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Useful info about secondary mirror alignment

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#351 wh48gs

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Posted 19 November 2009 - 12:49 AM

Your F’ and my F’ are the same. That is, my “S” is the same as your “S-z.”



Jason, that's not the way to go. We have defined "S" as the primary-to-diagonal separation; by definition, it does include the sagitta.

Here is where your math is off. See attachment. I hope you don’t mind uploading an annotated pic from your website but this is the easiest way to convey my point. In your math, you are being inconsistent with the definition of “A”. You defined it as the minor axis of the diagonal which is the vertical cross section running through the diagonal center (blue segment) then you redefined it as the vertical cross section running through the primary/secondary intersection point (red segment).



No, why should I mind, that's what it's made for. A is defined as shown, by the major axis so I don't see discrepancy. There will be a slight difference if starting out with the minor axis determined by the perpendicular cone cross-section at the diagonal's geometric center (blue line), because the corresponding major axis needed to cover the cone is slightly larger than by a factor sq.rt.2. But it only accounts for up to a few 1/100 mm difference in the shift value. Otherwise, the (D-A)A/4S shift formula is inaccurate only because it assumes S=S-z, which makes its value only up to a few 1/100 mm smaller.

Vla

#352 Jason D

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Posted 19 November 2009 - 03:01 AM

Jason, that's not the way to go. We have defined "S" as the primary-to-diagonal separation; by definition, it does include the sagitta.


I did not account for sagitta in the my derived formulas but I see your point.

In this case, every (S) in my formulas will be replaced by (S-z), every (F) will be replaced by (F-(z/D)), and every (F’) will be replaced by (F’-(z/D))

A is defined as shown, by the major axis so I don't see discrepancy.


You have defined (A) as (x2-x1) which is the horizontal green arrow but that is equal to the major axis divided by sqrt(2) based on your diagram. Once you define (A) you need to remain consistent with your definition. But you changed the definition of (A) later to the vertical red arrow when you should have used the vertical blue arrow. Note the blue arrow has the same length as the green arrow.
Mathematically speaking, I do not have an issue with either using the red or blue line segments as long as you stay consistent in your formulas.

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#353 wh48gs

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Posted 21 November 2009 - 10:48 AM

But then why has the discussion been so focused on the difference between apex derived offset and focal plane derived offset? Why worry about offset at all?



The discussion was too lengthy, but it is a piece of information that can be useful. It specifies how much the diagonal needs to be decentered vs. focuser axis, and how much of pointing error it can cause.

So are you advocating using the simple formula A^2/4H for offset and aligning from the focal plane because it's "close enough". I don't have a problem with that either, it just didn't seem to be the way the discussion was going.



The formula is about as simple as it gets, and it is equally accurate for any vantage point (i.e. with H defined as the diagonal-to-point separation).

Quote:
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Nope, it is only appropriate for the BO shift and collimating from the apex. For collimating from the focal plane level, the diagonal shift for centering it in the focuser (which is only important because it determines disparity vs. pointing axis and the degree of decentering of the diagonal's image in the primary) is (A^2)/4H'.


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Are you saying that ((D-A)A/4S) is not appropriate for unidirectional offset?



It is derived for BO when collimating from the apex. It is based on apex-to-diagonal separation H'=SA/(D-A), thus it can be written as (A^2)/4H' (the exact form would have S minus mirror sagitta instead of S, but the difference is negligible). The latter is the general form for needed UO shift, that is valid for any collimation point height, when substituted for H' (I made a typo for collimation from the focal point; according to our convention, it should have H in the denominator).

General relation for BO shift is [sq.root(H^2+A^2)-H]/2, with H being the collimation point height. It is different in form but gives practically identical result as (A^2)/4H, which is simpler.

So it is (A^2)/4H shift relation form that does it all.

Vla

#354 wh48gs

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Posted 21 November 2009 - 11:05 AM

You have defined (A) as (x2-x1) which is the horizontal green arrow but that is equal to the major axis divided by sqrt(2) based on your diagram. Once you define (A) you need to remain consistent with your definition. But you changed the definition of (A) later to the vertical red arrow when you should have used the vertical blue arrow.



