles on one of the lens elements.
With the opening and closing of the telescope which draws in the air some old telescopes are often filthy and need careful cleaning.
Although I used a brass and high quality leather 25 to 40×2 1/4 inch ships telescope for 10 years without any real problems.
I'm not sure whether shifting these relay elements would be better or worse than using doublets. Possibly better?

1- Shifting the second relay lens (close to image) by "Delta", makes the image shift by "Delta"

Actually....more like "minus dellta"...not a bad thing, though.


2- Shifting the first relay lens (close to objective) by "Delta", makes the image shift by "Delta" X (Magnification of the relay system)

(similar answer)

3- Shifting the objective by "Delta", makes the image shift by "Delta" X (Magnification of the relay system)

Yes...you've got it. The improvement is, you don't shift the
incoming cone by as much of an angle.
That's why common binoculars are comfortable with the arrangement.


Am I right? Also, are the above statements valid when the relay lenses change position as in a zoom system?

In a zoom system, the sensitivities and shifts go a bit haywire...

If you mean to continuously adjust the offset, beware: the sensitivity is tricky.
Tiny disruptions can give you collimation issues you only recognize later,
with a nasty headache and eyestrain.

Binastro said:

. I have in my hands now a beautiful miniature Broadhurst Clarkson relay lens from an 18 times telescope.
This certainly does not have achromatic doublets. Neither do tens of thousands or may be hundreds of thousands of other similar telescopes.
They have two sets of two widely spaced single elements and the one I'm holding is absolutely beautifully made with a sliding fit to perfection.
The field is narrow, but you certainly don't need doublets.
The only downside of the traditional system is that dust is in focus when it settles on one of the lens elements.
With the opening and closing of the telescope which draws in the air some old telescopes are often filthy and need careful cleaning.
Although I used a brass and high quality leather 25 to 40×2 1/4 inch ships telescope for 10 years without any real problems.
I'm not sure whether shifting these relay elements would be better or worse than using doublets. Possibly better?

Click to expand...

Here's the thing (and the narrow field is a clue):

---They work because a shorter focus in one lens (say, at blue)
is compensated for by the different resulting magnification
bump when played through its partner. This is also the essence
of the Ramsden eyepiece, which cancels chromatic effects. Your two singles
are actually doing what an Achro-doublet does.
Only perfectly on-axis, though.

In fact, looking through a Ramsden into a cheaper astro scope can be
remarkably sharp and color free...........but:

You pay a price:

----the field of view is less than other eyepieces
----this method does not tolerate fast (low f/ratio) objectives...
the color disintegrates again and spherical issues multiply.

So, you get a sharp, clear, but tiny view.


Those beginning astros are at least an f/10 or f/12 optic.
Ramsdens of past centuries were awesome in big observatories...
...with at f/22 objective (!)
Binoculars are about f/3.5 - f/4.0 .... that scheme would not produce
a pretty field. Relay lenses would suffer even more than eyepieces.

Uzi makes a dandy little periscope....2 feet rise and a field that's still
usable. They have achromats for the relay set though.

------------------------

So I should have said "of a decent field width".
The color performance of non-doublet relay pairs is very good,
but only for long instruments and reduced views.

Considering how easy it is to get surplus achros in smaller sizes, or
take them from damaged 'parts' binoculars, you might as well use them
these days. I would also stick to a plan of f/6 to f/10 for the overall
thingie, to keep from being driven mad compensating for shperical
aberration. Binoculars would only have two elements if all the others
weren't playing aberrations back and forth to compensate for each other.

OPTIC_NUT said:

In a zoom system, the sensitivities and shifts go a bit haywire...

If you mean to continuously adjust the offset, beware: the sensitivity is tricky.
Tiny disruptions can give you collimation issues you only recognize later,
with a nasty headache and eyestrain.

Click to expand...

Thanks for confirming my conjectures! :t: By a zoom erector I meant something like the system that is commonly used in rifle-scopes. In these scopes, a pair of doublets are used as a variable-power zoom system/erector. A spiral-grooved cam is used to move both lenses back and forth along the optical axis. The picture below shows the erector assembly of a cheap Chinese scope.

Now, if we keep the second erector lens at a precise shift "delta" with respect to the optical axis as it moves back and forth, the image will be displaced by same amount "delta" irrespective of zoom factor, right?

