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Effect of level on ASPA - with figures

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#1 freestar8n

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Posted 22 November 2013 - 01:57 PM

Hi-

This is a follow up of a recent thread on the effect of level on ASPA. The vast majority seem confident that the ASPA alignment process is unaffected by a mount that is not level, and I have created some figures that I hope will show that level does in fact matter.

First I should say that I think there is good agreement that under normal use, ASPA does work pretty well. There is some debate on how best to do it, and what matters to accuracy, but I hope these figures will clear some things up.

Unfortunately, they will clear things up by making the process look much more complicated than people may think - but this is a consequence of the 3D rotations involved, and the fact that mounts are adjusted with alt-az motions.

First I will summarize some of the basics that most people know:

1) For good goto accuracy, a mount doesn't have to be level and lat/long don't matter at all. They only matter for the first alignment stars. Once the mount has seen some stars in the sky, it has its bearings and knows how the mount is related to the celestial sphere.

2) You can have excellent GoTo accuracy even if the mount is not polar aligned.

3) You can have excellent polar alignment even if the mount is not level and the lat/long are wrong.

The point of this thread is to convey the following:

4) If the mount is not polar aligned, and if the mount is not level or lat/long is wrong, then the ASPA procedure will lose accuracy - possibly by a very large amount

5) This is a fundamental limitation of the lack of information when aligning the polar axis using an arbitrary star in the sky.

But - again - under normal use and with a reasonably level mount - everything should be fine. There is no need to take extreme care in this stuff. But there is a need to be aware that big errors in time, coordinates, or level could be a real problem.

Frank

#2 freestar8n

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Posted 22 November 2013 - 02:05 PM

Originally I was going to do schematic figures, but I realized they might be construed as inaccurate. So these are accurate 3D renderings of the process based on the exact rotations.

I have intentionally chosen a star that is toward the west and not close to the meridian in the south because it shows the process better - but the principles are the same for all stars. It is just much worse for a star in the west.

Here is a view of the geometry for a normal ASPA polar alignment with a level mount. The location is 20 degrees latitude and the polar axis of the mount is a bit off in alt/az - but the pier is exactly level. The two adjustments of the pier for polar alignment are in the az and alt direction and the axes are shown.

During ASPA, the user moves the mount in alt/az to center a star after having moved the mount backwards. This is equivalent to moving the mount from the star to a specified location on the celestial sphere. The purpose of this motion is to cause the polar axis to move in exactly the right way to land on the celestial pole. In this case it works because the mount is level.

Frank

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#3 freestar8n

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Posted 22 November 2013 - 02:12 PM

In the process above, the mount is moved first in alt, then in az - resulting in the strange path of the scope itself - but note that the pole does exactly the right thing. The key thing to notice is that the alignment star is moved in alt/az motions that are not simple x/y motions, and they are very different from what happens to the polar axis.

Now let's see what happens if the pier is tipped 10 degrees. Everything else is the same - because the polar axis is still pointing to the celestial sphere as before.

Even if the mount is perfectly calibrated to the sky and has good goto, it has absolutely no awareness that the pier is tilted - and it therefore has no idea how the mount will actually move relative to the sky when the user performs ASPA. It *has to* assume the mount is level and everything is normal. It does know exactly where the polar axis is pointing on the sky and how far off it is - but in order to tell the user how to move the mount - it has to assume something about the geometry - so it assumes it is level.

Here is what happens when the pier is tilted 10 degrees. The target location is exactly the same - because it was calculated in the first place with the assumption the mount is level. But when the user moves the mount to center the star - very different things happen - and the polar axis does something different as a result - and lands in the wrong place.

Frank

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#4 mpgxsvcd

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Posted 22 November 2013 - 02:23 PM

I want to believe you. However, the CG-5 manual says that the Level of the Tripod does not affect ASPA. I tend to believe Celestron’s documentation unless you have some measurements that contradict that.

From the CG-5 manual. This is referring to manually setting the Polar Alignment without using the ASPA routine.

Level the tripod. There is a bubble level built into the mount for this purpose.

NOTE: Leveling the tripod is only necessary if using this method of polar alignment. Perfect polar alignment
is still possible using other methods described later in this manual without leveling the tripod.