It is a technicality, rather than change in definition. The difference between the blue and red sections is in proportion to the difference between sq.rt.(2)A major axis, and the one that actually covers the cone, which is slightly larger. An actual diagonal will have major axis larger by a factor of sq.rt.2 than minor axis. So you are slightly off calculating fully illuminated field diameter either way: if you go with the minimum length along the minimum minor axis, the field diameter in the major axis plane will be slightly smaller. If you base it on the minimum major axis, the field diameterin the minor axis plane will be slightly larger.

In fact, going with the alternative minor axis - determined based on the minimum major axis - gives slightly larger value for H'. This doesn't validate the result obtained by your H' formula, which is slightly smaller than H' obtained based on the minimum minor axis.

Vla

#355 Jason D

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Posted 21 November 2009 - 12:08 PM

So are you advocating using the simple formula A^2/4H for offset and aligning from the focal plane because it's "close enough". I don't have a problem with that either, it just didn't seem to be the way the discussion was going.



The formula is about as simple as it gets, and it is equally accurate for any vantage point (i.e. with H defined as the diagonal-to-point separation).


In this thread we have defined (H) as the distance between the diagonal and the focal point. Our discussion was about your statements that A^2/4H is the accurate/proper formula for calculating UO and D(D-A)/4S is the accurate/proper formula for calculating BO. What Vic and I were stating that these formulas are independent of UO and BO but rather they are about the difference between calculating the offset from the focal point versus the apex point.

If you replace H by H’ then D(D-A)/4S becomes equivalent to A^2/4H’ and now you are able to calculate H’. If the calculated H’ turns out to be the same as H then you must be using a minimal sized diagonal.

No one is questioning the accuracy of A^2/4X where X being the separation between the diagonal and any point. This was not the heart of our discussion.


You have defined (A) as (x2-x1) which is the horizontal green arrow but that is equal to the major axis divided by sqrt(2) based on your diagram. Once you define (A) you need to remain consistent with your definition. But you changed the definition of (A) later to the vertical red arrow when you should have used the vertical blue arrow.



It is a technicality, rather than change in definition. The difference between the blue and red sections is in proportion to the difference between sq.rt.(2)A major axis, and the one that actually covers the cone, which is slightly larger. An actual diagonal will have major axis larger by a factor of sq.rt.2 than minor axis. So you are slightly off calculating fully illuminated field diameter either way: if you go with the minimum length along the minimum minor axis, the field diameter in the major axis plane will be slightly smaller. If you base it on the minimum major axis, the field diameterin the minor axis plane will be slightly larger.

In fact, going with the alternative minor axis - determined based on the minimum major axis - gives slightly larger value for H'. This doesn't validate the result obtained by your H' formula, which is slightly smaller than H' obtained based on the minimum minor axis.

Vla


Think mathematically – forget about illumination and offset for a second. You have written A=x2-x1, correct? Therefore, you have locked in the definition of (A) as being the major axis divided vy sqrt(2) of the diagonal. Then half-way in your derivation, you switched the definition of A to be the red line segment. You can’t do that mathematically. It is OK to state that you are simplifying your math by redefining (A) but you did not state that.

Jason

#356 wh48gs

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Posted 21 November 2009 - 03:10 PM

The formula is about as simple as it gets, and it is equally accurate for any vantage point (i.e. with H defined as the diagonal-to-point separation).


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In this thread we have defined (H) as the distance between the diagonal and the focal point.



It is pretty simple read: the formula is accurate for any point height H above the diagonal. That difines the formula in this specific context.

Think mathematically – forget about illumination and offset for a second. You have written A=x2-x1, correct? Therefore, you have locked in the definition of A as being the sqrt(2) of the major axis of the diagonal. Then half-way in your derivation, you switched the definition of A to be the red line segment. You can’t do that mathematically. It is OK to state that you are simplifying your math by redefining (A) but you did not state that.



Mathematically, the minor axis A in the formula specified as it is - corresponding to the exact major axis length - will give the correct field of full illumination diameter in the plane of major axis. Like I said, you can't have it both ways with an actual diagonal. So, just use A as defined, if formalities mean that much to you.

If your formula for H' uses minor axis A slightly enlarged in proportion to the exact major axis, it gives identical result to that of (much simpler) formula posted by Vic, using unadjusted A value. And the diameter of fully illuminated field - and so the apex point height H' - will be still slightly different in the planes of the minor and major axes. Take the average? Not worth it :smirk:

Vla

#357 Jason D

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Posted 21 November 2009 - 05:41 PM

It is pretty simple read: the formula is accurate for any point height H above the diagonal. That difines the formula in this specific context.


