One of the key things that must be done prior to a session of astrophotography is a good polar alignment. I have spent a good bit of time trying to determine just how good is good. I derived the basic formulae and have presented them here. Most experts on the subject of polar alignment suggest using a declination drift method of polar aligning the mount. This is certainly the preferred method, but even that method can be made more precise if a CCD camera is utilized in the process. This can be accomplished in a number of ways, but the method I have found the easiest and most quantifiable is to use the Track and Acculmulate routine built into CCDOPS v4.x from SBIG. I will describe this method in detail and then give suggestions on how to adapt this routine to other software packages utilized by other cameras. Anyone with more than a basic familiarity with their CCD camera and software should be able to extract enough information from this article to adapt to their specific situation. Even an ST-4 can be used for this process as a stand alone unit.
Let me first say that this isn't a quick process if done with a high degree of accuracy. To fully align my mount took almost three hours, but I had to figure out what I was doing along the way. This process started out as an idea then sort of took shape. Having tried it I'm very pleased with the result. It's very precise. This is particularly effective in an observatory setting where the alignment will be more or less permanent. For portable setups, I'd recommend a visual version of this. I'll include several references to the visual method at the end of the article.
The first step is to grossly polar align your scope as closely as possible. I use a polar alignment scope for the Astro-Physics 1200 mount that gets me very close, but not perfectly aligned. The closer you are in the gross alignment, the quicker you will be able to achieve perfect alignment.
Move to the next step by setting up the CCD camera and focusing it. I find that focusing a CCD camera works best on a star higher in the sky that isn't as affected by atmospheric turbulence, so you probably want to focus on a different star than you use for alignment. Once focused, choose a medium to lower brightness star close to the eastern horizon. Choose one that will not saturate within two or three minutes on your camera. This star needs to be close to the eastern horizon, but up around 10 to 20 degrees, so the atmospheric turbulence won't affect the accuracy of the process to much. It should also be within 5 degrees of the equator, hopefully right on it. With the sensitivity of a CCD camera, there's almost no reason not to have one very close. Check your digital setting circles in the RA and DEC mode to verify this position, take an image and choose a fairly nice star in the image field.
You must now correlate the movements of the scope with movement of the star in the CCD image. This is akin to the calibration routine under the tracking menu of CCDOPS. Enter the Find and Focus mode, and select the manual pause feature so you can move the scope in between images. If you're trying this with another camera and software, it's still easy. Integrate an image and simply note the position on a star in the image and locate it's exact postion with crosshairs (any really good software should have a crosshair information routine). In the find and focus mode you may use the Max Value number and watch it's coordinates, but don't have to. I just visually watch a particluar star.
Set your guiding rate to 1x sidereal rate if you can. Don't set the rate greater than that. Now take the hand controller and press the "North" button for 5 to 20 seconds. This wil actually depend on the focal length of your scope. My focal length is 64 inches (1642 mm), so I used 5 seconds. Integrate the a new image and simply note the movement of the star. Write down it's movement direction only. For me it was X+, or to the right in the image. That's important later when you decide which direction to move the mount in compensation for DEC drift. Now reverse direction for the same amount of time and verify that the movements reverse just to check yourself.
You may test the East and West movement, but since you're really only interested in DEC drift, you only need to really know the North and South movements. To recap, for purposes of this example, my X+ was a northward movement. A negative X movement (left in the image) was a southward movement. So the X axis of the image (right and left) is our declination axis. This can be done with other softwares and cameras in the find and focus modes in a simlar manner.
