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# Useful info about secondary mirror alignment

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### #326 Jason D

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Posted 01 November 2009 - 12:18 PM

You do realize that you just called Vic Menard and Nils Olof Carlin secondary alignment ideas irrelevant!!!!

Gosh, am I supposed to start trembing, or what We are not discussing names here, are we. Frankly, names do not matter, yours and mine included.

Vla

No, I did not expect you to â€œtrembleâ€ but I did expect you to show more "respect" to collimation ideas presented by Vic Menard and Nils Olof Carlin. After all, both have significantly contributed to improving and clarifying collimation and both are well-acknowledged collimation experts among the amateur astronomers.

FYI: The (D-A)A/4S formula is not exact but a highly accurate approximation. The mathematically accurate formula is long and involves the solution of a quadratic formula. For D=300, S=1250, A=70, the exact offset is 3.228337732mm, the exact H' is 376.2239073mm, the F'-ratio for the extended apex cone is 5.420746358. The (D-A)A/4S formula gives 3.22mm. Of course, pursuing offset precision beyond 0.1mm would be absurd; therefore, the (D-A)A/4S formula is more than adequate.

Well, thank you, Jason - I appreciate you acknowledging something posted by me as valid and useful. You seem to have missed it, but I did state that the above expression for BO shift is not absolutely accurate, since it neglects mirror sagitta. When it is taken into account, the formula is only a bit more complicated: BO=(D-A)A/4[S-(D/16F)].

Vla

Do not be too presumptuous!!!! Sagitta has nothing to do with the point I was making. My point is that (D-A)A/4S is not an exact formula â€“ mathematically speaking â€“ for calcuating the offset for a line segment slicing an isosceles triangle at 45 degree angle.

In addition, despite your claim that you have independently derived the above formula (D-A)A/4S, you do not seem to be aware that the formula assumes the eye is placed at the extended apex point â€“ not at the focal point.

Let's see. What you are proposing is to place sight tube's pupil at the apex levelâ€¦â€¦. What do you gain by doing collimation in this manner? The field of full illumination gets centered around focuser's axis, as opposed to being 1.7mm decentered if you collimate from the focal plane level.

For several pages in this thread we were debating the optimal placement of the eye to center the illumination field. You kept insisting that the eye has to be placed at the focal point to center the illumination field. You did not even have a concept of the extended apex point. Are you agreeing with us now? That is, are you agreeing that the optimal eye placement to center the illumination field is the extended apex point?

What about the other subject that consumed countless number of posts? I am referring to your incorrect formula:
UO/BO OFFSET = AS/(D-A)Hâ€™
Do still believe the formula is accurate?

Jason

### #327 Vic Menard

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Posted 01 November 2009 - 02:53 PM

Let's see. What you are proposing is to place sight tube's pupil at the apex level. For our exemplary 300mm f/5 Newtonian with minor axis A=70mm and diagonal-to-focus separation H=250mm, that is 380mm above the central axis.
That would require use of 4-5 inch extension tube, every time you collimate or checking on it.

No extension tube is necessary. With the focal plane already 250mm away from the central axis, the apex point is 130mm above the focal plane. Considering the focal plane is usually close to the fully racked in focuser position and a 1.25-inch sight tube is about 150mm long (2-inch sight tubes are longer), it's quite easy to position the sight tube pupil close to the apex point.

What do you gain by doing collimation in this manner?

Well, you commented in an earlier post that, "The purpose is to specify what the pattern is supposed to look like." Doing sight tube collimation in this manner, "...the pattern with a correctly placed pupil (and correct length sight tube barrel) is three identical circles--the bottom edge of the sight tube, the actual edge of the secondary mirror, and the reflected edge of the primary mirror."

I'll tell you one thing: no mortal is going to notice the difference.

And once again, as I stated earlier, "...I agree, the pupil placement (and the sight tube barrel length) doesn't need to be exact--and neither does the offset. Close is almost always good enough..."

And in order have illuminated field exactly centered, you make collimation both more complicated (by the need to determine apex location, and use of extension tube), as well as less accurate (due to smaller apparent pattern size and possible extention tube play).

Apex location--easy.
Extension tube--unnecessary.
Less accurate--debatable, but in practice, it's just not true.

I am yet to see someone collimating 300mm f/5 Newtonian in the manner you propose.

It's pretty common among users who align the secondary mirror using the three concentric circles described above. And it's the reason CatsEye collimation tubes are adjustable.

...The "gain" of having exactly centered field of full illumination is not a match to the gain of collimation being as simple and accurate as possible.

I suspect you're talking about two different things (axial collimation and secondary mirror collimation), which doesn't surprise me too much, as we've been talking about two different things (axial collimation and mechanical alignment) all along.

Whether or not you use the apex point to align the secondary mirror, the offset math ((D-A)A/4S) does.

### #328 Howie Glatter

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Posted 01 November 2009 - 03:11 PM

Vic said: "I suspect you're talking about two different things (axial collimation and secondary mirror collimation),. ."

Because the term collimation has been used to describe both angular (axial) alignment and lateral (offset) alignment of the secondary mirror, I would suggest using the term "secondary positioning" when describing lateral adjustment of the secondary mirror, in order to avoid misunderstandings.
Regarding everything else, my head is spinning.

