jfletcher I'll get to my point... I have both an RST-135 and RST-135E mount. I can get them both to guide around 0.8 rms but I'm sure both of these mounts should be able to do much better, especially the RST-135E.
Me too; I have recently added an RST-135E to my existing two RST-135. My first RST-135 has serial number 13 from the first production run.
If you are using ASIAIR multi-star guiding, the limitation of the RainbowAstro mount is actually caused by the Centroid estrimation error from the ASIAIR itself.
The gist of the problem is this... strain wave gear mounts (ZWO mounts, RainbowAstro, etc) have high harmonic terms. So, even when the period is long (430.82 seconds), there are strong harmonics at 2nd, 3rd, and even 9th and higher harmonics.
The slope of the periodic curve determines how fast a guide star is moving (measured in arcseconds of movement per second to time), and that determines how short a guide exposure should be to avoid exceeding long star trailing.
Higher harmonics are especially troublesome since they contribute large amounts to the slope. From the maths, the Nth harmonic has N times the worst case slope than the fundamental. Practically, you can think of the N-th harmonic to represent a signal whose period that is N times shorter than the fundamental. So, for a mount whose fundamental period is 430.82 seconds, a 5th harmonic's slope would look like a signal whose period is only 430.82/5 = 86.2 seconds!! The problem is worse with cheaper systems that have 287 second fundamentals (my believe is that the shorter periods are the result of using larger ratio pulley/belts to make poor strain wave gear PE amplitude "look" better on paper -- while smaller amplitude PE helps keep a targer in the FOV of a visual telescope, the shorter periods make autoguiding much worse -- i.e., be careful when you read specs. Smaller PE amplitude is better -- but not if there are large harmonics. Don't fall for the trick.
Fortunately, the amplitude of the higher harmonics tend to fall as N gets large. It is just that for strain wave gears, they don't fall very fast, unlike worm gears.
Because of the large slope that results from the higher harmonics, we need to use short guide exposures. Of the order of 0.5 seconds.
So, we enter the next road block -- short exposures are terrible when "seeing" is poor (or even average). To autoguide, we need to measure the centroid of a star to better than the accuracy of the centroid measurement. If you want to guide better than 0.5" RMS, and your guide scope/camera has a plate scale of 3" per pixel, you need to be able to measure the centroid of a star to much better than 0.1 of a pixel. If you watch a star at 2FPS (0.5 second per exposure), unless you are luck to like on Mauna Kea, you will see the star jump around by a couple of pixels-- there is no way to get 0.1 pixel type measurement.
This is where multi-star centroid comes in. Just like doubling exposure time reduces the variance of the centroid error by 2 (reducing RMS error by 1.414 for each doubling), using multiple stars will also reduce the error variance by the same amount (i.e., 2 stars give a varaince reduction of 1.414. 4 stars give 2x, 8 stars give 2.82, 16 stars give a factor of 4, etc).
I.e., using 8 stars at 0.5 second exposure should be the same as using an 8 second guide exposure.
But, this is not true in ASIAIR. ASIAIR uses SNR weighted centroid averaging!
If there is one star whose SNR is much larger than the SNR of the other stars, the result of mult-star guiding is equivalent to only using single star guidng for that one star!
Somewhere earlier I had posted a SNR weighted distributed stars using the stellar magnitude of a region in the Hipparcos star caralog (HYG catalog). And the result was that even if you include 12 stars, the ASIAIR SNR weighting is only equivalent to only using 2.5 stars or somewhere around there. I.e., with 0.5 second exposure, it is only equivalent to 1.25 second exposure. And we know that a single star at 1.25 second exposure performs terribly.
I had also posted that by increasing the gain of the guide camera, you can make ASIAIR ignore the brightest stars,and result in a much better SNR distrribution.
Recently, I came up with an effective method ("algorithm") for ASIAIR users (who have little control of autoguiding since ZWO thinks flexibiilty will confuse their customers; they think their customers are just as uneducated in astronomy as they are). But now I am waiting for some clear nights (may have some in a weeks time) to come up with real numbers.
Basically, start with very low guide camera gains, and start increasing it util you are seeing between 11 and 12 stars being selected (in my case, with a 55mm aperture and 260 mm focal length and a ASI178MM camera, that gain is typically in the region of 6 dB to 10 dB ("60" to "100" in ZWO's gain units). Then add a gain of between 20 dB to 30 dB (I had told @Kevin earlier to not be shy about applying gain :-). In my case, the gain to just get 12 stars is 70, and the gain to actually use is 270 to 370.
It is not sufficient to just get 12 stars. You need to make the ASIAIR ignore the bright stars so that the remaining stars have a more even SNR distribution.
I need some clear nights to measure the centroid error vs gain. If I have some results, I will post it here in the future.
What I have been seeing (without detail measurements) is that with a 12 star and a gain of 100 or so, the centroid estimation error is of the order of 0.35" RMS. If RA and declination are independent, the total RMS centroid measurement error is 0.5" RMS.
This means that even if your mount has 0.1" RMS error, the wrong centroid will result in sqrt( 0.12 + 0.52) = 0.1" total RMS.
With a gain above 300, I have been able to get the centroid measurement error below 0.25" RMS or so. And with that, I was able to get the 0.4" total RMS type guiding with an RST-135 and seemingly 0.35" total RMS with the recently bought RST-135E.
I.e., if you cannot get better than 0.5" total RMS from an RST-135, take a look at the internal centroid estimation in an ASIAIR or raw PHD2. And it seems that by increasing the camera gain (by a lot) to skew the SNR distribution, I think we can overcome the poor choice of SNR weighting in ASIAIR.
The problem with ZWO is that they copy, without understanding the fundamentals (it is everwhere, ASIAIR, filter wheels). It is very obvious that they superficailly copied the RST-135 in appearance, but have no idea about mount modeling and such that is in the RST-135 firmware. That is why you can accurately GOTO a star on an RST-135 (after calibrating the mount's home offset) but you still cannot do it in the ZWO mount -- they have no idea that there has to be a mathematical model beyond just mvonf a stepper motor by N streps, hoping that your OTA now points to the correct direction to within an arcminute.
The short story is, (1) strain wave mounts need short exposures. (2) to be able to do short exposures, you need to average the centroid from multiple stars, (3) the ASIAIR does not properly average stars (due to stellar magnitude distrubution, which ZWO had not studied).
Chen