#5 freestar8n

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Posted 22 November 2013 - 02:26 PM

As I said before - I don't think this stuff is obvious, but I hope that the figures convey some of the issues involved. It is not as straightforward as people think. Underneath it all is the need for a model of what the mount will do when the user moves it in alt/az. If the mount does not do what is expected, then even if it points exactly at the alignment star as requested, the polar axis - which is what matters - may be off.

As a corollary to this - note that the alt/az adjustments of a mount may not be ideal if they are not exactly orthogonal. Any departure of the mount motion from what's expected - whether due to level, time, lat/long, or mechanics - will affect accuracy. As a result, there is good reason to expect that if the mount is very far off and you do ASPA to get close, then doing it again may indeed improve things. But once it is close, I don't think another one would help much.

Another thing that should be clear from these figures is that you get most accuracy using a star low in the south (for northern users) and near the meridian. This is because the alignment motion is alt/az. The equator has no special role here at all - and in fact should be avoided for low latitudes because it is high up.

But once again - if people do this stuff in a reasonably sane manner with a reasonably level mount - it should work pretty well.

Frank

#6 freestar8n

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Posted 22 November 2013 - 02:30 PM

I tend to believe Celestron’s documentation unless you have some measurements that contradict that.


You are welcome to believe any other source of information you choose.

Note again that I am in agreement that level is not "critical" to aspa working well - but it does indeed matter.

As I recall, in the previous thread, a celestron engineer did in fact confirm that level does matter - so it is not uncommon for manuals and documentation to have slight errors.

Frank

#7 Whichwayisnorth

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Posted 22 November 2013 - 03:21 PM

I want to believe you. However, the CG-5 manual says that the Level of the Tripod does not affect ASPA. I tend to believe Celestron’s documentation unless you have some measurements that contradict that.

From the CG-5 manual. This is referring to manually setting the Polar Alignment without using the ASPA routine.


Level the tripod. There is a bubble level built into the mount for this purpose.

NOTE: Leveling the tripod is only necessary if using this method of polar alignment. Perfect polar alignment
is still possible using other methods described later in this manual without leveling the tripod.


Doesn't that quote support what Frank is saying though? If you are using ASPA the level DOES matter but if you are using other methods it doesn't?

#8 Skunky

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Posted 22 November 2013 - 03:26 PM

I tend to believe Celestron’s documentation unless you have some measurements that contradict that.


:roflmao: :lol:

#9 freestar8n

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Posted 22 November 2013 - 03:37 PM

Doesn't that quote support what Frank is saying though?


Thanks - Whichway. I hadn't read the quotation completely and it does look like the documentation is correct. There are many ways to polar align and aspa is fast and works well - but it does benefit from a level mount that has been accurately aligned and calibrated - preferably with a 2+4. If the motion needed to polar align is many degrees, and if alignment is important for imaging, then doing it a second time may help. But if the mount is pretty level and the polar alignment is close already, and if a star low in the south is used, then it should work pretty well directly.

Frank

#10 NOMH

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Posted 22 November 2013 - 06:22 PM

Frank, thanks for stating this. When I had my CGEM I used ASPA and it worked great. But I too think that the mount must be level for best results. To me it is so basic and simple to do I can't imagine a reason not to do it. There are enough things that go wrong during an imaging session and I see no reason to create additional complications in a set up.

JB

#11 mpgxsvcd

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Posted 22 November 2013 - 08:58 PM

I want to believe you. However, the CG-5 manual says that the Level of the Tripod does not affect ASPA. I tend to believe Celestron’s documentation unless you have some measurements that contradict that.

From the CG-5 manual. This is referring to manually setting the Polar Alignment without using the ASPA routine.


Level the tripod. There is a bubble level built into the mount for this purpose.

NOTE: Leveling the tripod is only necessary if using this method of polar alignment. Perfect polar alignment
is still possible using other methods described later in this manual without leveling the tripod.


Doesn't that quote support what Frank is saying though? If you are using ASPA the level DOES matter but if you are using other methods it doesn't?


