292 replies to this topic

[Jason D]

what would happen if 4 was aligned to the right of 1 instead of to the left? It seems to me the primary mirror axis would move to the left of the pupil?

Good point, Vic
I reran ray simulation and sure enough I can achieve two Stars of David when both focuser/primary axes are parallel using the off-axis-pupil-AC -- see attachment. The two stars of David can be achieved by either having the AC axis run through the primary center (desired) or by having the pupil axis run through the primary center (undesired). These are the only two cases I found.

I suppose you could verify the alignment by rotating the autocollimator. Properly aligned, the 2-4 hexagram should orbit the 1-3 hexagram--I think...

Another good point . Rotation will be the key to tell us if the AC axis (same as the focuser axis) coincides with the primary axis (perfect collimation). It will tell us if we have met the (desired) or (undesired) axial alignment as mentioned in the previous paragrpah.
Only and only when the AC axis coincides with the primary axis, 1/3 images and 2/4 images will rotate around their respective centers. In addition, 2/4 images center will rotate/orbit around 1/3 images center. In other words, the two Stars of David form will persist. If AC/primary axes do not coincide then the two Stars of David will disintegrate fast. This makes sense because image 1 is special in the sense it does not undergo any AC reflections. Therefore, unless the AC axis runs through the center of image 1, any AC rotation will give an orbital motion to image 1.

I still see advantages for the circular donuts. True that AC can be rotated to align the tips 1 and 4 triangles but that assumes focuser axial alignment – it is a catch 22.

Vic, do you agree with the two fundamental additional benefits for above scheme (off-axis-pupil-AC)?
1- All images will persist upon perfect collimation – no more disappearance acts
2- Image 3 alignment against image 1 for Primary axial adjustment has 4X sensitivity

Bottom line: 2X accuracy for focuser axial alignment (CDP) and 4X accuracy for Primary axial alignment and no more disappearance acts.

Jason

EDIT: Updated the illustration to show how to tell if the desired or undesird "8" shape was reached. The desired will maintain the "8" shape as the AC is rotated. The undesired 8 shape will maintain the two circles (or two stars of David) but the distance between them with vary with rotation.

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[Vic Menard]

...Vic, do you agree with the two fundamental additional benefits for above scheme (off-axis-pupil-AC)?
1- All images will persist upon perfect collimation – no more disappearance acts
2- Image 3 alignment against image 1 for Primary axial adjustment has 4X sensitivity...

I agree on both points. But I'm uncertain about the procedure for using the tool without first using an autocollimator with a centered pupil to reduce the axial errors sufficiently to make the off-axis pupil autocollimator primary mirror axis sensitivity useful (boy that's hard to read!).

It's one thing to utilize rotation (with the retaining screw tightened to reduce precession/epicycling) to verify the autocollimator--but using it as part of the collimation procedure...

Still--the concept certainly qualifies for the most interesting "out-of-the-box" autocollimation idea I've heard in quite some time!

[Jason D]

I agree on both points. But I'm uncertain about the procedure for using the tool without first using an autocollimator with a centered pupil to reduce the axial errors sufficiently

Using the cheshire is still a recommended tool to use with today's AC. I suppose using a quality cheshire will bring it close to start making use of the off-axis-pupil AC.

It's one thing to utilize rotation (with the retaining screw tightened to reduce precession/epicycling) to verify the autocollimator--but using it as part of the collimation procedure...

Rotation will be used to ensure the "desired" 8 shape was reached -- not the "undesired" 8 shape -- refer to my last updated post. Rotation can also be used to align the tips of images 1 & 4 tips once a relatively good focuser axial alignment is reached. However, for the final fine tuning adjustments, rotation will not be part of the fine tuning procedure.

Still--the concept certainly qualifies for the most interesting "out-of-the-box" autocollimation idea I've heard in quite some time!

Jason

[Jason D]

Note: The following post was updated based on feedback from Vic.

Assuming we have an off-axis-pupil-AC with a pupil offset equals to the primary center spot radius. These are the steps for the proposed tool.

Step 1: PRE-WORK: Use any collimation tool(s) of your choice to bring collimation as close as possible to perfection.