Vla, I am perplexed by your reply.

Where did any of us questioned the accuracy of A^2/4H formula? Our discussion is not about the formula but rather about your insistence of using A^2/4H for UO and the D(D-A)/4S for BO. Vic and I kept arguing that your approach did not make sense. That is, why are you advocating referencing the focal point for UO (using A^2/4H) and the apex for BO (using D(D-A)/4S)?

Mathematically, the minor axis A in the formula specified as it is - corresponding to the exact major axis length - will give the correct field of full illumination diameter in the plane of major axis. Like I said, you can't have it both ways with an actual diagonal. So, just use A as defined, if formalities mean that much to you.

If your formula for H' uses minor axis A slightly enlarged in proportion to the exact major axis, it gives identical result to that of (much simpler) formula posted by Vic, using unadjusted A value. And the diameter of fully illuminated field - and so the apex point height H' - will be still slightly different in the planes of the minor and major axes. Take the average? Not worth it :smirk:

Vla


I have repeatedly stated that D(D-A)/4S is highly accurate. HOWEVER, our discussion is from a mathematical perspective – not practical perspective. In Mathematics, you can’t redefine symbols without at least making a note of it. Your mathematical derivation is flawed because you redefined (A). This discussion is PURE mathematics.
Again, D(D-A)/4S formula derivation involves redefining (A) which makes the formula an approximation (a very good approximation) but “mathematically” the formula is flawed – which was my point.

Jason

#358 Vic Menard

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Posted 22 November 2009 - 08:43 PM

...if the plane defined by segments "H" and "S" is perpendicular to the alt/dec axis, mechanical offset in that plane (or lack thereof) will have no impact on encoder driven DSC pointing accuracy (assuming the alt/dec axis is orthogonal to the az/RA axis).



There is still pointing error, as a slight wobble due to axial disparity. It culminates at the zenith, where the rotation in the azymuth plane would result in the pointing axis projecting a small circle on the sky, with the radius equal to the angular disparity. For the focuser on the side, the error would grow from zero at the horizon (if adjusted there) to the angular disparity at the zenith.

Just got back in town. I saw your comment here and thought I would respond. You are correct regarding the angular disparity for the focuser on the side (with an altazimuth mount). In this case, with a 0.2-degree disparity between OTA axis and optical axis (all mechanicals orthogonal), the error at the horizon is 0.2-degrees azimuth, 0.0-degrees elevation. With the scope pointed to the zenith, the error is 0.2-degrees elevation (89.8-degrees), and 89.8-degrees error in azimuth. If the scope is rotated in this position, it will draw a 0.4-degree diameter circle around the zenith.

But with an altazimuth scope with the focuser on top (where the plane defined by segments "H" and "S" is perpendicular to the altitude axis), given the same angular disparity (OTA to optical), at the horizon the optical axis will point 0.2-degrees above the horizon and azimuth will be unaffected. At the zenith, the optical axis will point 0.2-degrees past the zenith, and the azimuth will only be affected as the optical axis passes the zenith, and then the error will be 180-degrees. But since the altitude error is constant, initializing the DSCs on actual stars will automatically correct the altitude error, and with the altitude error corrected, an indication of 90-degrees altitude by the DSCs will correspond to the zenith. Azimuth error will be zero, and rotating the scope in this position will not impact the scope's optical axis alignment with the zenith.

#359 Vic Menard

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Posted 22 November 2009 - 09:05 PM

...and that BO does not have fully illuminated field exactly centered....

Did you mean UO here?



No, I was talking about BO from the focal point level. If it is decentered, it gets sort of clipped off at the diagonal, so it is always slightly ellipsoidal.


But if BO is collimated from the apex, then the illuminated field is centered, correct?

...the assumption was that D, S and A are identical. H only varies with A when collimating from the apex. That is not a requirement for proper optical collimation.

But it the offset changes relative to the distance from the secondary mirror (from the focal plane to the apex), doesn't that change the secondary mirror alignment (placement) and the field illumination (as you stated above)?

(D-A)A/4S is a better "root formula" when "A" is greater than minimum, delivering a more precise offset value.


