KC_Astro_Mutt I aim for less than 1arc minute.

That should be enough to introduce enough drift so that the real declination error is ony to the North or to the South.

I.e., you don't want perfect Polar Alignment, since you will not be able to use North-only or South-only declination guiding. The N-only and S-only will make sure your declination motors will only to commanded to move in one direction, and thus no backlashis possible. Ignore the YouTube novices who try to get within 1 arc second polar alignment without knowing what it means. The seminal paper on field rotation is Hook's by the way:

https://adsabs.harvard.edu/full/1989JBAA...99...19H

(Before days of PDF, so this is a scanned document, unfortunately).

By the way, when you autoguide, the field will rotate around the guide star (or the average centroid of multi-guide stars) instead of your plate center. But again, good post proessors will handle it.

If you need more details, this is what I wrote in an email in 2012 to an ex-Apple colleague. Unfortunately the original paper that I referred to is no longer on the web, but you can probably follow from below:

... you take two stars at the same declination, the difference in N-S drift between a star at the center of the image and a star at a different RA is
[ sin(RA1) - sin(RA2) ].∆/T
The worst case magnitude for the above is 2.∆.sin( | RA1- RA2| )/T
Similarly, from Equation 11, a star at the edge of an image frame that is at the same RA as the central star has an E-W drift of
[ sin( decl1) - sin(decl2) ].cos(alpha).∆/T
worst case magnitude (cos(alpha)=1) again in the same form of
[ sin( decl1) - sin(decl2) ].∆/T
And again using the sin(A0-sin(B) formula, the worse case magnitude difference is 2.∆.sin( |decl1 - decl2| )/T
Ergo, if for an image frame is P degrees wide and P degrees tall, and assume the central star is perfectly tracked, the worse case (due to field rotation) movement of any other star is
∆.sin( P )/T.
Since sin(P) is smaller than P, we can bound this by
∆.P/T .
∆ is the angle error of the polar axis. T is 3.8 hours per radian.
So, if the polar axis is off by 1 degree, the worst case movement of a star at the edge of a frame that is 45 degrees wide (a typical 50mm lens and a full frame 35mm camera) in 1 hour, is
0.017*0.78/3.8 = 0.00351 radians = 0.2 degrees.
If the width (or height) of a frame is 1000 pixels), the worse case drift at the edge of a frame is 1.7 pixels.
Not too bad as worse case for a 1 hour exposure and a 50mm lens when the polar axis is off by 1 degree. With a 100mm lens (and same pixel resolution), image rotation for a 1 hour exposure is not a problem. If we only need 10 minute exposure, it should be easy to polar align and get no rotation problem.
We just need to track the central star to better than 1 pixel.

I had bolded the part that should be interesting for you. The ex-colleague is an Eclipse chaser -- he has flown to every solar eclipse since about 2007, so the focal lengths are in terms of camera lenses.

If the above is not enough, and you need to drill in further, you might be able to find the original paper from the WayBack site. I havent tied, but it is this one:

http://www.whim.org/nebula/math/drift.html

In your case, you can just look at the drift on the graph, then choose North- or South- only depending on the correction pulses.

Note from the magnitude of numbers that someone who tries to get within 1 arc second of polar error (just check the ZWO Facebook site) is either very stupid or very ignorant (probably both, if they use Facebook in the first place).

Now, after a Meridan flip, a German mount (the ZWO mount has pretty much the same behavior as the original Fraunhofer mount), I think that you will need to also flip N-only and S-only. Just watch the declination drift, if it is drifting away without correction pulses, just toggle to the other compass direction.

Chen

Ah... I think I have found a way to find out if the max RA duration is set too short.

I was just setting up a test run getting ready for clouds to clear one of these nights to attempt some measurements to determine centroid accuracy versus SNR.

The transparency is still terrible tonight with clouds passing through, but I can at least be able to find stars on a 55mm guide scope, reduced and flattened to 200m focal length for the experiment -- I usually use the 55mm objective at its native 250mm focall length. To counter the transparency, I also had to set the sensor gain way beyond my usual comfort level (that part of the sky is prbably at Bortle 6).

By setting the max RA duration lower than what the slope of my mount needs (I had set it to 40 ms :-), I see a bunch of correction pulses all with the same amplitude! Of couse (hindsight is always 20-20) -- the autoguider is sending the 40 ms pulses and not be able to keep up with the slope -- so all the pulses are at max duration.

Notice this guide graph, where halfway through, I had changed the max RA duration for a short time from 80 ms to 40 ms. Notice a flat top comb of 40 ms correction pulses. The rest of the guide graph are at 80 ms max pulse, and you can see the pulse height (duration) vary.

So, this is a simple way to determine how low you can go. But you may need to run it for a few hours for it to find where the worse case slope is, so measuring the slope might still waste less time. But at least it is a way to determine max RA duration if you don't even have a record of the periodic error curve (or no record of when the max slope happens). And it is a good sanity check that you have not made the max duration too small.

Notice no flat topping when the max duration is set to 80 ms for this mount. (Yeah, ASIAIR defaulted it to 2000 ms. Geniuses at work.)

Chen

Hah. I also got the onset of the flat topping of the guide pulses when I kept the max pulse at 80 ms, but reducing the guide rate to 0.25 x sidereal. Completely predictable from our "sawtooth" graph.

But, 0.25x sidereal guide rate worked fine when max RA and declination pulses are increased to 160 ms for my mount. 160ms RA + 160ms Dec is still shorter than my exposure time of 0.5 sec, so unless I discover something unforseen, I'll probably will be using 0.25x sidereal guide rate from now on.

I am seeing this (RST-135) at 0.25x sidereal guide rate, even with clouds:

Bin1 on ASI178MM 0.5 second exposure, 55mm Borg objective with Borg 7880 reducer, to get f/3.6 200mm focal length guide scope.