Aha....I see the temptation. You quickly grasp how a zoom is
just an adjustable erector. Neat bit of trivia: you can invert an image with
just one lens.......however, the divergence of the light is murderously fast so
it's hard to get magnification any more. The second lens is to cancel out that
convergence/diveregence once you did the flip. And...the zooming is just
having fun with the divergence.

Let's see if I got your scheme:

-----you have an inverting pair
-----you shift one off-axis and move them both the usual way

It would take some ray-tracing to test:
"the image will be displaced by same amount "delta" irrespective of zoom factor",
but it doesn't feel right, because the displacement itself is magnified more or less as the
zoom power shifts around. You are off-center going in, and that makes the exiting ray
(if it's, say, a parallel-to-axis one) skew off at an angle that changes as you zoom.
That's the divergence / convergence talking.

OPTIC_NUT said:

Let's see if I got your scheme:

-----you have an inverting pair
-----you shift one off-axis and move them both the usual way

Click to expand...

Yes, that's exactly what I had in mind! If the lens which is displaced off-axis is the second one (the one close to the image), the image shift should remain constant. Why do you think this doesn't feel right?

Because the image shift is affected by the magnification in that case, or, you could say,
the divergence of the light cone. Only lines that stay parallel (to the prior lines) aren't shifted
more/less, but that seems impossible when your divergence is changed by the zooming.
Everything else in the image is scaled: why wouldn't that be?

OK, so if the light entering the second erector lens is convergent (I have shown it being collimated in my drawings) then a displacement of "delta" to the lens, does not lead to the same displacement in the image it forms? hmmm.. I have to think about it.

I have OSLO (student version) so I'll try to model it.

One more question (if you don't mind): In the case of divergent/convergent beam entering the second erector lens, does displacing the lens cause any aberrations? Or the image will be sharp as before, just being shifted?

Thanks!

Omid said:

OK, so if the light entering the second erector lens is convergent (I have shown it being collimated in my drawings) then a displacement of "delta" to the lens, does not lead to the same displacement in the image it forms? hmmm.. I have to think about it.

I have OSLO (student version) so I'll try to model it.

One more question (if you don't mind): In the case of divergent/convergent beam entering the second erector lens, does displacing the lens cause any aberrations? Or the image will be sharp as before, just being shifted?

Thanks!

Click to expand...

Off center lenses are always a mess, the aberrations are intolerable and cannot be corrected for by the remaining set of lenses. Why not using a Porro-prism to shift (and erect) the image?

Cheers,
Holger

With one lens, you get more aberration than on-center simply by tapping closer to the edge,
which has more aberration.

With two or more lenses, the damage cam be multiplied, because the rays have strayed more and more
off course. In a relay pair, the two do a good job compensating for each other's aberrations, so that
go wrong a bit quicker when they are not lined up. The damage depends on the overall f-ratio, though.
At f12 you can catch the view off-center or tilted and not cause as much trouble as in an f/4 or f/6 world.
A gun scope probably does have a bit of leeway, but just w/respect to the front.

With a high f-ratio you can steer your view pretty easily just by tilting the objective or shifting it.
That takes advantage of its view-point up front...lots of extra degrees and light go to waste.
You could put 6 different eyepieces behind an f/10-12 and get pretty good views from each..not like
at f/4.

Right...Holger's idea with tilting prisms is very popular in binos as well.
You can tip the carriage they are in more practically than the prism itself.
Just needs a very fine-pitched screw.

Thank you very much Holger and Optik_Nut!

So, the following two solutions are recommended for shifting the image:

a) using a prismatic erector and shifting the prism housing (no aberrations, can't have zoom)

b) using an achromatic erector pair and shifting the objective (low aberrations, can have zoom)

Thanks again!

The prisms are interesting if you are doing x-y adjustments (like a gun sight),
since in a Porro pair, the prisms are at right angles to each other. If it actually
is on a gun, though, protection from mechanical shock is tough.

Thinking outside the box (or back into it)....what about simply adusting the barrel
all together? Just checking. It has the lowest sensitivity, so is easier to adjust.

. Would mirrors work, and would they work better than prisms?

As opposed to a lens pair or prisms, mirrors have the usual issues with aligning so many exactly.
If you use them (first-surface mirrors) to reverse or fold the path, you can steer with them, though.
I really prefer the prism scheme, though. You get image reversal, physical path shortening,
and x-y steerage and the element count stays lower.

Don't ever think about steering two binocular barrels! Constant collimation pain. One barrel only,
just a telescope, unless you want to put two giant wedges up front over both sides at once.