### #329 Jason D

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Posted 01 November 2009 - 03:58 PM

Vic said: "I suspect you're talking about two different things (axial collimation and secondary mirror collimation),. ."

Because the term collimation has been used to describe both angular (axial) alignment and lateral (offset) alignment of the secondary mirror, I would suggest using the term "secondary positioning" when describing lateral adjustment of the secondary mirror, in order to avoid misunderstandings.
Regarding everything else, my head is spinning.

Howie, I see your point. It is often confusing for beginners to differentiate between secondary alignment and focuser axial alignment. But I believe Vla understood what we were talking about.
The issue is not miscommunication but rather technical misunderstanding by Vla.
He talks about the importance of the (D-A)A/4S formula which references the extended apex then he belittles and importance of the extended apex.
He makes a big deal about the importance of the secondary offset then states that a 1.7mm offset away from ideal is not a big deal. Vla said: â€œWhat do you gain by doing collimation in this manner? The field of full illumination gets centered around focuser's axis, as opposed to being 1.7mm decentered if you collimate from the focal plane level.â€

A good portion of this thread has been dedicated to correct wrong statements made by Vla which are listed below:
1- Full-offset is critical for visual observation
2- There is a measurable difference between partial and full offset values â€“ as much as 20-30%
3- The optimal placement for the eye is center the secondary mirror under the focuser is at the focal point
4- He implied the apex for the (D-A)A/4S formula is the focal point even though the formula clearly does not factor in the focal length
5- In general, he had no concept of the extend apex and its impact of secondary positioning.

Jason

### #330 Vic Menard

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Posted 01 November 2009 - 06:30 PM

Because the term collimation has been used to describe both angular (axial) alignment and lateral (offset) alignment of the secondary mirror...

When it comes to axial alignment, I like to think of a simple, thin beam laser. The laser beam is first a representation of the focuser axis, as the beam is coaxial with the focuser drawtube. Focuser axis alignment can be corrected by changing the alignment of the focuser itself or by adjusting the secondary mirror to aim the focuser axis at the center of the primary mirror. The return beam is simply the reflection of the focuser axis, until the focuser axial alignment is fully corrected, at which point the return beam represents the primary mirror axial alignment.

Secondary mirror collimation (note that I'm not saying adjustment) is completely different from axial collimation (again--note I'm not saying adjustment). Depending on how the secondary mirror is mounted, the collimation (or "positioning") may have lateral, longitudinal, centering and/or rotational error components relative to the axial collimation. I usually consider angular misalignment as a variance of intercept perpendicularity or as a variance of the optical axis from perpendicularity to the immediate axis of rotation. Since either is practically impossible to measure without some serious precision measurement and mathematical analysis, I try to focus on simple axial and secondary mirror alignment.

I would suggest using the term "secondary positioning" when describing lateral adjustment of the secondary mirror...

Lateral adjustment (I assume you mean an improperly centered spider or tilted focuser board), rotational adjustment, and offset adjustment (both directions, longitudinal and centering, whether they're implemented or not) affect the secondary mirror "positioning". Each aspect can be misaligned in the presence of "perfect" axial (focuser and primary mirror) alignment. Assuming the reference axis is the focuser axis, optical collimation is correct when the axial alignments and the secondary mirror alignment have been corrected. If the reference axis is the OTA axis (or if the primary mirror axis must be made perpendicular to the immediate axis of rotation), the optical collimation must be made to coincide with the mechanical reference axis, which necessarily complicates the process.

Regarding everything else, my head is spinning.

Mine too!

### #331 Jason D

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Posted 02 November 2009 - 02:43 AM

Let's see. What you are proposing is to place sight tube's pupil at the apex level. For our exemplary 300mm f/5 Newtonian with minor axis A=70mm and diagonal-to-focus separation H=250mm, that is 380mm above the central axis.
That would require use of 4-5 inch extension tube, every time you collimate or checking on it.

{{
For A=70, D=300, S=1250, F=5
If the eye is placed at the focal point
H=250mm
Secondary offset = 4.807549857mm
100% illumination size = 23.0411458mm
100% illumination shift = 1.898939266mm (8.24151404% of the 100% illumination area)

If the eye is placed at the extended apex point
H=376.2239073mm (126.2239073mm above the focal plane)
Secondary offset = 3.228337732mm
100% illumination size = 23.28533729mm
100% illumination shift = 0mm

In the above example, the secondary mirror is WAY oversized by 19.49494949mm (38.6%) â€“ the minimal secondary size is 50.50505051mm.
The extended apex point is around 5 inches above the focal plane in this example because of the unreasonably oversized secondary.
}}

{{
If we assume a more reasonable secondary size of A=55mm -- same D, S, and F

For A=55, D=300, S=1250, F=5
If the eye is placed at the focal point
H=250mm
Secondary offset = 2.989257362mm
100% illumination size = 5.310517359mm
100% illumination shift = 0.346352795mm (6.52201606% of the 100% illumination area)

If the eye is placed at the extended apex point
H= 277.3050993mm (27.30509925mm above focal plane)
Secondary offset = 2.70083561mm
100% illumination size = 5.363387957mm
100% illumination shift = 0mm
}}

Maybe ~10% shift of the 100% illumination area between the focal point and the extended apex is small for visual observation, but it could be discernable for astrophotography. But the point is that for a reasonably sized secondary mirror, the extended apex point sets around 1â€ above the focal plane. There is no need for anyone to calculate the location of the extended apex point. All that is need is to rack the focuser/sight-tube outward until the edge of the secondary mirror coincides with the primary mirror reflection as seen from the sight-tube pupil.