Oh yeah, I can also confrm that South-only declination correction needs to be changed to North-only after a meridian flip. And vice versa.

Chen

OK, skies are darker now (we don't leave astronomical twilight until after 10 pm local time nowadays). And guiding has also improved with the improved SNR. Settings unchanged from the above post -- same Bin1, same 0.5 second exposure and (sigh) still needs lots of gain because of poor transparency.

This might also be a calmer stretch of the periodic error curve too, but the 0.25x sidereal guide rate is showing promise.

If your periodic error slope is large, the 0.25x guide rate may not be fast enough (i.e., the leading edge of the sawtooth has to be so long as to stretch over the guide exposure time, especially when combined with the declination pulses), so you have to test this yourself for your own mount. Please don't blindly use my data point.

In the past, I would not even report the actual max durations, etc that I use in fear that someone might just copy it for use with their mount. But since we are discussing the mathematics of things, I figure it doesn't hurt as long as informed people don't just blindly copy my 160 ms @ 0.25x sidereal tracking. The monkey-see-monkey-do types have left threads like this one a long time ago :-).

Sort of a conclusion: the sawtooth model appears quite valid since it is preditive of results. Remember that up until now, I hadn't used 0.25x sidereal, but by staring at the sawtooth graph, it was apparent to me that gentler guide rates should work quite well, as long as the slope of the periodic error is not too large. But I didn't have clear nights to try it until tonight.

Oh, all tonight, I was getting 12 guide stays consistently with the large FOV of the 200mm focal length and ASI178MM.

Chen

Good for you!! I am glad it worked! But I still have a difficult time understanding how so small values work better. The guider is trying to compensate for the bad tracking and secondary harmonics of the harmonic drives that sends it in every directions. How is reducing the aggressivity and the length of the pulse helping any of that?
If I go any lower than 400ms on mine (Phd2), I need to increase agressiveness to the 80% so it can keep up with the erratic behavior (and recover from dithers). I'm using 1 sec interval.

KC_Astro_Mutt I wish I understood how all of this works as well. I'm afraid I'll be of little help in that regard.

Go back and look for a post of mine that shows a sawtooth waveform. Post 43 on this thread:

https://bbs.astronomy-imaging-camera.com/d/15989-getting-the-best-performance-from-my-am5/84

Once you understand that, all will be clear. That sawtooth is the basis (as I discovered after looking into the actual feedback mechanism) of pulse autoguiding. Pulse guiding does not instantaneously move the mount. The mount slews at two different rates throughout autoguiding, and the movement never stops -- the guide star is always moving during an exposure, and the smaller the sawtooth, the smaller will the guide star movement be. (And since the main OTA is sitting on the same mount, the main OTA will also be moving along the same sawtooth.)

There are two slew rates during autoduing. The rate at the leading edge of the sawtooth is caused by the guide pulse (and if you are pedantic, minus the slope of the periodic error). The rate at the trailing edge is (opposite direction) the slope of the mount's periodic error.

You track a star when the amplitude leading edge of the sawtooth is precisely the same as amplitude of the trailing edge of the sawtooth.

In your case, the slope of your periodic error (trailing edge) is small enough that with a pulse that is no more than 100ms, it is sufficient to overcome the trailing edge of the mount.

Remember that the leading edge is quite violent -- at 0.5x sidereal rate, the slope of the leading edge is 7.5 arcsecond/second (minus the slope of the mount), while the trailing edge is only around 0.1 to 0.4 arcsec per second for most mounts. If your mount's PE slope comes in at 0.5 arsec/second, it is best to get rid of it.

This is why you can often (won't work with the crummier ZWO mounts with terrible slopes) use an even milder than 0.5x sidereal rate (with my RST135, I got away with 0.25x sidereal and 160ms max pulse durations -- but again do not blindly copy that; that number won't work for you. Measure your own mount's slope and use that to determine the max pulse duration given a guide rate. Even if you go out and buy an RST-135, you still cannot use my numbers since the strain wave gears perform quite differently even from the same manufacturing batch -- check out that NASA conference paper that I had posted before to see the details of strain wave gears (not specific to guiding).

Yes, it is too bad you need to apply some technical skills. This is a technical hobby. Until the manufacturers themselves start to understand the mounts that they are selling and give you instructions on how to guide their mounts, the unwashed will just have to live with larger guide errors than their mount is capable of.

But I would venture to guess that at least half of the ZWO mounts (before they changed over to 288 second period) can guide below 0.4" total RMS through a whole night. For the mounts that have large slopes, just chalk it up to the ZWO lottery, where their QC did not measure and reject the ones with poor slopes (the geniuses were probably rejecting perfectly auto-guidable mounts that have large PE amplitude, instead of rejecting mounts that have large PE slopes. The 288 second period will make the slope worse, of course.

Chen

KC_Astro_Mutt you adjusted aggression before adjusting duration

No, I leave my aggressiveness low always. Don't even be tempted to raise it even though it migh help momentarily. I just prefer slow, smooth, damped feedback loops.

If your RA is swinging both positive and negative within a 10 second type region, your aggressiveness is set too high. Now, if you write your own code, I will have the solution in my white paper (where the feedback is based on the centroid of a moving star -- unlike today's paradigm, where it is assumed that the guide star is a snapshot of the current location of the star; if you look really carefully at a guide star exposure, it is a short line that is perhaps 0.1 to 0.5 arcseconds long, reflecting the sawtooth waveform).

I would occasionally see a large spike in DEC that would send the guide graph to .75" or thereabouts.

Didn't I tell you earlier to pull the declination aggressiveness parameter down to below 40%?

I will stop now giving advices on your mount, since you just ignore them.

Chen