Does not matter; the formula gives correct result for UO shift for any H value, not only the minimum size. It is based on the equality of apparent angles, not on any particular vantage point.


Yes, but H has been defined as the secondary mirror to focal plane distance, and the offset value (and the subsequent alignment) is different when A is larger than the minimum size.

#360 brucepiano

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Posted 26 November 2009 - 09:20 AM

Is this picture(# 3033065) viewing the secondary without a collimation tool?

Happy Thanksgiving!

Bruce

#361 Jason D

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Posted 26 November 2009 - 10:19 AM

Is this picture(# 3033065) viewing the secondary without a collimation tool?

Happy Thanksgiving!

Bruce


Correct...

#362 brucepiano

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Posted 26 November 2009 - 11:17 AM

That is how it looks for my scope- but I don't see the primary mirror clips- perhaps they are obscured by the colored paper I use to block the primary.

Bruce

#363 Jason D

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Posted 29 November 2009 - 12:04 AM

Ummmm, I seem to have forgotten to mention a very important and simple mod which will ease off secondary alignment. I thought I had mentioned it in this thread but apparently I did not. I came up with the following idea years ago. I made a perforated disc from a Milk jug then inserted it between the secondary adjustment screws and the secondary mirror holder. Not only the disc will protect denting the holder but more importantly it will allow you to fine tune your secondary mirror alignment by adjusting only one screw WITHOUT the need to touch the other two. This is possible because the Milk jug discs are somewhat elastic. I use 2 stacked discs with by XT10 to get more elasticity.
I had originally detailed this mod in the following thread
I HIGHLY RECOMMEND THIS MOD -- it is simple and highly effective. It is much better than the common metallic washer mod.
Jason

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#364 Starman1

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Posted 29 November 2009 - 12:54 AM

Jason,
Even better is two metal washers with a nylon or polyethylene washer between them: You can still "slip" rotate the secondary, and the screws seat on metal.

#365 Jason D

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Posted 29 November 2009 - 01:23 AM

Jason,
Even better is two metal washers with a nylon or polyethylene washer between them: You can still "slip" rotate the secondary, and the screws seat on metal.


Don, it is much easier to compress the polyethylene milk jug washer when it is placed directly under the set screws based on the simple force/area principle. I no longer see the need for a metallic washer.
Jason

#366 wh48gs

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Posted 29 November 2009 - 09:43 PM

That is, why are you advocating referencing the focal point for UO (using A^2/4H) and the apex for BO (using D(D-A)/4S)?



Jason,

That's not quite what I was saying. Because it is based on the equality of apparent angles, as a function of diagonal size and eye separation, A^2/4H can be applied with either BO or UO, and will give correct shift value - for all practical purposes - for any eye-to-diagonal separation H (disregard for the moment that H has been defined as focus-to-diagonal separation; I sort of run out of meaningful superscripts, and can't use subscripts in this format). On the other hand, (D-A)A/4S is based on the geometry with the eye at the apex, and can't be applied to any eye-to diagonal separation (it will still work for both BO and UO with eye at apex).


Again, D(D-A)/4S formula derivation involves redefining (A) which makes the formula an approximation (a very good approximation) but “mathematically” the formula is flawed – which was my point.



And you were correct. There is no practical consequences, but it is good to keep the concept clear. So I went through it again and got out with the following:

- the coordinate system solution, and the resulting shift value given by A/4F' - which is the basis for slighly rounded off shift relation (D-A)A/4S - is applicable when the starting point is the desired field of full illumination, which is the basis of determining apex-to-focus distance, focal ratio F' of the cone converging to the apex, and needed minor axis A to cover the field.

- when starting with a known diagonal, the above approach still can be used, but can't avoid slight inaccuracy due to the needed offset being defined in terms of F', and thus of field diameter and eye-to-focus distance, neither of which is accurately defined without knowing the offset value first. Better concept for this scenario is the simplest one, based on similar triangles, which defines BO offset as:

{(S-z)-sq.rt.[(S-z)^2-(D-A)A]}/2

where "z" is the mirror sagitta z=D/16F (there is no appreciable change if the sagitta is omitted). With the BO offset known, the exact value of F' is given by:

F'=(S-z-a-BO)/(D-A-2BO)

The details are on my Newtonian diagonal page .