Jason

### #332 sixela

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Posted 02 November 2009 - 08:18 AM

All that is need is to rack the focuser/sight-tube outward until the edge of the secondary mirror coincides with the primary mirror reflection as seen from the sight-tube pupil.

/begin{sarcasm}
Gosh, Jason, surely you aren't advocating using a visual cue to place a tool properly in a collimation procedure, without using any formula at all?
/end{sarcasm}

Despite Vlad's claim that he has yet to see anyone use the extended apex, I just collimated two scopes (my new 400mm Dob and a 200mm GSO f/4 Newt) using a CatsEye TeleTube to place the secondary. On both scopes, I had no problem racking out the focuser until my eye was placed properly.

Note: I didn't compute the proper sight tube aspect ratio for both scopes to make the sight tube's inner edge the right size. I copped out and used the visual cue, and it took me the better part of at least one minute to set the tube's length accordingly each time.

### #333 Jason D

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Posted 02 November 2009 - 10:05 AM

A sight-tube with the proper aspect ratio is the optimal way to go. Using visual cue is doable but might take an additional iteration or two -- I adjusted mine this way.

### #334 Jason D

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Posted 08 November 2009 - 11:55 PM

Yet another animation

The animation starts off with an on-axis star with its parallel light rays reflecting off the primary mirror then the secondary mirror and finally onto the focal plane to form its image. The starâ€™s light cone is completely intercepted by the secondary mirror.

Then the animation shows a close off-axis star. Even though its light cone is reflected off at an angle, it is still completely intercepted by the secondary mirror because the secondary mirror is slightly over-sized.

Finally, the animation shows a farther away off-axis star. Its light cone is reflected off at a wider angle; consequently, it gets clipped by the secondary mirror. As a result, the formed image will be dimmer because less light makes it to the focal plane. In addition, because a smaller area of the primary mirror contributes to forming the image, the starâ€™s image will have less resolution. In theory, the secondary mirror can be replaced by a larger one to ensure all light cones of all stars in the FOV are intercepted by the secondary mirror; unfortunately, doing so will reduce contrast due to the larger central obstruction. So, the secondary size is a compromise between illumination vs. resolution vs. contrast.

Jason

### #335 wh48gs

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Posted 09 November 2009 - 01:25 AM

Quote:
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You do realize that you just called Vic Menard and Nils Olof Carlin secondary alignment ideas irrelevant!!!!

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Gosh, am I supposed to start trembing, or what We are not discussing names here, are we. Frankly, names do not matter, yours and mine included.

Vla

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No, I did not expect you to â€œtrembleâ€ but I did expect you to show more "respect" to collimation ideas presented by Vic Menard and Nils Olof Carlin. After all, both have significantly contributed to improving and clarifying collimation and both are well-acknowledged collimation experts among the amateur astronomers.

I can only repeat: I am not discussing the names, only the facts. You have a wrong idea of "respect" if it should prevent you from expressing your opinion.

Do not be too presumptuous!!!! Sagitta has nothing to do with the point I was making. My point is that (D-A)A/4S is not an exact formula â€“ mathematically speaking â€“ for calcuating the offset for a line segment slicing an isosceles triangle at 45 degree angle.

In addition, despite your claim that you have independently derived the above formula (D-A)A/4S, you do not seem to be aware that the formula assumes the eye is placed at the extended apex point â€“ not at the focal point

I am not being presumptuous (btw. you'll be soon running out of the exclamation marks if you keep using them at this rate ): I am merely stating the fact. I don't just "claim" that I derived the BO shift formula; I show how I did it (already posted before, but apparently you've missed it):

http://www.telescope...t/newtonian.htm

And, yes, the only thing that doesn't make it absolutely accurate is that it doesn't take into account that the actual focal ratio number is slightly smaller than f/D (D being the aperture diameter and "f" the mirror focal length), equaling (f-sagitta)/D.

For several pages in this thread we were debating the optimal placement of the eye to center the illumination field. You kept insisting that the eye has to be placed at the focal point to center the illumination field. You did not even have a concept of the extended apex point. Are you agreeing with us now? That is, are you agreeing that the optimal eye placement to center the illumination field is the extended apex point?

There is no benefit of using the apex point for collimation, because there is no benefit of having fully illuminated field exactly centered. On the other hand, it makes collimation more complicated and less accurate (remember, the primary purpose of collimation is to bring best image point to the field center).

So, no - I don't agree that the apex point is the optimal one for collimation.

What about the other subject that consumed countless number of posts? I am referring to your incorrect formula:
UO/BO OFFSET = AS/(D-A)Hâ€™
Do still believe the formula is accurate?