Step 2: FOCUSER AXIAL ALIGNMENT: Insert the off-axis-pupil-AC into the draw-tube. Rack the drawtube to place the AC mirror surface as close as possible to the focal plane. You might see reflections similar to figures A or D. Rotate the off-axis-pupil-AC to line up the triangle tips of images “1” and “4”. In case the tips are separated (figure B) or overlapped (figure B’), fine adjust only the secondary mirror until the tips of triangles “1” and “2” touch. If your starting point is figure D, then either ignore images “2” and “3” or minutely adjust the primary to get images “2” and “3” out of the way then proceed touch the tips of triangles “1” and “4” as described above. Now focuser axial alignment is met with 2X accuracy. This step is based on Vic’s CDP method.

Step 3: PRIMARY AXIAL ALIGNMENT: Adjust only the primary to bring images “2” and “3” into the view as shown in figure. In the process, image “2” might orbit image “1 which remains stationary. Note image “3”. Proceed to form two hexagons as shown in figure E. Again, ignore any rotation or orbiting motions. Aligning images “1” and “3” will be more sensitive than images “2” and “4” because image “3” is 2X more sensitive than image “2”. Now primary axial alignment is met

Step 4: ELIMINATING RESIDUAL AXIAL ERRORS: Rotate the off-axis-pupil-AC to line up images “1” and “4” triangle tips again then fine tune the secondary to touch both triangle tips. This fixes any focuser axial residual error. Then proceed to re-form the two hexagons by fine tuning the primary. This fixes any primary residual axial error.

Jim, if you ever consider building a prototype, I will be more than happy to evaluate it for you . 4X primary axial alignment accuracy, eliminating disappearance act, and eliminating the final CDP step (restoring primary axial alignment) might sound appealing

Jason

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[Vic Menard]

Jason,
I don't know where to start...
There's one true axial reference--reflection 1. The autocollimator pupil itself has a known displacement from the focuser axis equal to the radius of the primary mirror center spot...

Since we know that the pupil is offset the radius of the center spot, it needs to be moved to the edge of 1. We know that when alignment is fully corrected, the foreground pupil will fall precisely between the two hexagrams. The background pupil is rotated 180-degrees relative to the optical axis, so it should appear on the opposite side of the 1-3 stack.

Given those conditions, the pupils should define the primary mirror axis, and rotating the autocollimator should cause the 2-4 stack (and both pupil reflections) to orbit the centered 1-3 stack.

What do you think?

[Jason D]

Vic, I see how I messed up the steps describing the pupil placement/movement. I need to revise.

The assumption of the proposed off-axis-pupil-AC is to have its pupil offset by at least the radius of the primary center spot -- not 1/2. Otherwise, both hexagrams will overlap and we’ll run into image blackouts during adjustments.

Come think of it, the starting point for the off-axis-pupil-AC should be equivalent to the regular AC. That is, we should use some sort of a quality collimation tool(s) to bring collimation close to perfection (at least the focuser axis alignment) then perfect it with the AC. Attempting to get to that point using only an AC might end up being a source of frustration. I was hoping to have an AC that does it all.

Later tonight, I will edit the steps in my previous post to start off from a “close” collimation point.

Jason

[Vic Menard]

...The assumption of the proposed off-axis-pupil-AC is to have its pupil offset by at least the radius of the primary center spot -- not 1/2...

My mistake, I've corrected the post.

[Jason D]

Since we know that the pupil is offset the radius of the center spot, it needs to be moved to the edge of 1. We know that when alignment is fully corrected, the foreground pupil will fall precisely between the two hexagrams.

Vic, wouldn't the foreground pupil be at 2X the radius which will place it in the center of image 4 -- not at the edge of image 1? I am thinking of the line running through ROC and pupil hole.
Jason

[Jason D]

I updated the last post describing the off-axis-pupil-AC steps...

Vic, here is another variation of the off-axis-pupil-AC.The following idea will eliminate the need to rotate the AC and also eliminate the requirement to have the pupil offset equal to the primary center spot radius.

Start off with a quality pupil-less AC then drill two pupil holes at 90 degree angle with the same offset from the AC center. The amount of offset is larger than the radius of all typical/known primary center spots.

Using donut primary center spot is better than a triangle for this method – will eliminate the need to rotate the two-off-axis-pupils-AC

Steps are easier:

1- Start off with a semi-collimated scope
2- Place the off-axis-2-pupil-AC at the focal plane. Look through pupils A and B and try to equalize the distance between images “1” and “4” by only adjusting the secondary. Ignore images "2" and "3" which can't look inlined through both pupils. They will look out-of-line at least through one of the two pupils.
3- Rotate the AC 90 and repeat step 2. Iterate between steps 2 & 3 until the distances between images "1" and "4" are equal regardless of the AC rotation. This step is necessary to deal with the unique scenario when the focuser axis intersect the 45 degree line between the pupils.
4- Adjust the primary to stack images 1/3 and 2/4. You can use only one pupil hole to complete this step. Stacking these images through one pupil hole will automatically stack them through the other pupil assuming excellent focuser axial alignment.
5- Re-iterate through steps 2, 3, and 4 as needed.