- for any given eye-to-diagonal distance H", the exact offset for either BO or UO is given by [sq.rt.(H"^2 + A^2)-H"]/2; obviously, that requires known diagonal size. If the change in the eye-to-diagonal distance due to diagonal shift is neglected, this simplifies to a very close approximation - accurate for all practical purposes - (A^2)/4H".

These two relations are probably having most of practical importance, not only because they can be applied to collimation from the focal point level as well, but also because collimation from the apex is actually done from a point somewhat closer to the diagonal (so that the primary's reflection is visible inside the diagonal). While the shift difference due to the latter may be only of academic interest, it is good to have a clear concept.

Vla

#367 wh48gs

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Posted 29 November 2009 - 09:54 PM

But with an altazimuth scope with the focuser on top (where the plane defined by segments "H" and "S" is perpendicular to the altitude axis), given the same angular disparity (OTA to optical), at the horizon the optical axis will point 0.2-degrees above the horizon and azimuth will be unaffected.



Yes, assuming there is no appreciable sideways deviation of the focuser from this plane.

Vla

#368 wh48gs

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Posted 29 November 2009 - 10:12 PM

But if BO is collimated from the apex, then the illuminated field is centered, correct?



Yes, and with UO as well.

But it the offset changes relative to the distance from the secondary mirror (from the focal plane to the apex), doesn't that change the secondary mirror alignment (placement) and the field illumination (as you stated above)?



It changes with any change in either diagonal size (A) or eye-to-diagonal separation, or both.

Does not matter; the formula gives correct result for UO shift for any H value, not only the minimum size. It is based on the equality of apparent angles, not on any particular vantage point.


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


Yes, but H has been defined as the secondary mirror to focal plane distance, and the offset value (and the subsequent alignment) is different when A is larger than the minimum size.



Yes; that is why I specified that the formula is still valid if H in it is any eye-to-diagonal separation, not only that measured from the focal point.

Vla

#369 Jason D

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Posted 30 November 2009 - 03:11 AM

Vla, I agree with your derived "offset={(S-z)-sq.rt.[(S-z)^2-(D-A)A]}/2" and "f'" formulas but I disagree with your derived V formula. I believe you meant to write {V=D(H'-H)/f'} instead of {V=DH'/f'}.
I also disagree with your statement "fully illuminated field is decentered by the differential in the shift value delta vs. eye at apex". Calculating decentering is a bit more complicated but it can be approximated with good accuracy by multiplying the offset differential by (f/S) where “f” is the actual focal length of the primary mirror and “S” is the distance between the primary mirror and the diagonal (since this is an approximation I would leave “z” out of the formula).
So, I believe your statement should read:
“fully illuminated field is approximately decentered by the differential in the shift value delta vs. eye at apex multiplied by (f/S)”
Jason


#370 wh48gs

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Posted 01 December 2009 - 10:06 AM

I disagree with your derived V formula. I believe you meant to write {V=D(H'-H)/f'} instead of {V=DH'/f'}.



Jason, I disagree with it too ;) A bit too much of a rush, I guess. It is obvious that the relevant parameter is deltaH (H'-H).

I believe your statement should read:
“fully illuminated field is approximately decentered by the differential in the shift value delta vs. eye at apex multiplied by (f/S)”



Correct. I added that from the top of my head. Multiplying it by f/S is as accurate as anyone may want, and then some (the error runs in hundredths of a mm).

Thanks for pointing out.

Vla

#371 Jason D

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Posted 01 December 2009 - 10:28 AM

Vla, I believe we have addressed all our disagreements. Now we are in total agreement ;) :waytogo:
Jason

#372 sixela

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Posted 01 December 2009 - 11:39 AM

This calls for a party.

:band:

#373 Vic Menard

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Posted 01 December 2009 - 02:27 PM

Funny thing is that collimation is a really simple process stuck in the middle of confusing parts.

After almost 400 posts, I think this quote from Jay Scheurie pretty much sums it up.

Seriously, it has been an arduous and passionate discussion, with some excellent contributions from the major players. Well done! :bow:

Now, I have to agree with Alexis, "Let's party!" :waytogo:

#374 Jason D

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Posted 01 December 2009 - 03:11 PM

"Let's party!" :waytogo:


:elephdance: :tomatodance: :hamsterdance:

#375 InkDark

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Posted 01 December 2009 - 09:20 PM

Very generous of you Jason. Thank you once again!


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