Yup, for anyone collimating from the focal plane level - which is what most people do - it is perfectly accurate. It is also accurate for any collimation point height H' other than the exact focal plane height.

Vla

### #336 Jason D

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Posted 09 November 2009 - 02:37 AM

First, I have no interest to address many of your sarcastic comments

I am merely stating the fact. I don't just "claim" that I derived the BO shift formula; I show how I did it (already posted before, but apparently you've missed it):

Your math is wrong.

Leave sagitta out of it.

Here is the correct math for your reference:

Referring to the attachment.
Given:
â€œAâ€ for the secondary minor axis assuming a secondary made off a 45 degree cross section of a cylindar
â€œSâ€ for the distance between the primary mirror and the secondary mirror (leave sagitta out of it)
â€œDâ€ for the primary mirror diameter

First, calculate Hâ€™ which is the distance between the secondary mirror and the extended apex point along the focuser axis.

Then calculate the secondary mirror offset

Offset = (H'*D^2)/(4*(S+H')^2-D^2)

We can figure out F' which is the F-ratio for the extended cone. It is the ideal F-ratio to reference when setting the sight-tube length
F' = (H'+S)/D

Another formula for the offset

Offset = A/(4*F')

and another

Offset = H'/(4*F'^2-1)

To figure out the smallest secondary mirror size "A(min)", then set H'=H and F'=F (H being the distance between the sceondary mirror and the focal point along the focusre axis)

A(min)/(4*F) = H/(4F^2-1)

A(min) = 4HF/(4F^2-1)

100% illumination area diameter = (H'-H)/F'

Above assumes a secondary mirror made from a 45 degree cross section off a cylinder where

Major axis / minor axis = sqrt(2)

For a secondary mirror made from a 45 degree cross section off a cone,

Major axis / minor axis = sqrt(2) / sqrt(1-1/(4*F'^2))

I derived all the above formulas without using any trigonometric functions (SIN, COS, TAN) .

It is just mathematicsâ€¦

There is no benefit of using the apex point for collimation, because there is no benefit of having fully illuminated field exactly centered. On the other hand, it makes collimation more complicated and less accurate (remember, the primary purpose of collimation is to bring best image point to the field center).

So, no - I don't agree that the apex point is the optimal one for collimation.

Vla, you did not even have a clue about the concept of the extend apex. After 10s of posts and 10s of diagrams, you seem to have finally comprehended the concept. But instead of admitting that you have learned something new from us, you are pretending that you knew about this concept all along but you disagree it is optimal reference point even though it is the only way to center the 100% illumination field. Very sad.

Besides, if you do not believe in referencing the extended apex is proper then why are you using the offset=D(D-A)/4S formula? As I have explained, this formula references the extend apex â€“ not the focal point. You still do not seem that you have comprehended which point is the D(D-A)/4S formula referencing.

What about the other subject that consumed countless number of posts? I am referring to your incorrect formula:
UO/BO OFFSET = AS/(D-A)Hâ€™
Do still believe the formula is accurate?

Yup, for anyone collimating from the focal plane level - which is what most people do - it is perfectly accurate. It is also accurate for any collimation point height H' other than the exact focal plane height.

I am dumbfounded. As I have explained repeatedly, the BO formula references the extended apex and the UO formula references the focal point. You are comparing apples and oranges. The ratio represents the difference between adjusting the secondary mirror from the focal point versus the extended apex point. It does NOT represent the difference between full-offset and partial offset.

Vla, I honestly have no interest to pursue this discussion with you. You are blinded by your arrogance. You have not brought anything new to the table. All you did in the last several pages of this thread is just stirring up dust.

Jason

EDIT: Made a typo correction and added more formulas

### #337 wh48gs

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Posted 09 November 2009 - 02:44 AM

Let's see. What you are proposing is to place sight tube's pupil at the apex level. For our exemplary 300mm f/5 Newtonian with minor axis A=70mm and diagonal-to-focus separation H=250mm, that is 380mm above the central axis.
That would require use of 4-5 inch extension tube, every time you collimate or checking on it.

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

No extension tube is necessary. With the focal plane already 250mm away from the central axis, the apex point is 130mm above the focal plane. Considering the focal plane is usually close to the fully racked in focuser position and a 1.25-inch sight tube is about 150mm long (2-inch sight tubes are longer), it's quite easy to position the sight tube pupil close to the apex point.

Standard sight tube is more like 5 inch long, on the average, and the height above the shoulder - which you optimally want to be laying on the top of focuser - is less than 1/3 of it, or about 1.5 inches. It can be pulled out so that only a small portion of the barrel length remains in the focuser, but that makes it more prone to play than an extension tube.

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What do you gain by doing collimation in this manner?

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Well, you commented in an earlier post that, "The purpose is to specify what the pattern is supposed to look like." Doing sight tube collimation in this manner, "...the pattern with a correctly placed pupil (and correct length sight tube barrel) is three identical circles--the bottom edge of the sight tube, the actual edge of the secondary mirror, and the reflected edge of the primary mirror."

Tighter circles are easier to read vs. collimating from the focal plane level, but at significantly longer extension and, consequently, smaller pattern make it harder. I still don't see it is worth the extra effort.