Highlights are the same as the one-off-axis-pupil-AC
1- 2X focuser axial accuracy (CDP) -- see Note below
2- 4X primary axial accuracy
3- All reflection images remain -- no disappearance acts
4- Here is another: Since only two images are stacked, the view will be less cluttered
5- The two off-axis-pupils-AC gives two ventage points to assess collimation.
6- The pupil size needs to be small enough only to reduce parallax. It does not have to be small enough to delay the disappearance act of images 3 and 4 since they will not disappear.

Note to other readers: Aligning images 1&4 (CDP) provides 2X focuser accuracy whereas aligning images 1&3 provides 4X focuser accuracy. However, what is unique about aligning images 1&4 (CDP) is focuser axial isolation. Both primary and focuser axes impact the alignment of images 1&3 – completing CDP first makes aligning images 1&3 sensitive only to primary axis.

Jim, are you still following this thread? I would love to get my hands on a off-axis-2-pupils-AC prototype if you ever decide to build one

Jason

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[Vic Menard]

Since we know that the pupil is offset the radius of the center spot, it needs to be moved to the edge of 1. We know that when alignment is fully corrected, the foreground pupil will fall precisely between the two hexagrams.

Vic, wouldn't the foreground pupil be at 2X the radius which will place it in the center of image 4 -- not at the edge of image 1? I am thinking of the line running through ROC and pupil hole.
Jason

You know--that makes sense. I've been thinking too "outside the box" with your offset pupil, but in the fifth edition, I actually show one of Jim Fly's simulations modeling parallel axes, and the foreground pupil does indeed fall inside 4 (and the background pupil falls inside 1). That simulation, of course, has a centered pupil, but there's no reason an offset pupil should behave differently. Of course, in your offset pupil experiment, the pupil has been offset exactly the right amount to make the distance between the pseudo parallel axes indicate precise axial alignment... this would require strict attention to build tolerances and precise rotational alignment of the pupil for an accurate read.

[Jason D]

That simulation, of course, has a centered pupil, but there's no reason an offset pupil should behave differently.

I guess for the parallel axes case, the term offset is immaterial

Of course, in your offset pupil experiment, the pupil has been offset exactly the right amount to make the distance between the pseudo parallel axes indicate precise axial alignment... this would require strict attention to build tolerances and precise rotational alignment of the pupil for an accurate read.

I am more excited about the second idea of having two pupils where the amount of pupil offset does not have to be equal to the radius of the center spot. I do see more merits to the proposed two off-axis pupils AC though the manufacture cost will be little more to drill a 2nd hole. But, the width of the pupil holes does not have to be too tight to avoid early disappearance act for images 3 and 4 – just enough to reduce parallax.
Jason

[Vic Menard]

...I am more excited about the second idea of having two pupils where the amount of pupil offset does not have to be equal to the radius of the center spot.

In this alignment scenario, the foreground pupil will still be aligned to 4 and the background pupil to 1, correct?

I do see more merits to the proposed two off-axis pupils AC though the manufacture cost will be little more to drill a 2nd hole.

Again, to realize 4X axial error resolution, the pupils will have to be very precisely aligned to the actual AC axis.

...Both primary and focuser axes impact the alignment of images 1&3 – completing CDP first makes aligning images 1&3 sensitive only to primary axis.

This seems to be the way to proceed (using the 2-pupil AC as a primary mirror alignment tool). But the user will still need to rotate the 2-pupil AC to carefully match the alignment separation observed in both pupils. In this respect, I think the single offset pupil AC benefitted from the close alignment of the two stacks. Perhaps combining the two concepts would simplify locating the precise rotational position of the AC?

[Jason D]

Vic, things are clearer and simpler in my head now.

