Polar Alignment Error

Performing a polar alignment on your mount is one of the most important tasks you need to perform to provide yourself the best conditions for deep sky imaging.  As you do this necessary task, the main question is just how accurate the polar alignment needs to be?  I’ll try to help answer this here through the use of the calculations below, which you should rarely need to do but you should understand how they work and how to use them.  The bottom line is that using auto guiding greatly reduces the needed polar alignment accuracy.

For unguided imaging, if the axis of the mount isn’t aligned with the celestial pole, your field of view (FOV) will drift in the declination axis.  This drift is at its largest at the celestial equator and at its smallest at or near the celestial pole.  You can calculate the amount of drift using the following equation:

Declination Drift = 

Where;  E = polar alignment error in arc minutes

             dec = Declination in degrees of the target being imaged

So, if your imaging a target at the celestial equator and you will not use auto guiding, the declination drift will be 0.26 arc seconds per minute for every 1 arc minute of polar alignment error.  If you choose to image unguided, you will need to have a very accurate polar alignment.

Most imagers choose to use auto guiding.  For this case, the problem you want to avoid is Field Rotation that happens around the guide star you using to auto guide with.  Field rotation will be the greatest at the farthest point from your guide star.  So we have to take this issue into account as well as what the polar alignment error is.  And just to note - Field rotation is largest close to the celestial pole and at its least near the celestial equator.  The equation for field rotation due to polar alignment error using auto guiding is:

Field Rotation =  

Where;  E = polar alignment error in arc mins

    f = telescope focal length

    g = angular distance from the guide star in degrees

  dec = Declination in degrees of the target being imaged

If you plug in numbers for each equation your particular setup, you’ll find that guided imaging is much more forgiving of polar alignment error than with unguided imaging.  Errors from Field Rotation in the guided scenario will be less than the Declination Drift in the unguided scenario.

Reference:  The Deep Sky Imaging Primer 3rd Edition, Charles Bracken