Quote:
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And in order have illuminated field exactly centered, you make collimation both more complicated (by the need to determine apex location, and use of extension tube), as well as less accurate (due to smaller apparent pattern size and possible extention tube play).

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Apex location--easy.
Extension tube--unnecessary.
Less accurate--debatable, but in practice, it's just not true.

Easy if the diagonal is already centered relative to the apex point (which it usually is not), not so easy if it is not. Either way, at the price of significant extention of the reference point height.

Extention tube - I count into it pulling the sight tube out of its fully enclosed position - is most often necessary.

In this particular case, going to the apex diminishes the apparent pattern size to 2/3 of its size from the focal point level. It does make noticeable difference.

Quote:
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I am yet to see someone collimating 300mm f/5 Newtonian in the manner you propose.

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It's pretty common among users who align the secondary mirror using the three concentric circles described above. And it's the reason CatsEye collimation tubes are adjustable.

And cost \$200+, the only "gain" being exactly centered field of full illumination. Well, let me take that back: there is a small gain in somewhat reduced disparity between pointing and optical axes.

Quote:
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...The "gain" of having exactly centered field of full illumination is not a match to the gain of collimation being as simple and accurate as possible.

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I suspect you're talking about two different things (axial collimation and secondary mirror collimation), which doesn't surprise me too much, as we've been talking about two different things (axial collimation and mechanical alignment) all along.

Those are different things, but it is all related and potentially important. Btw. axial collimation, as the alignment between mechanical and optical axes, is not in focus for a while.

Whether or not you use the apex point to align the secondary mirror, the offset math ((D-A)A/4S) does.

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'.

Vla

### #338 wh48gs

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Posted 09 November 2009 - 03:38 AM

Your math is wrong.

Leave sagitta out of it.

Here is the correct math for your reference:

Given:
â€œAâ€ for the secondary minor axis
â€œSâ€ for the distance between the primary mirror and the secondary mirror (leave sagitta out of it)
â€œDâ€ for the primary mirror diameter

First, calculate Hâ€™ to the extended apex

Then the offset

Offset = (H'*D^2)/(4*(S+H')^2-D^2)

It is just mathematicsâ€¦

Maybe you would elaborate where exactly my math is wrong?

For D=300mm, S=1250 and A=70, your H' formula gives:

H'=200,000+811=200,811

Must be a typo.

Vla, you did not even have a clue about the concept of the extend apex. After 10s of posts and 10s of diagrams, you seem to have finally comprehended the concept. But instead of admitting that you have learned something new from us, you are pretending that you knew about this concept all along but you disagree it is optimal reference point even though it is the only way to center the 100% illumination field. Very sad.

Why should I pretend I knew it? I only care of what it is, and already said what I think. If you expected me to congratulate you on it, sorry it won't happen.

Using the apex point does make it different from the standard collimation from the focal point level in the procedure, not in the end result; I am inclined to favor focal point level in that respect.

Vla, I honestly have no interest to pursue this discussion with you. You are blinded by your arrogance. You have not brought anything new to the table. All you did in the last several pages of this thread is just stirring up dust.

There's nothing much left to pursue, anyway. You seemed to be interested in pursuing discussion as long as you had the excuse to label my points as "wrong" because I was talking about collimating from the focal plane level. Now when we have come to comparing actual advantages of the two different reference points, you are out. But, again, not much left to be said, anyway.

Vla

### #339 Jason D

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Posted 09 November 2009 - 03:56 AM

Your math is wrong.

Leave sagitta out of it.

Here is the correct math for your reference:

Given:
â€œAâ€ for the secondary minor axis
â€œSâ€ for the distance between the primary mirror and the secondary mirror (leave sagitta out of it)
â€œDâ€ for the primary mirror diameter

First, calculate Hâ€™ to the extended apex

Then the offset

Offset = (H'*D^2)/(4*(S+H')^2-D^2)

It is just mathematicsâ€¦

Maybe you would elaborate where exactly my math is wrong?

For D=300mm, S=1250 and A=70, your H' formula gives:

H'=200,000+811=200,811

Must be a typo.

Yep, a typo. The numerator should have been enclosed in parenthesis.

I corrected the original post and added few more interesting formulas

You seemed to be interested in pursuing discussion as long as you had the excuse to label my points as "wrong" because I was talking about collimating from the focal plane level.

You are "wrong" because you are talking about collimating from the focal plane level using a formula that references the extended apex D(D-A)/4S. You are being inconsistent. Even in your response to Vic, you are dismissing the importance of the extended apex point yet you insist in using the very formula that references it. Did you read my earlier post? D(D-A)/4S formula has no focal plane or focal ratio information included in it. Two scopes with two different focal lengths but the same A,D, and S will end up with the same offset when using the formula D(D-A)/4S â€“ interesting, isnâ€™t it?

Jason

### #340 wh48gs

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Posted 10 November 2009 - 09:10 AM

Yep, a typo. The numerator should have been enclosed in parenthesis.

