Survey of Polar Alignment Methods
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:
- Simple - if the procedure is too complex it will be prone to error
- Deterministic - based on quantifiable values, no estimates
- Precise - one or two iterations to arrive at the required tolerance
- Automated - the procedure should be automated as much as possible
- Fast - the entire procedure completed 30 minutes before astronomical twilight
- Repeatable - the procedure should work reliably every time
Drift Method
If you are not familiar with the drift method, see this link. The drift method is very popular and can be very accurate if you are willing to spend enough time at it. It's main strength is it's simplicity...it can be performed with no special equipment other than a reticle eyepiece. However, the method is not deterministic requiring one to estimate the drift and subsequent adjustment. This leads to multiple iterations and that takes up time. The procedure is completely manual and does not lend itself to automation (but read on; variations of this method can be automated).Iterative Method
The iterative method works by pointing at two different stars and adjusting the mount on each iteration. The first star is used to set the setting circles, or to synchronize the mount's pointing model. The second star, usually Polaris, is then pointed to. If the mount is out of alignment the second star will not be centered so the mount is adjusted to center the star and the procedure is repeated. The assumption with this model is that when pointing to the second star the error is primarily due to the polar alignment error. It is, however, incorrect to assume that the pointing error in right ascension and declination is equivalent to the alignment errors in altitude and azimuth. For this reason the method seems to converge faster if only 1/2 to 2/3rds of the error is corrected on each iteration. The method is simple, deterministic, relatively fast, and repeatable. It is fairly manual and often requires many iterations. Whenever I set up at a location where I cannot see Polaris (like my driveway), I use this method to get a rough alignment. The process can be started just after sunset using bright stars. By the time it gets dark enough to start using the camera, I can be aligned within a degree or less of the NCP.Dr. Clay's Kochab's Clock
Anyone who owns a Meade telescope is no doubt familiar with Dr. Clay Sherrod. Dr. Clay has documented a method whereby the mount can be polar aligned with decent accuracy by using the angle formed by Polaris and Kochab, the other bright star in the Little Dipper asterism.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.
CCD Polar Alignment
This is an interesting method which uses a CCD camera to mimic the procedure many observatories used to use to measure the polar alignment error. It is really quite simple. First, an exposure is started. A star is allowed to drift while the tracking motors are turned off creating a star trail. Then the tracking is turned back on and the rate is set to twice the sidereal rate which creates another star trail. When the mount is misaligned there will be two star trails, one laid down by the earth's rotation, the other by the mount's rotation. When the lines lie on top of each other the mount is in perfect alignment.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.
Declination Drift Measured with an Autoguider
I wrote about this method in 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.
Declination Drift Measured by Moving in RA
I also wrote about this method in 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.
Gemini PAC
I own a Losmandy G11 with the Gemini feature. As of the level 3 firmware the Gemini provides a function it calls Polar Axis Correct, or PAC. The process works by first building up a pointing model by aligning to several stars. Part of this pointing model is a model of the azimuth and altitude (a.k.a. elevation) errors. When performing the PAC the Gemini manual instructs you to point to a star at the intersection of the meridian and the equator. It then offsets that star based on the polar alignment error. Adjusting the mount in altitude and azimuth to recenter the star is all that is needed to be aligned.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.
PoleAlignMax
One of the coolest polar alignment methods to come along is the freeware PoleAlignMax by Larry Weber and Steve Brady. The method has some hefty prerequisites in that it works with a CCD camera, either CCDSoft or MaxIm DL, and either TheSky or PinPoint for plate solving (some versions of MaxIm provide PinPoint). The method works by taking images at three points in the sky and plate solving to get the actual coordinates. Then through powerful mathematical magic it calculates the azimuth and altitude error. The program then uses a reference star to calculate a positional offset and so that moving the star to the offset position corrects the axis. This procedure is performed on each axis individually.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.