No this quote is referring to manually setting the alignment. The "other" method is ASPA. Level has no affect on ASPA according to the Celestron documentation.

#12 mclewis1

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Posted 22 November 2013 - 10:12 PM

Travis,

What is the date is on the front of the manual you are referring to? Any CG-5 manuals I've seen were written long before ASPA was even thought about.

AFAIK the most up to date manuals are the CGEPro manual and the Advanced VX manual. The CGEPro is the most appropriate for any Celestron gem with the latest v4.xx firmware, the AVX for v5.xx firmware.

Neither of these manuals state that a level tripod is required for ASPA. The only reference to a level tripod is under using the latitude scale to do a rough polar alignment. The ASPA procedure does reference the latitude scale section for setting up but that's hardly a definitive statement about requiring a level tripod.

To me this reads from Celestron's point of view that being level is something useful but not absolutely required. "No effect" is not a statement from Celestron.

I tend to agree with Frank's analysis ... that a level tripod does actually make a difference to ASPA but being off by a small amount is not enough to make it a big deal and can be ignored.

#13 freestar8n

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Posted 23 November 2013 - 06:42 AM

The figures I showed earlier make the situation look worse because the star is in the west. Here is a more typical view for a user at 40 degrees latitude with a star low in the south and near the meridian. Level still matters, but the motion is much more in well defined orthogonal x/y directions - but not exactly.

Here is a view from the side, but it is hard to see the motions involved.

Frank

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#14 freestar8n

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Posted 23 November 2013 - 06:44 AM

Here is a view from the south of the alignment star showing the nearly perpendicular motions involved.

Frank

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#15 freestar8n

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Posted 23 November 2013 - 06:46 AM

Here is a view of the polar axis moving precisely to the pole since the mount is level.

Frank

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#16 freestar8n

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Posted 23 November 2013 - 06:56 AM

Note that when the scope goes down in the south, the polar axis goes up in the north - and when the scope goes west in the south, the polar axis goes east in the north. But there are always subtle angles involved that make the motions not exactly x/y.

For people who might want to check this stuff, keep in mind that it requires that the mount be off polar alignment in the first place. If the mount is perfectly polar aligned, then ASPA won't tell you to move the mount much - even if all your coordinates, level, and time are wrong. The issue with level, gps, and time comes in when the mount is not aligned at the start, and ASPA tries to tell you how to move the mount.

The first clue that these factors matter is if you read the alt/az polar alignment error. The values you get will depend on time and lat/long for a given polar misalignment - but will not depend on level at all because ASPA has no idea the mount is not level.

But if you then do the procedure and aim the scope at the alignment star by moving the mount - the result you get will depend on level.

The possible errors may not be small. You could end up with the mount 90 degrees off polar alignment and tracking from south to north instead of east to west.

Note also that if you center the star by using the tripod leg rather than the alt/az adjustments, you will get a different result. This is because when you shorten the leg, the path in az is now different - and the final direction of the polar axis will be different in the two cases.

I hope this stuff is more clear now and it isn't just a matter of believing me - but having an understanding of the process based on views of the 3D rotations involved.

Frank

#17 dragonslayer1

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Posted 23 November 2013 - 10:21 AM

Well I for one have always tried to level my mount as best as possible and will continue to do so, as some say just to alleviate possibly entering a factor that compounds the final process, :jump:,, Thank you Frank for putting that all together, I appreciate the work you did.
Kasey

#18 Cliff Hipsher

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Posted 23 November 2013 - 10:36 AM

Perhaps taking a look at this will help.

I started out with a fork mount on a wedge. Getting the mount level matters. I've always leveled my mount and until I can find a mount with a gyroscopic leveling mechanism, I always will.

#19 korborh

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Posted 23 November 2013 - 11:25 AM

Thank you Frank for putting this together. Appreciate the effort you put into this for illustrating the concepts about ASPA. This thread should be made sticky for future reference.

Rather than believing someone or some documentation, I like to understand the underlying fundamentals of what is being claimed. So thanks for this ...it really explains why levelling the mount matters for ASPA.