For D=300mm, A=70 and S=1250, that gives H'=376.22. It is slightly less than the actual value H'= (S-z)A/(D-A)=379.29, where "z" is the mirror sagitta. Neglecting the sagitta, it reduces to the relation posted by Vic awhile back, H'=S/[(D/A)-1].

We don't use trigonometric functions explicitly, but we do use them implicitly, because we use prortions that determine angles of convergence. For strict accuracy, mirror sagitta has to be taken into account. I was little lazy, but finally I posted the relevant geometry:

http://www.telescope...t/newtonian.htm

It also shows the derivation of BO shift given by A/4F'. Note this F' is not quite identical to F' you use, which neglects the sagitta. Practically, there is no appreciable difference.

You are "wrong" because you are talking about collimating from the focal plane level using a formula that references the extended apex D(D-A)/4S. You are being inconsistent. Even in your response to Vic, you are dismissing the importance of the extended apex point yet you insist in using the very formula that references it. Did you read my earlier post? D(D-A)/4S formula has no focal plane or focal ratio information included in it. Two scopes with two different focal lengths but the same A,D, and S will end up with the same offset when using the formula D(D-A)/4S â€“ interesting, isnâ€™t it?

Using the apex point for collimation is only imperative for full (bidirectional) offset. It is not imperative for axial (unidirectional) offset, which is what we were talking about.

But you are making a good point. I haven't been thinking about it, and that should be clarified. Most sources, including BO shift calculators, don't specify the vantage point, or state that it is the focus point, the "most used eyepiece position", or so. But BO shift required also changes with the vantage point, and there will be dicrepancy if someone tries to use BO shift value obtained from a calculator, or some of classical formulas, while collimating from the proximity of focal plane, or any point other than the apex. The pattern won't appear concentric in the focuser, and that gets confusing.

The BO shift for any vantage point on the focuser axis at the height H above the tube axis can ge obtained using the same geometry as for the UO shift. It gives that same familiar formula (A^2)/4H, which means that the two shifts, either BO or UO, are identical when collimated from the focal point, or from any identical vantage point height H.

So, both BO and UO from the focal point have nearly identical diagonal shift - it is slightly smaller for the UO, due to its focus height being slightly larger - and the degree of decenter of the diagonal's image in the primary (the difference is that BO does not induce disparity between optical and mechanical axes, and that BO does not have fully illuminated field exactly centered).

No need for separate, more complicated BO shift math; it is all unified and generalized with one simple formula.

I have to say that I was wrong when saying that nothing much is there left to be said

As for the BO shift being identical for two telescopes of identical D, S and A, regardless of the focal length, this is not surprising. Since S=f-H, it implies that H does change with the change in focal length. Although it is not explicitely in the formula, all that really matters for the shift are minor axis A and vantage point height H. That is reflected in the "root formula" (A^2)/4H.

Vla

### #341 Vic Menard

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Posted 10 November 2009 - 10:45 AM

I think we're approaching consensus. I'm still a bit fuzzy on these two quotes (which seem to contradict each other).

...Using the apex point for collimation is only imperative for full (bidirectional) offset. It is not imperative for axial (unidirectional) offset, which is what we were talking about.

and,

...both BO and UO from the focal point have nearly identical diagonal shift

I don't understand why you feel that using the apex point for secondary mirror alignment is "imperative" for bidirectional offset, but not for unidirectional offset, considering both BO and UO have nearly identical diagonal shift (from the focal plane).

I still feel that aligning the offset secondary mirror (whether the offset is bidirectional or unidirectional) with the sight tube pupil at the apex and the sight tube length adjusted so that it's consistent with the focal ratio of the apex derived light cone is the only way to achieve similar alignment circles (the bottom edge of the sight tube, the actual edge of the secondary mirror, and the reflected edge of the primary mirror).

Your webpage link (8.1.3, and the updated Newtonian collimation webpage 8.1.2) appear to cover the salient points, but your pointing error discussion could lead the reader to believe that no better DSC or tracking precision should be expected. Depending on the initialization stars, the target location, and even considering "noise" from build tolerances (and read tolerances when a cross hair reticle is not being used), I often find the pointing error with my 22-inch f/4 w/4-inch UO secondary mirror to be within 0.1-degree (+/-) relative to the center of the fov.

Similarly, given the same set of variables, I don't believe the user should expect the pointing accuracy to be constrained to the derived optical/mechanical axial deviation either! For the user who suspects DSC errors attributed to unidirectional offset (and assuming he has investigated Best Pair or similar software), I usually suggest trying a centered (no offset) secondary mirror alignment followed by a DSC trial run (with no change to the other parameters). If the user notices a significant gain in pointing accuracy, he can choose to continue with a centered secondary mirror alignment or make the necessary mechanical accommodations for bidirectional offset.

### #342 Vic Menard

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Posted 10 November 2009 - 02:02 PM

A few more puzzlers...

...the difference is that BO does not induce disparity between optical and mechanical axes...

Since BO shift is typically relative to the OTA axis, this assumes the OTA axis is precisely orthogonal to the alt/dec axis (or at least more precise than the disparity generated by the UO shift). Also, 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).

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

Did you mean UO here? If so, is the fully illuminated field a decentered circle or is it a centered ellipse?