See attachment

Figure A is a normal AC with a single centered pupil – for reference. The relationship between images 1 and 4 is simple. Image 4 will ALWAYS be on the opposite side of image 1 across the pupil axis regardless of the primary axial alignment and focuser axial tilt. The distance between the pupil axis and image 1 is the displacement between the focuser axis and the primary center at the primary surface (focuser axial error at the primary). Note how the distance between images 1 and 4 is twice the focuser axial error hence the 2X accuracy. Stacking images 1 and 4 implies no focuser axial error. I just described your CDP. Few more notes: The pupil shadow shown in these figures is the location of the pupil axis. The pupil shadow in the figures does not represent the location of the foreground/background pupils which are not shown. It is always safe to assume the center point between images 1 and 4 correspond to the pupil axis. If the pupil is centered then it also represents the AC axis hence the focuser axis.

Figure B is an AC with a single offsetted pupil. The same rule governing the relationship between images 1 and 4 apply regardless of the offset. However, stacking images 1 and 4 implies focuser axial error equals to the offset at the primary and 1/2 the offset at the EP.

Figure D shows how keeping the distance between images 1 and 4 twice the offset amount “will” lead to focuser axial alignment. If the offset happened to equal the radius of the center spot then touching images 1 and 4 will align the focuser axis, or will it?

A single offset-pupil will lead to ambiguity as shown in Figure E. There are infinite possibilities where the midpoint between mages 1 and 4 is equal to the offset but only one of these possibility will place image 1 center on the top of the AC axis.

To solve the issue, we can introduce another pupil. The rule governing multiple pupils with the same offset is that they can’t be on opposite sides; otherwise, disappearance acts will be introduced which is the very problem we are trying to avoid in the first place -- in addition we can't have a centered pupil. So, the second pupil can be placed at 90 degree angle as shown in Figures F and G. Now we can eliminate most of these infinite possibilities but there is still one class of ambiguity as shown in Figure H where the AC axis falls along the 45 degree angle between both pupils. To eliminate this special and last ambiguity, we can introduce a 3rd pupil located at 135 degrees from both pupil. (I promise, no more pupils – just three )

Figure J with 3 pupils placed strategically eliminates all ambiguities. All we need to do is equalize the distances between images 1 and 4 across all 3 pupils. All other images will be moved out of the way and ignored. Equalizing the distance between images 1 and 4 will guarantee focuser axial alignment with 2X accuracy – it is CDP across 3 pupils.

OK, let us place the three pupils at 120 degrees as shown in figure K – symmetry is desirable.

Once focuser axial alignment is met then we can focus on stacking image 3 on the top of image 1 and image 2 on the top on image 4. Only one pupil can be used. If the focuser axial alignment was done properly then creating two stacks (1/3 and 2/4) through one pupil hole will guarantee the same through the other two pupils. Stacking 3 on the top of 1 gives the 4X primary axial alignment accuracy. None of the images will disappear.

Foreground pupil will be centered in the middle of images 2/4 stack and the background pupil will be centered in the middle of images 1/3 stack regardless of the offset.

Jason

EDIT: With the 120 degree 3 pupil setup, it might finally make the secondary adjustment easy. If the initial AC orientation is placed correctly, then each pupil might be better aligned with each of the 3 secondary set screws. In addition, with three 120 degree pupil we can keep the triangle center spots where we can align the tips of images 1 and 4. Ummm, now a triangle center spot sounds more appealing since stacking will form hexagons which are easier the view than stacked donuts. Just a thought.

EDIT: Updated some of the "pupil" terms used in this post to "pupil axis" for clarity

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[Jason D]

In this alignment scenario, the foreground pupil will still be aligned to 4 and the background pupil to 1, correct?

This is a true statement regardless of the offset amount. If the offset is small then images 3 and 4 along with the background pupil will disappear and introduce error -- not to mention the clutter created by 4 images.

Again, to realize 4X axial error resolution, the pupils will have to be very precisely aligned to the actual AC axis.

When it is time to correct the primary axis using the 4X resolution, only one pupil will be used to stack image 3 on the top of image 1. Since only one pupil is used, offset precision is not critical at all for the primary adjustment.
For the 3 pupil AC, the distance between the pupils and the AC axis needs to be precise for focuser axial alignment which I assume is not more demanding than the precision needed to place a single pupil in the middle of the AC. I do not believe Jim Fly will have an issue with drilling the 3 pupils with great precision.

This seems to be the way to proceed (using the 2-pupil AC as a primary mirror alignment tool). But the user will still need to rotate the 2-pupil AC to carefully match the alignment separation observed in both pupils. In this respect, I think the single offset pupil AC benefitted from the close alignment of the two stacks. Perhaps combining the two concepts would simplify locating the precise rotational position of the AC?