#20 Per Frejvall

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Posted 23 November 2013 - 11:27 AM

It must matter if you are using any method that measures stars NOT at the pole itself. For a Polaris alignment the effect of an unlevelled mount is small. ASPA, from what I can gather, measures stars and thus must assume that the mount is level or there is no maths available for it to operate on.

I include a post that I made on SGL on the matter of a not so level tripod. ;)

/per

I thought I would write a word on how to fail with a pointing and target model. As some of you know, I use the 10Micron mounts, the GM1000HPS and the GM2000HPS. Both are formidable gems (pun intended) that give me unguided performance and lots of hassle-free imaging runs. Currently I have the GM1000 on the balcony pier and wanted to start the season off with some close-ups of the Elephant Trunk Nebula. So, after having returned from my arctic venture I put the 190MN on the mount. Hell broke loose!

The mounts hold a model of the sky and I use my own software (Model Maker) to produce them. This is different to other mounts that use advanced modeling in that the model is actually in the mount, not in a PC on the side. The accuracy of the absolute encoders in the GM1000 and GM2000 are rediculously good: more than 10 million counts per axis revolution. In order to produce unguided performane, the model needs to be very precise, and when it is there it will model the sky, your scope problems and your polar alignment error. Naturally, phenomena such as random flkexure cannot be modeled, but predictive and regular flexing can be (and is).

So I start off with a 20-point model in order to adjust the polar alignment. This takes about ten minutes as I use a low slew rate setting (8°/s) in order to not disturb the neighbours when the minimal sound of the mount travels through the concrete. I adjusted the polar error and ran a 50-point model with the net result of a polar alignment error of 47 arc-seconds. Good enough!

First ten-minute sub was a mess with zig-zag stars. I figured something got stuck and checked the rig. Let it run for the night and found 23 bad subs when I woke up. Gah!

Over the next couple of nights I ran different models, checked the pier and did various things, all without any improvement worth mentioning. Had my trustworthy high-tech companion failed me?

Well, the answer came last night. I took the mirror cell out of the 190MN and realized that my rubber padding around the moveble part of the cell was a little loose. I could actually move the cell a tiny fraction of a millimeter back and forth. RANDOM FLEXURE!

How bad is this? Well, let's do a simple number calculation. Assume you have a perfect tripod, model your mount with a telescope completely free of flexure and the let one of the tripod legs sink one millimeter into the ground.

The tripod I use when I use a tripod is the 10Micron Centaur. Very sturdy, and the distance between one foot and the perpendicular line between the other two is about 80cm with the legs in their unextended position. Back to school:

tan(v) = 1 / 800
v = atan(0.00125) = 0.0716 degrees = 4.3 arc minutes

This should give an indication as to the "power of the error". A very small error can throw things off considerably. The solution last night was evident when I swapped scopes and put the Takahashi FSQ-106 on the GM1000. Ran one 10-star model, left the polar alignment at its indicated 3'17" and added ten more stars to the model. I then ran a quick ten minute Ha sub of the trunk and found perfectly round stars. Phew! No need to send the mount back, but definitely some more time to spend on the 190MN! You may notice the drop in focal length (1000mm to 530mm), but I assure you that it is completely insignifficant next to the flexure. If the 190MN had a stable mirror cell it would give the same unguided performance as the Tak.

The message here is clear and easily understood. The magnitude of the problems that are caused by flexure is, however, unimaginally big!

Notes to self (and others):
=====================
Flexure is a key enemy
The smallest error will shoot the best model to pieces
Cheap scopes may not be a good idea in the sub arc-second precision arena
The pier needs to be rediculously stable
I know a few of you with 10Micron mounts sometimes have problems obtaining the cool unguided performance. I promise, the problem liess in the scope or the rig, not in the mount itself. And for the record, I have produced one-hour subs with the 190MN on the GM2000HPS - right after I modded the mirror cell...

Have a nice Tuesday!

/per


EDIT: 10 million ticks (less than what is in the 10Micron mounts) is 0.13 arc-seconds. The assumption then is that the mounts ideally can produce about 0.1 arc-seconds of unguided tracking performance, which is about twice better thanwhat you get with off-axis guiding at 2"/px and 1/10th pixel guide-star movement detection(!)