As for the BO shift being identical for two telescopes of identical D, S and A, regardless of the focal length, this is not surprising. Since S=f-H, it implies that H does change with the change in focal length. Although it is not explicitely in the formula...

The value of "H" is not fixed because it varies with "A" (only "D" and "S" are fixed). (A^2)/4H returns the proper shift value and puts the pupil at the focal plane only for the minimum "A" value.

...all that really matters for the shift are minor axis A and vantage point height H. That is reflected in the "root formula" (A^2)/4H.

But as "H" changes (with "A" values greater than the minimum), the offset also changes--which is also reflected in the "root formula". (D-A)A/4S is a better "root formula" when "A" is greater than minimum, delivering a more precise offset value.

### #343 Jason D

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Posted 10 November 2009 - 02:51 PM

It also shows the derivation of BO shift given by A/4F'. Note this F' is not quite identical to F' you use, which neglects the sagitta. Practically, there is no appreciable difference.

Vla,

Your Fâ€™ and my Fâ€™ are the same. That is, my â€œSâ€ is the same as your â€œS-z.â€ In your case, you decided to account for sagitta but you kept subtracting it in the following terms (S-z), (F-1/16F), and (f-z) which complicated your formulas unnecessarily. I suggest you do all your math without sagitta then account for it in the final formulas.

For D=300mm, A=70 and S=1250, that gives H'=376.22. It is slightly less than the actual value H'= (S-z)A/(D-A)=379.29, where "z" is the mirror sagitta. Neglecting the sagitta, it reduces to the relation posted by Vic awhile back, H'=S/[(D/A)-1].

Here is where your math is off. See attachment. I hope you donâ€™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 â€œAâ€. 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). The difference between the two segments is small and the resultant formula D(D-A)/4S is simple and highly accurate; however, D(D-A)/4S is not mathematically exact but rather a very good approximation which was my point.

I was going to address the inconsistencies in the remainder of your post but Vic has already pointed them out.

Jason

### #344 Vic Menard

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Posted 10 November 2009 - 03:35 PM

...Standard sight tube is more like 5 inch long, on the average, and the height above the shoulder - which you optimally want to be laying on the top of focuser - is less than 1/3 of it, or about 1.5 inches.

I suppose you're talking about a combo tool. I think 5.25-inches is about right for an AstroSystems LightPipe, and, IIRC, the aperture is about 1-inch, so the tool is operating at about f/5. And you're correct, the pupil is already 1.25-inch (37mm) above the focal plane, which means the remaining 93mm will need to be split between racking out the focuser and sliding out the sight tube--probably less than 2-inches each.

...Tighter circles are easier to read vs. collimating from the focal plane level, but at significantly longer extension and, consequently, smaller pattern make it harder. I still don't see it is worth the extra effort.

I can't argue with that. 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?

...it's the reason CatsEye collimation tubes are adjustable.

And cost \$200+, the only "gain" being exactly centered field of full illumination. Well, let me take that back: there is a small gain in somewhat reduced disparity between pointing and optical axes.

FTR, AstroSystems 1.25-inch LightPipe is \$45. CatsEye TeleCat XLS 2-inch Combo Tool is \$111. 2-inch tools do cost more, but, at least IMO, they're worth it (added functionality (adjustable), precision, ease of use).

...The "gain" of having exactly centered field of full illumination is not a match to the gain of collimation being as simple and accurate as possible.

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.

Whether or not you use the apex point to align the secondary mirror, the offset math ((D-A)A/4S) does.

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'.

Are you saying that ((D-A)A/4S) is not appropriate for unidirectional offset? Using ((D-A)A/4S) for my UO 22-inch f/4 w/4-inch minor axis secondary mirror and 15-inch intercept I get 0.25-inch offset. Solving arcsin (offset/S) I get 0.2-degree disparity vs. pointing axis which agrees well with your derivation. I'm still not sure about "the degree of decentering of the diagonal's image in the primary". Are you saying the decentering changes if one solves for ((D-A)A/4S) vs. (A^2)/4H'? If so, I think we're on the same page.

### #345 Jason D

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Posted 10 November 2009 - 03:54 PM

Are you saying the decentering changes if one solves for ((D-A)A/4S) vs. (A^2)/4H'? If so, I think we're on the same page.

Vic,

Vla is mixing between partial/full offsets and the formulas ((D-A)A/4S) vs. (A^2)/4H'. Both are independent. The first formula corresponds to placing the sight-tube pupil at the extended apex and the second formula corresponds to placing the sight-tube pupil at the focal point. Placing the sight-tube pupil at either point is independent of partial/full-offset.

If the extended apex happened to be at the focal point then we have a minimally sized secondary which means

(D-a)a/4S=a^2/4H where â€œaâ€ is minimal A

4HD-a4H=a4S
HD=a(S+H)
But S+H is f â€œfocal lengthâ€
HD=af
a=DH/f
But f/D is F â€œF-ratioâ€

Solving for â€œaâ€ we get
a=H/F

The above is an approximation because we used the approximated formula (D-A)A/4S

The exact formula is
a = 4HF/(4F^2-1)

Jason

### #346 Johndob

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Posted 14 November 2009 - 05:57 PM

Wow,I'm glad my Z10 has a large secondary to catch the light cone with room to spare.