The 3 off-axis pupils AC eliminates all rotations. Just insert the proposed AC, equalize images 1&4 displacements by adjusting the secondary then stack image 3 on the top of 1 by adjusting the primary.

Jason

[Jason D]

Before this thread fades away, I just wanted to document few more info about the 3-pupil-AC in this post and the next one. Both posts are based on my own analysis. Any corrections would be appreciated.

Attachment illustrates image formation:
Images 1 and 3 locations are fixed on the primary surface and their location shifts according to the natural/intuitive 3D perspective rules as they are observed from different pupils
Images 2 and 4 are split to form equilateral triangles. The distance between the center of the triage and any of the tips is twice the offset of the pupils from the AC center. Only one of the 3 triangle images is visible through each pupil as shown by pupil A, B, and C illustrations

Note: For reference, images 1 & 3 coincide only and only when the AC mirror surface/plane is perpendicular to the optical axis. In other words, when the AC axis is parallel to the optical axis or coincides with it. Their separation indicates an AC mirror tilt, i.e. the AC mirror plane is non-perpendicular to the optical axis. In this case, the straight line connecting the centers of images 1 and 3 points in the horizontal direction of the maximum slope line of the tilted AC plane. Furthermore, if images 1 & 3 coincide then images 2 & 4 will also/always coincide. This info is also true for the traditional centered/single-pupil AC...

Note: Another FYI: The line connecting the centers of images 1 and 3 is always parallel to the line connecting the centers of images 2 and 4. If both lines coincide (all images fall on the same line), then it is an indication that both the pupil axis and the primary axis are co-planar. This is also true for the traditional centered/single-pupil AC which combines both the pupil and the AC axes to one axis by definition.

Jason

EDIT: Updated illustration

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[Jason D]

AC placement: Do your best to rack the drawtube to place the AC mirror surface as close as possible to where the primary focal plane will end up. Placing the AC mirror surface noticeably above/below the final placement of the primary focal plane will introduce image size/relation asymmetry and image fuzziness which might impact the accuracy of the adjustment procedure. This is also true for the traditional centered/single_pupil AC.

Focuser axial alignment: Move image 1 close to image 4 using any of the pupils (only one of image 4 triangles is visible – you do not have a choice). Repeat the step through the 2nd and 3rd pupil. The goal is to equalize the distance between images 1 and 4 across all 3 pupils. If the pupil offset happened to equal the center spot radius then images 1 and 4 will touch which will facilitate this step though this is not a requirement. Note: Ignore the pupils reflections at this step. There locations are loosely related to the focuser axial alignment.

Primary axial alignment: Stack images 3 and 1. Any pupil will do. When this is achieved, images 2 and 4 will also end being stacked and the same 2 stacks will be observed through the other two pupils. The foreground pupil reflection will be in the center of images 2/4 stack and the background pupil reflection will be in the center of images 1/3 stack

What will a 3-pupil AC provide over a single/centered pupil?

1- 4X primary axial accuracy (see note below)
2- CDP is visible even when perfect collimation is achieved – no need to decollimate.
3- All reflection images remain which means no disappearance act for images 3 and 4 when perfect collimation is about to be achieved and no false stacking as the case with the bow-tie scenario
4- Two stacks (two images per stack) means less clutter as opposed to stacking 4 images. If we use a triangle center spot instead of a donut, then the stacks will form two hexagrams. Even better, a triangle enclosed within a ring will provide the benefits of a donut to align the focuser axis and the benefits of a triangle to align the primary axis.
5- Different pupils give different perspectives to better identify axial residual errors.

Jason

Note: The quoted 4X primary axial alignment assumes perfect focuser axial alignment. Any focuser axial alignment error will propagate to the primary axial alignment. Therefore, the theoretical 4X primary axial alignment accuracy is built on the top of the 2X focuser axial alignment accuracy which implies the true primary axial accuracy is somewhere between 2X and 4X. Well, some might argue that, mathamatically, the accuracy should be 2X which is the lowest of the two.

EDIT: Updated illustration

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[CatseyeMan]

Jason,

Your reflection analyses and illustrations of AC off-center pupil concepts are magnificent and interesting indeed. As time permits, I plan to validate your hypothotheses with a PovRay simulation. If that proves out, actually "making" a prototype would be the next step; it can be done, but 3 registered off-center holes through both eyepiece and mirror surface is not a "piece of cake"

Jim

[Jason D]

Your reflection analyses and illustrations of AC off-center pupil concepts are magnificent and interesting indeed.

Jason