maged So I have a humble request to have the main calculation equations to help with calculating the following guide settings:
Calibration steps
The way autoguiding works is that the program (be it PHD2 or Laserta MGEN, or anything else) measures the position of a star (or a collection of multiple stars and averaging them, in the case of multi star guiding) on the "photographic plate" (i.e., a frame from the guide camera).
Since there is atmospheric turbulence, the "position" of a star can only be estimated roughly, and the usual method is to (for lack of any better way) use the centroid of the star image as it's position.
The position of this centroid is in the coordinate system of the camera sensor's frame, usually denoted in PHD2 as x and y (and any small movement of the centroid as dx and dy) where x is usually the long axis of a sensor and y is the short axis of a sensor.
The program (e.g., PHD2) then uses dx and dy to move the telescope so that dx and dy can be reduced back to zero.
The only way, however, for the program to do that is to issue movement commands to the RA axis motor or the declination axis motor. For many mounts, these are actually sent as commands to the mount to slew the telescope, but at a very slow slew rate (we will come to that later).
Unless your camera angle is precisely rotated to match the x and y axis of the sensor, x and y will be at some angle relative to RA and declination.
(I actually make it a point to rotate my guide camera angle so that it matches the RA and declination angles in the sky -- i.e., do a plate sove, and rotate the camre angle so that it is within a degree of two of the four cardinal directions. You need not do this (as explained below) but I want to make sure there is zero contamination between the RA movement and the declination movement. I am OCD, what can I say? Most good engineers are :-). )
Now, to move the RA (or declination), the mount would perform the slew for N milliseconds. The slew rate is set to some guide rate. You will often see guide rates given in terms of sidereal rates (i.e., 1x sidereal rate is the the motion the stars are moving in the skies). Since sidereal rate is about 360º per 23 hours 56 minutes (this is why a star rises 4 minutes earlier each passing day and we see different stars in the nigh sky depending on the seasons) a guide rate of 0.5x sidereal will correspond to a slew of abour 15 arcseconds per second of time multiplied by 0.5, i.e., 7.5"/second. A guide rate of 0.25x sidereal will correspond to about 3.8"/second, etc.
So, as far as guiding goes, you really don't command the mount to move by N arcseconds, but rather, you ask the mount to slew for M seconds of time (at the guide rate) and then stop the slew. And this is why guiding is usually expresssed in milliseconds of time, instead of arcsecond of star position.
This is also why you hear people refer to these corrections as "pulses."" They are literally a pulse to the RA motor that lasts N milliseconds.
Wgen you measure dx and dy on the sensor, you willl need to convert that to how many arcseconds you want to move the RA motor or declination motor. And hence, you need to calibrate. In the process of calibration, you move the RA axis by N milliseconds at a time and then measure how much the star has moves in the x and y axis. This is the so called East-West movement. Similarly, to calibrate the declination direction, you move the declination axis by N milliseconds at a time and measure x and y for that direction (this is often stated as "North-South movement).
So, whay you have is a relationship ∆x = A.∆RA+ B.∆Dec, ∆Declination = C.∆x + D.∆y. Engineers among you will notice that this is just the matrix equation
[∆x] = [ A B ] [∆RA]
[∆y] [ C D ] [∆Dec]
So, by inverting the [ABCD] matrix, you end up with the [abcd] matrix that give the relationship
∆RA = a.∆x + b.∆y
∆Dec = c.∆x + c.∆y
I.e., you now know precisely how long (in milliseconds) to move the RA and the decination motors when you see the star moves y ∆x and ∆y of the sensor!
To get A, B, C and D, PHD2 wants you to move the mount for some 25 pixels. It wants about 8 to 20 (don't need to be precise) RA and dec movements to make this 25 pixels total movements.
So this is where the calibration steps come in. It is the number of milliseconds to slew the RA motor so that after 8 to 20 of these steps, you have moved by 25 pixels.
The matrix ABCD also determines the camera angle. So, PHD2 will compensate for the guide camera angle when doing the calibration.
So... calibration has noting to do with guide dynamics (i.e., no one cares about it while autoguiding). It is simply to measure the plate scale and camera angle of your guide system.
So, now you know why RA, declination and calibration steps are stated in miliiseconds, instead of arcseconds, and how "calibartin" works.
Just adjust the "calibration steps" so that it finishes calibrating in bewteen about 8 and 20 steps. If you have a premium mount (hint: ZWO mount is not a premium mount), the mount's mechanism is precise enough that 8 steps is often more than enough. For poorer mounts with sloppy gears and belts, you may wanto to do 20 steps so that the noise gets averaged out.
Let me repeat that "Calibration Steps" has nothing to do with the autoguiding dynamics. Tweaking it will not get you better or poorer guiding. The Calibration Steps id completely ignored during autoguiding.
Chen
