p099gll will there be any benefits for having encoders on the RA and DEC axis ?
Servo motors (and for cheap mounts, stepper motors) and the gears are not precise enough for the tracking accuracy that one needs in astronomy. The accuracy that is needed depends on your plate scale, anywhere in the range of between 0.5 arc second to perhaps 10 arc seconds RMS.
Basically, if your optics and seeing is capable of rendering a star at 2 arc pixel size, then a 5 arc pixel error will bloat the star to 7 arc pixels. If the error is random (and independent) for both axes, the star will remain round but larger, and have an unfocused appearance. If only one axis predominantly has the error, then the star will end up being a larger oval blob instead of a larger round blob. If you remember math from college, by approximating the error as Gaussian, the two axes will create a Joint Gaussian point spread function on the sensor, and thus appear radially symmetric on the photographic plate.
To mitigate this problem, you can use a shaft encoder that is connected directly to the actual RA (or declination) shaft (after the gears, etc). Even a 2 arc-second encoder (there are over one million arc seconds in a 360 degree rotation) is not cheap. The 0.5 arc second shaft encoders cost more than some of the cheaper mounts in the market. For that reason, you will not find cheap mounts that come with shaft encoders.
The save a bit on the cost, many mounts use relative shaft encoders instead of absolute shaft encoders. The encoder gives you an accurate measurement of how much the shaft has moved, rather than the precise absolute angle.
To further save on costs, many mounts that come with encoders only have one encoder for the RA axis (counting on the declination axis not moving at all, when the polar alignment is precise).
So, what the mount electronics does is to constantly monitor the shaft angle (either absolute or relative) and feed back the position error relative to the desired shaft position.
We now go on to a second method of getting precise angle of the shaft. And since we are in the ASIAIR thread, I will use the ASIAIR as the example.
Remember that I had mentioned above that you read the accurate value of the shaft back and use that to feed back an error term for the mount to correct for server motor, stepper motor and gear errors?
Well, we have a very precise way to measure shaft errors, and that is by using the position of a star in the sky. The only disadvantage is that atmospheric turbulence ("seeing") will disturb the exact location of the star (to perhaps a couple of arc seconds RMS on a good night, unless you are up on Mauna Kea or Cerro Paranal).
So, we simply point a second telescope (the guide scope) up in the sky and use a star to measure relative movements of the shaft!
The error, just like with a regular encoder, is fed back to the motors by PHD2 in ASIAIR as short RA and Declination slews (as short pulses, and this the name "pulse guiding").
To move the mount by a desired angle, PHD2 in ASIAIR would start a slew at a slow rate (this is the "guide rate," usually 0.5x sidereal rate -- sidereal rate is just a tad larger than 15 arc seconds in the sky per one second of time). If PHD2 finds that the mount has drifted by 1 arc second, it would start a slew at the 0.5x sidereal guide rate, and 1/15 of a second (67 millisecond second) later, turn off the slew again; the mount (and ASIAIR) must of course not have any latency that will affect the accuracy of this 67 millisecond example.
So why do people manufacture and sell encoders? Well, most devices (robotic arms, etc) do not have stars that they can use to guide their shafts. And for astronomy buffs who do not use computers, and also for hobbyists who are too lazy to set up an auto-guiding system. Also if you want precision even when atmospheric turbulence ("seeing") is poor -- although If your seeing is poor, the stars will bloat anyway, even if you have the world's best encoder, just not by as much as if you use a star's position.)
As an aside, this is where multi-star guiding comes in. The atmospheric turbulence is different and independent for each star (since the air masses that perturb the star locations are kilometers or hundreds and thousands of kilometers apart). The indication of how small the air masses are, notice that stars twinkle while planets do not.
As a result from college probability theory, the variance of the star location will he halved if you average the centroid of two stars. I.e., the RMS error drops by by a factor of sqrt(2); with the total RMS error being 0.707 of the RMS error from a single star. Each time you double the star count, the variance again drops by a factor of two. By the time you use 16 stars, the error of star centroids is reduced to 0.25 of the original.
By the time you use 256 stars, you will likely beat the best shaft encoder that NASA can buy, even when the seeing is relatively poor.
So, the short answer is: you can correct for shaft errors by using a shaft encoder (money to pay for shaft encoder) or you can correct for shaft errors by using auto-guiding (money for guide scope and camera, and the time to calibrate, and a computer like the Raspberry Pi in the ASIAIR).
The choice of whether to depend on shaft encoders or on auto-guiding is yours.
Again, with multiple stars, auto guiding should wipe the floor with these shaft encoders.
A concrete example I will use here is the RainbowAstro RST-135 mount (just because it is what I use and I have solid numbers to quote) that has a very large peak-to-peak periodic error of 70 arc-seconds (nope, not a typo -- the strain wave gears ("Harmonic Drive [trademark]") have that much error, but shines in the amount fo torque that they produce; thus not requiring even a counterweight).
With multi-star guiding using PHD2 (not available, at least yet, on ASIAIR), these little mounts are capable of 0.5 arc second RMS performance even if you dump an 8" SCT on top of them -- no mean feat since the mount itself only weighs 7 lbs, and remember, no counterweight either).
RainbowAstro also sells a version (RST-135E) that comes with an encoder on the RA shaft. The advertised performance is 2.5 arc seconds error.
So, in this case, you get to decide if you want to go without autoguiding but pay for the encoder, to get 2.5 arc seconds accuracy, or use autoguiding without an encoder, and get 0.5 arc seconds type accuracy.
The answer is obvious if you are already using an ASIAIR to control other aspects of astrophotography. But there are people who travel with the RST-135 (at 7 lbs, it is perfect for air travel) and only do visual astronomy and do not want to carry a computer with them, and don't want to bother with autoguiding. The difference in price is about $1600 between the one that has no encoder and the one that has a single encoder on the RA shaft; but hey, you don't need to buy a guide scope and guide camera [sarcasm].
By the way, if the encoder is good to 2 arc seconds, and autoguiding with no encoder is good to 0.5 arc seconds, adding an encoder is not going to make autoguiding more precise as long as the guide rate can handle any large native periodic errors of a mount that has no encoder.
Synopsis: You already have a "shaft encoder" in the form of stars in the sky. With autoguiding, especially with multi-star auto-guiding, auto-guiding will be more precise than shaft encoders; as long as you include the stuff needed for auto-guiding (guide scope, guide camera, computer to run autoguiding routine, and a mount that can use either pulse guiding or ST-4 guiding).
Chen