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.
In my experience the method works very well. However, the method is complex due to its heavy prerequisites and a somewhat cumbersome procedure. Since my camera does not have "live view", I personally find it tedious and time consuming to move a star to a location in the image.
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.
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 undercompensate 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.
I want to thank Drew Sullivan for helping me rethink the problem in this direction. Drew helped me realize that the alignment process is really a two phase process: measurement and correction. If we think about each of those phases independently and find optimal solutions for each, we can combine them into an optimal hybrid solution.
Without realizing it, Drew help me understand that my dissatisfaction with PoleAlignMax was primarily on the correction phase. As it turns out, PoleAlignMax can measure the alignment error in about one minute with my setup taking 3 images 15 degrees apart and solving the plates with PinPoint. The PoleAlignMax correction phase is then omitted in lieu of my Star Offset Positioning correction technique which takes on the order of about four minutes. Since my camera is in place on my imaging OTA I use my 66mm guidescope for the visual correction and it does a fine job with it. Another one minute with PoleAlignMax to validate the correction and the entire process is completed in about 6 minutes! In a very few occasions a second iteration is needed, the process completes in about 11 minutes, which is still a vast improvement over any thing else I have tried in the past.
This is no exaggeration! I have thoroughly tested this procedure and I can get sub-arc minute alignments in 6 minutes. I have validated the alignment by using various other methods including the drift method and Gemini's modelling. Simple, Deterministic, Highly Accurate, Automated, with Speed and Reliability. My quest is over! Stick a fork in me, I am done.
One note on accuracy. The current version of PoleAlignMax (2.0.55) has a slight, but important defect. It calculates the error from the J2000.0 celestial pole not the epoch of date. This results in about 3.4 arc minutes of error in 2010. Drew has created a spreadsheet which can be located on the Yahoo FMaxUG group Files section which provides the necessary corrections to the alignment error numbers. As of the writing of this, Steve Brady is aware of the defect and is working on a solution. Great service, considering the program is freeware!