Once the positions in the image are established, you are now ready to test your mount. Start this routine with all fittings on the mount securely tightened. Go into the Track and Accumulate mode of CCDOPS (find and focus with other software packages). Set your exposure time 20 sec and you want to test for at least 5 minutes, so the number of exposures should be 15. Since you can always cancel the routine, you can even go longer if you think you're close. Start exposing. You are now presented with a really nice plot of exactly what is happening to the drifting star. You only need to watch the axis that your star moved when you tested for declination movement. In my case this was the plot of the X axis. Since each axis is separately plotted, then I note movement in the X axis. When I intially tested, there was a slow, but steady movement in the X positive direction. This meant that my star was drifting Northward. You should now stop the Track and Accumulate routine, or let it finish whichever you prefer. I stopped the routine when I was sure of the direction of the drift. If you drifted over five pixels very quickly, your alignment is way off and you'll have to move the mount a fair amount so you may as well prematurely terminate the routine. In other software packages, simply note the direction of movement of the brightest pixel in the field. If it's a X+ movement, then that's as good as a plot. When using other software packages and watching coordinates, it's imperative to ingnore the coordinates that aren't on the dec axis. They will actually fluctuate more, because they represent movement in RA, which is usually induced by periodic error in the drive gear (a good way to quantify the quality of the gear in your mount.)
If the star drifts north (in our case X+), you should move the mount a tiny bit in a southward direction. If the star drifted in a south (X- direction in our case), then you must move the mount northward or up in the declination axis. For those you who are directionally challenged, raising a scope in the declination axis means steepening it's angle to the ground. How much to move the mount is a matter of trial and error, but move in small increments at first unless you were way off. Tighten the mount back up (tightened fittings do affect the alignment).
Reenter the Track and Accumulate mode and restart a series using the previous parameters. Repeat the process until there is no drift at all along the declination axis (X axis in our example). If you overshoot and go to far, then the direction of drift will reverse and you will have to move the mount in the opposite direction. Once you you have achieved zero declination drift, you can test for up to 20 minutes for further drift if you wish, but if you were way off in East-West alignment, you're going to be doing this again so don't bother.
Now select a star near the meridian and very near the equator via the find and focus mode and your digital setting circles. This is a test of East-West alignment. Remember you are only testing for declination drift, so you will be watching the same plot (the same coordinate with other software packages). This does seem confusing at first, but remember this is a declination drift method. Reenter the Track and Accumulate mode with the parameters set as above. Start the series. Watch for drift along the dec axis (X axis in our case). Once the direction of drift and the rate seems apparent, stop the routine.
If there was northward movement (X+ for us), then you must move the mount towards the east. If there was southward drift (X- for us), then you should move the mount towards the west.
The amount should be proportional to the rate of drift. Since you have some experience at this from the first axis, use your instincts and you'll probably be close. For you directional first graders, east means moving the part of the mount nearest the north star to the east, westward movement is the reverse. Repeat this process until you get zero drift along the dec axis.
Now you must decide whether to go through the whole routine again. If huge movements were made in either the Dec or RA axis then you will probably have to revisit the routine. Since I started with a polar alignment scope, I didn't have to since only small movements were required. I was surprised that the polar alignment scope wasn't as accurate as I had hoped.
The final test of alignment is to do a 10 minute Track and Accumulate series of exposures. The increment of the subexposure is up to you. I chose 30 second integration times for the individual sub-exposures. See if the star drifts in either axis. You will notice some movement due to periodic error in the drive gear, but tracking should be very close. If you accomplish this your mount is as aligned as possible.
One further suggestion for those of you who have periodic error and the abililty to autoguide with your camera. Now is a good time to go through the PEC guiding routine and let the autoguider do the guiding for you. Add in PEC to this equation and you'll have very accurate tracking.
Here's to round stars ...
References:
These are the visual methods of drift alignment
Astronomical League's Astro Note 15, Three Star and Declination Drift Polar Alignment Methods
Chuch Vaughn's Drift Method of Polar Alignment
Note: On this method Chuck indicates you should use a star at 20 degrees of declination from the equator in direct contradiction to the Astronomical league article. I chose to use a star along the equator, for what it's worth. Chuck is an excellent astrophotographer, so I'm sure he has his reasons.