### #347 Jason D

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Posted 15 November 2009 - 01:42 PM

Wow,I'm glad my Z10 has a large secondary to catch the light cone with room to spare.

You have the right attitude about sizing the secondary mirror. I own an XT10 and I have read about how others replaced they stock 2.5" secondary mirror with 2.14" to improve "contrast" but by doing so they reduced the effective aperture of their scope. In my case, replaced my 2.5â€ stock secondary mirror with a 2.6â€ premium.

My scopeâ€™s specifications are
F = 4.76
S = 36.8â€
D = 10â€
A = 2.6â€

Referring to the formulas I listed in this post
H' = 12.75247â€ which means the optimal sight-tube pupil placement is ~2" above the focal plane.
H = 10.8â€
F' = 4.955247â€
Offset = 0.131174
Secondary minimum size = 2.294222â€
100% illumination = 0.39402â€

Interestingly, when I plugged in the same specifications in NEWT I ended up with slightly different values
Offset = 0.130707â€ 4.06% less than above
100% illumination = 0.428261â€ 8.67% more than above

Apparently, NEWT uses the simplified formulas
Offset = A/4F
100% illumination = (D(AF-H))/S
Which was surprising to me. NEWT could have utilized the more accurate formulas.

Jason

### #348 Jason D

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Posted 15 November 2009 - 02:35 PM

Even though aligning the secondary mirror from the extended apex point will round and center the 100% illumination area, the illumination reduction gradient will not be the same in all direction. That is, the 100% illumination area will be symmetrical but illumination reduction will be asymmetrical.
Jason

### #349 wh48gs

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Posted 18 November 2009 - 11:44 PM

I think we're approaching consensus.

Phew! It was about time. I had the BO offset out of focus, and didn't realize that the "classic" formula is for the apex point (part of it was having mental picture of Suiter's illustration, with the origin of coordinate system at the focus point). So, Jason, and Don before him, were right: from one same point, BO and UO shift are practically identical.

It's odd that illustration I made - and I tried to be as accurate as I could - was showing UO shift as somewhat larger. But when I make it as large as can fit computer screen, and using screen numericals, I do get it nearly the same. The lesson: can't really depend on hand drawing for subtle differences.

I don't understand why you feel that using the apex point for secondary mirror alignment is "imperative" for bidirectional offset, but not for unidirectional offset, considering both BO and UO have nearly identical diagonal shift (from the focal plane).

What I ment is "classial" BO, the one that is calculated for the apex point, which is probably includes both "full offset" formulas, as well as shift values given in online calculators.

Your webpage link (8.1.3, and the updated Newtonian collimation webpage 8.1.2) appear to cover the salient points, but your pointing error discussion could lead the reader to believe that no better DSC or tracking precision should be expected. Depending on the initialization stars, the target location, and even considering "noise" from build tolerances (and read tolerances when a cross hair reticle is not being used), I often find the pointing error with my 22-inch f/4 w/4-inch UO secondary mirror to be within 0.1-degree (+/-) relative to the center of the fov.

I'll be going over it as soon as I get some time. But keep in mind that this is for the UO offset from the focal plane level, so the offset is somewhat larger than from the apex. Also, in the focuser inclination factor, it is implied that it can both, increase or reduce the final disparity (as it can less than perfectly squared *untilted* primary).

Similarly, given the same set of variables, I don't believe the user should expect the pointing accuracy to be constrained to the derived optical/mechanical axial deviation either!

If all the variables are taken into account, it should; the problem is that they are not, and that they usually cannot be all specified.

### #350 wh48gs

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Posted 19 November 2009 - 12:23 AM

Since BO shift is typically relative to the OTA axis, this assumes the OTA axis is precisely orthogonal to the alt/dec axis (or at least more precise than the disparity generated by the UO shift). Also, 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 woble 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.

Quote:
--------------------------------------------------------------------------------

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

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

Did you mean UO here? If so, is the fully illuminated field a decentered circle or is it a centered ellipse?

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.

Quote:
--------------------------------------------------------------------------------

As for the BO shift being identical for two telescopes of identical D, S and A, regardless of the focal length, this is not surprising. Since S=f-H, it implies that H does change with the change in focal length. Although it is not explicitely in the formula...

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

The value of "H" is not fixed because it varies with "A" (only "D" and "S" are fixed). (A^2)/4H returns the proper shift value and puts the pupil at the focal plane only for the minimum "A" value.

Well, 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.

Quote:
--------------------------------------------------------------------------------

...all that really matters for the shift are minor axis A and vantage point height H. That is reflected in the "root formula" (A^2)/4H.

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

But as "H" changes (with "A" values greater than the minimum), the offset also changes--which is also reflected in the "root formula". (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.

But for the BO shift, it is slightly different; on the first sight, it seemed to me it unfolds the same as the UO formula, but it doesn't. BO shift is given by [sq.root(H^2+A^2)-H]/2, also for any value of H. Although the form is different, it is still dependant on the two same basic parameters, and gives practically identical (to UO with H adjusted - increased - for the shift value) result.

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