Those who take long exposure photos of the stars understand the importance of an accurate polar alignment.    By using the "drift" method the astrophotographer can achieve very precise alignment by watching the movement of a star through the eyepiece as the scope tracks and then making adjustments to the declination or RA axes on their polar mount.   But astrophotographers also understand how long it takes to get it right while in the field.  Wait awhile, correct the drive, wait awhile, correct the drive...on and on until the star doesn't move in your most powerful eyepiece for at least 20 minutes or so.   

Go to an annual, week long star party and you can find who's drift aligning.  That person will be the one who hasn't taken his first photo until the third day of the star party.  Only then has the mount been perfectly aligned to suit the astrophotographer's tastes.

In a world of PEC and smartdrives, autoguiders and GOTO scopes, there ought to be a better way to polar align a telescope with some amount of precision.  

That's where the iterative method comes into play.  30 minutes is all it takes to get a reliable polar alignment with your scope, and the more practice the technique, the quicker it becomes.  The only prerequisite to using this method is to have either a GOTO scope or one equipped with digital setting circles (DSCs).

Some people call this method "ping-ponging" because it involves the use of two named stars in the sky in a process where you bounce the scope back and forth between them. The objective is to make each star appear in the center of the eyepiece after a "slew" of the scope according to their given celestial coordinates.  In other words, if the scope knows precisely where the stars are susposed to be, then you can use these stars to make adjustments to your mount to achieve proper polar alignment.  With each "iteration," an adjustment is made to the mount.  The more iterations, the more accurate your polar alignment becomes (less drift), which also increases greatly the amount of precision in the pointing accuracy of your GOTO or DSC-equipped scope.

The iterative method is not new to astrophotographers.  Meade and Celestron both give iterative alignment techniques in their scope manuals.  But the method I will describe is a refined method which takes fewer iterations and shorter time between "ping-pong" moves. No waiting around to detect star movement and the more you do it the faster it gets:

Step 1: Set-up your scope normally in Polar mode.  Make sure your location, time, and date settings are as accurate as possible.  Knowing that this information is precise removes some of the variables should the iteratively alignment fail.  In other words, if you still have a significant amount of drift after several iterations then you can focus solely on hardware/OTA alignment issues as the source of your problem.

Step 2: Do the normal set-up procedure for your scope using two-star alignment.  This will get your scope close enough to Polaris to start the procedure.  Alternatively, simply eye-ball Polaris and center your scope with an accurate finderscope, then sync your computer to another known star.

Step 3: Choose a known star at least 90 degrees from Polaris in declination.  I normally choose the stars  Regulus in Leo during the Spring,   Antares in Scorpius during the Summer, Fomalhaut in Piscis Austrinus during the Fall, and Rigel in Orion during the winter.  (We will choose Regulus for this explanation.)

Step 4: Enter Regulus (Star 100 for me) on the keypad and have the scope automatically slew to this point.  Center the star in your eyepiece using your handpad controls (choose the EP giving the widest field of view) and sync your handpad on that star.  

(Incidently, many people choose an illuminated reticle for this procedure.  I find that the field of view is not sufficient enough with this eyepiece to begin with.  I simply shoot for the center of my eyepieces using my best guess.  Precision while centering isn't tremendously important.)

Step 5: Enter Polaris (Star 19 for me) on the keypad and have the scope automatically slew to this point.   Using your wedge/mount adjustments ONLY move Polaris HALF-WAY to the center of your widest eyepiece. (Depending upon how far off Polaris is from the center you may have to use your finderscope initially.)

Step 6: Enter Regulus again on your keypad and slew the scope automatically.  Center the star once again in your eyepiece using the handpad. Sync the computer to the new star location.

Step 7: Enter Polaris on the keypad and have the scope automatically slew to it.  Again, use the wedge/mount adjustments ONLY and move Polaris HALF-WAY to the center of your eyepiece.

Step 8: Repeat STEPS 4 through 7 until you cannot detect Polaris is off-center.  At that point increase the power of your eyepiece and continue the procedure.   

I often find that once I've been able to work my way through an 8.8mm eyepiece (284x on my scope) that I've achieved all the accuracy I need.  

A few points to remember while doing the procedure:

1.) Autoguiders are able to compensate for a certain amount of drift.  While accurate polar alignment is important to keep your autoguiders from working too hard, there's really no need to go overboard with excessive tendendencies.  People seek perfect alignment to eliminate any field rotation around the guidestar in their photographs.  Unless you are using scopes with lots of focal length or are not using an autoguider then 5 to 10 iteratiions may be all you need.   Alternatively, working through your largest usable eyepiece should give you all the precision you need.

2.) As you increase the number of iterations, the amount of adjustments to the wedge/mount will become less and less.  Having precise controls for declination and right ascension on your wedge or mount is required once you work your way through your more powerful eyepieces.  At this point, only a little turn of a knob can go a LONG way.

3.) Sync on Regulus (or other star).  Wedge/mount adjustment on Polaris.  You will NEVER sync your computer on Polaris!

4.) For accurate alignments on permanent, pier mounted scopes you can always compensate for drift AFTER it is noticed in practice.  It just makes sense to use the iterative method until you are sure that it has taken you as far as it can.

Keeping these steps and rules in mind, you should be able to get your iterative techniques refined in such a way that accurate polar alignment can be achieved within 10 to 15 minutes of set-up.  If the scope still doesn't slew accurately to objects at this point, or if you still detect some drift over time, then you've either reached the theoretical ability of the scope OR information in your computer is inaccurate OR your scope is misaligned within itself; that is, uneven fork arms or a skewed OTA.  At that point you'll either need a "supercharge" of your scope by Doc Clay or you can do it yourself with help of the MAPUG archives. 

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