I have used several methods of polar alignment over the years. Although all of these methods work with varying results, I am not really happy with most of them for one reason or another. For me, the ideal polar alignment procedure should be:
I have only played around with this method a few times. It can get you reasonably close, depending on your requirements, but is really not accurate enough for serious astrophotography. It's main weakness is its lack of quantifiable data; the angle to Kochab has to be estimated. However, if you are looking for a quick and dirty method to get reasonably close, this is it.
The method is essentially the drift method with a much speedier method of learning the magnitude and direction of misalignment. The method is not deterministic since it is relatively difficult to ascertain the exact alignment error and the adjustments to the mount still need to be estimated. Since, like the drift method, many iterations are required it suffers from low precision and the time requirements. Still, I know of no better way to test the accuracy of your alignment once your chosen method has completed.Measuring Polar Axis Alignment Error. Essentially it makes use of autoguiding software to measure the declination drift during drift alignment. I have been experimenting with this method using the freeware GuideDog and an inexpensive Philips webcam. I have found that I can get accurate measurements of alignment errors in less than two minutes of drift, especially when the error is large. The cool thing about using a webcam is that you can start the alignment procedure very early in the evening. I have been able to start this procedure just 15 minutes after sunset. There were no stars visible to the naked eye, but the scope could find them and the webcam had no problem showing them either.
By itself, the method is only partially deterministic since once the measurement has been quantified, the adjustment to the mount still needs to be estimated. However, combined with my Star Offset Positioning technique the method converges rapidly (usually two iterations gets within 3 arc minutes). A disappointing reality is that when the alignment error is small, atmospheric seeing can make it difficult to measure the error accurately. I have tried averaging the last few measurements and even tried linear regression of the entire dataset, but unless the data has been collected for a longer time period, the measurement is not very reliable when the error is small which makes the method not much more accurate than the classic drift alignment method.Measuring Polar Axis Alignment Error. The article is recommended reading as it provides many illustrations which show the geometry of a misaligned mount. After closely studying these diagrams it occurred to me that waiting on the earth's rotation was not necessary to reveal the magnitude and direction of polar alignment error. The method requires coordinate resolution to about an arc second (just about all "Go To" mounts nowadays). By synchronizing on one reference star near the equator and moving the mount in right ascension to a second reference star we can measure the declination deviation (essentially the declination drift in the classic drift method). If the mount is not in perfect alignment the second star will not be centered, but will appear either north or south of where the mount moved. When we recenter the second reference star the mount's declination reading will change. The declination movement required to recenter the star is the declination deviation.
By combining this method with my Star Offset Positioning technique, I have been able to achieve 1 arc minute alignments in twenty minutes. Since the method is purely visual, I have even been able to start the procedure before sunset! It is true, if your mount has decent pointing capability and you can get aligned on a fairly bright star (I used Arcturus), you can locate stars down to about mag 3 or 4, even before sunset. Try it sometime.
The only downside to this technique, is that it does take some skill to center the stars precisely. Atmospheric seeing will conspire against you in this regard, but with enough patience the method will reward you with very accurate alignments. Much of the procedure can be automated. It would not be too difficult to script the entire operation, only pausing to instruct the user to center a reference star, etc.
I have used the PAC method for years and use it most often from my tree-challenged horizon at my home site. I've had some problems with the method in the past not converging or taking several iterations to converge, but I have recently discovered the reason for this difficulty. I use a freeware planetarium program called Cartes Du Ciel which uses an ASCOM driver to connect to the Gemini. Unbeknownst to me, Cartes sends coordinates already precessed to the epoch of date. Guess what? Unless told otherwise, Gemini assumes epoch J2000 and precesses to the epoch of date as well. There is a setting in the Gemini ASCOM driver to bypass precession in the Gemini. After clearing that setting the PACs are now working wonderfully. I almost always get within 2 arc minutes of the pole within two iterations, sometimes with the first iteration.
A small deficiency that I have noticed is that if you have a significant amount of backlash in your Dec gear, the PAC adjustment may under compensate the altitude adjustment. When Gemini performs the star offset positioning it does not compensate for backlash and the star may not get moved far enough. This is easily dealt with. Simply take note of the elevation number (E) after your last Additional Align prior to the PAC. If E is positive, center the PAC star by finishing in a northern direction. Conversely if E is negative, finish centering in a southern direction. This will take out the backlash and Gemini will move the PAC star the correct angular distance for a very accurate alignment.
The method works extremely well. It's biggest drawback is that it requires you to build up a pointing model by centering several stars. This takes time. Then, to validate the alignment after making the adjustments to the mount, the model has to be rebuilt from scratch, taking even more time.
In my experience the method works very well. An error was discovered in the software. It calculates the alignment error from the J2000.0 celestial pole not the epoch of date. The last I heard (this was some time ago), the authors were aware of the defect and working on a fix. However, it seems the software is no longer being supported. The link I had for this is now broken. If anyone knows of the official site, please let me know.
I seemed to have stumbled upon the mathematics that are used in PoleAlignMax which I briefly discuss in my Measuring Polar Axis Alignment Error article. I have been experimenting with this with some VBScripts and currently this is my preferred way to measure the alignment errors. I then use my Star Offset Positioning to make corrections to the mount. I can usually get to within 1 arc minute in two iterations and the whole process takes about 15 minutes or less.