#21 Alph

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Posted 23 November 2013 - 02:15 PM

The vast majority seem confident that the ASPA alignment process is unaffected by a mount that is not level, and I have created some figures that I hope will show that level does in fact matter.


They are right and you are wrong. Mount level does NOT matter. You did not think hard enough, Frank. You still don’t get it. Your figures reveal and confirm your lack of understanding of the problem. You need to understand that the horizontal system of coordinates is not needed and it is not used to describe the polar axis misalignment. Polar axis misalignment is defined and measured in the equatorial system of coordinates. The following figure shows the relationship between the equatorial coordinates, the telescope coordinates and the polar axis misalignment.

Posted Image

The first rotation is around the actual polar axis and the second rotation is around the new X axis. This transformation leads to a following set of equations that describe telescope pointing errors in the equatorial coordinates due to the polar axis misalignment.

Posted Image

where
ME is the north-south component of the polar misalignment
MA is the west-east component of the polar misalignment

The MA and ME values can be computed from a two star polar alignment and these are the values that the Nexstar controller displays after the two star alignment is completed.

The equations give the distance and the direction in the equatorial coordinates that the telescope will slew to move away from the ASPA star. The equations do not reference the horizontal system of coordinates and the mount level is irrelevant.


#22 freestar8n

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Posted 23 November 2013 - 07:01 PM

You are focused on the misalignment of the polar axis as referenced to the celestial sphere. As I said - this is known exactly as long as the mount is aligned to the sky - and level does not matter at all for that. It is shown as the blue cylinder representing the polar axis in my figures - which points to the celestial sphere. Indeed - it is easy to know exactly how far off the polar axis is and where it points in the sky without assuming mount level.

But an alignment like ASPA uses that as only one small part of the process. The real trick is to determine the point on the celestial sphere representing the shift from the alignment star that the mount should move by alt-az motions. That target point is shown as the yellow dot in my figures.

What I hoped would be obvious from my diagrams is the fact that - even if this target location is known, and even if you point to it exactly, the final direction of the polar axis could be very different depending on mount level. This, by itself, should make anyone realize that there is no single point on the sky you can point to in a general way to make the polar axis end up aligned, and therefore you can't do it without knowing how the axes of the mount adjustments are oriented.

Just by looking at the figures I provided and the behavior of the polar axis depending on mount level, it should be clear that you cannot do a process like ASPA without knowing the orientation of the mount axes to the celestial sphere. That is all independent of knowing where on the celestial sphere the polar axis points.

If you could look up the polar axis and see where it is currently aimed - then you could just move it to the pole directly. That is what is done with a polar scope. But with ASPA, you take some star in the sky, and you move the mount in alt/az away from that star to a particular target location - so that magically the polar axis lands in the right place. That involves much more than simply knowing where the polar axis is currently pointing.

Frank

#23 freestar8n

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Posted 23 November 2013 - 07:10 PM

As an addendum - you should really simply provide a pointer to material that isn't your own, rather than copy a figure - particularly if you don't even cite the source. As often happens, you appear to be using material out of its context. The source itself may be fine - but it isn't talking about the ASPA process. It is talking about mathematical ways to reorient a coordinate system - and nothing about how to polar align a mount using its two physical adjustment axes. "Just rotate around the new X" would be quite a challenge - physically - for someone to do, since the mount doesn't have such an adjustment axis.

Frank

#24 freestar8n

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Posted 23 November 2013 - 07:28 PM

It must matter if you are using any method that measures stars NOT at the pole itself. For a Polaris alignment the effect of an unlevelled mount is small. ASPA, from what I can gather, measures stars and thus must assume that the mount is level or there is no maths available for it to operate on.


That sums it up.

The same target location (yellow dot in my first two figures) produces two different polar alignments when the only difference is the tilt of the pier.

All you know for sure is that - when you aim at the target location - the polar axis is somewhere on a possibly large circle that includes the pole. But if you know the mount is level, you can get it aligned deterministically - because you have all the information you need to model the adjustment motions relative to the sky.

Frank

#25 dragonslayer1

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Posted 23 November 2013 - 08:08 PM

:gotpopcorn:My money is on Frank, Kasey






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