Over the years, there has been a spate of messages vilifying the star drift alignment method of polar aligning a telescope mount. Part of the problem, as I see it, is that in attempting to explain it, most actually complicate it. What gets lost is the simple notion that what you can use to align the mount is the very effect you want to avoid in your images in the first place - objects drifting in declination. And even if you don't bother to determine which direction to adjust the mount to correct the drift, all you have to do is make an adjustment and determine if the drift increased in speed, decreased in speed or, better yet, reversed direction, from which you could extrapolate the appropriate adjustment. In fact, with the neat tools available to us today, such as DSLR Focus or ImagesPlus, or even a web cam, within a few attempts you gain a terrific feel for the process. Part of the difficulty has been that at one time you needed to use an illuminated reticle eyepiece and after making an adjustment you had to re-acquire a star, all while bending your neck...well, you've been there and don't want to go back.
So, without any equations or ditties to remember, let me relay two variations on the method I used recently. (Although, I do use an exercise to determine the correct movement - later below.)
First of all, from where my telescope is set-up, I cannot see the pole - so I don't use a polar alignment scope. Not that I have anything against them, I just feel it is just as easy, and more direct, to simply monitor the effect that I want to correct for in the end product - declination drift in the final image. Once you have gained even a rudimentary familiarity with the sky, a rough aligning to the north celestial pole becomes second nature. (If you see Orion, say, or Perseus, you have a very good idea where the NCP is located.) And the beauty of it is, the farther off you are, the more quickly you will see that show up in the drifting of a star.
To illustrate, just the other evening, I used ImagesPlus in its focus mode, along with the camera I image with, to align the mount. Again, this could be any image capture program. The advantage here is that once you select the region of the initial image for focusing, you can enlarge that portion and see any movement at the pixel level. Then, manually "release" (trip the shutter), wait a few minutes, perhaps the length of your sub-exposures (sometimes more quickly than that depending on how far off you are) make an adjustment and repeat the process. Actually, you'll see the movement show up pretty quickly since it is magnified.
And perhaps an even easier method is to use a web cam (or the guide cam you use in a separate guide scope but installed in the main instrument) and monitor the drift. I tried this last night using Craig Stark's PHD Guiding program. And, since PHD now includes a grid overlay as well as a bulls eye option, it's a matter of placing a star conveniently on the screen and watching the drift in real time, as opposed to snapping pictures with the DSLR.
And, of course, another advantage to using a camera, of any type, is you can rotate it within the focuser to get the movements to parallel the mount - i.e., north is up, etc.
As far as the general process, here is a technique I find helpful to understand the mechanics of what is happening with respect to the movement of the mount versus the path of a star across the sky. Imagine two circles, such as two hula hoops, overlapping and lying in the same plane. The outer circle is the earth's equatorial plane. The inner one is the equatorial plane of your mount. Now, imagine tilting the inner circle backwards (say, below the pole) and envision the effect along the meridian versus at the horizon. The arc formed by each circle/loop is nearly parallel close to the meridian. But, near the horizon (either east or west) the arcs of the two loops form an angle where the two circles intersect. That is why altitude adjustments are to be made with a star near the horizon. And if you picture the two intersecting circles and imagine a star moving along from left to right, you will see that they diverge on the eastern horizon and converge towards the west. So, with a star tracking along the true equatorial plane and your mount tracking along the inner circle, the star will "fall" when pointing east. Now, put the circle back in the same plane and then imagine rotating it (turning the base, say, towards the southeast). Now you see a similar effect - near the meridian, the arcs will intersect, one rising, the other falling. In fact, when I see the star drifting northward, (I don't like remembering ditties), I stand with my arms outstretched and my body tilted back, facing what I believe to be south, then I turn slightly southeast and rotate my body and notice the arc formed by my arms (representing the equatorial plane of the telescope) versus that of the supposed equatorial plane. In this case, my arms will trace a falling arc at the meridian. So, a star moving along the true arc will appear to rise in the field of view. And if you turn towards the southwest and rotate, your arms will trace out the reverse pattern, your arms crossing upward and the star falling. So I must be west of the pole and adjust accordingly. (This really needs a graphic, but, try to visualize it, which in itself will reinforce your understanding.)
Now, you might be tempted to simply let the auto guiding program eliminate any drift, or at least any residual drift. True, but you will still have field rotation to deal with later in post processing. And, true, some amount of misalignment at least enables applying declination corrections in one direction, thus avoiding over-correcting in declination, what with backlash and all. But, only enough to overcome variations in seeing.
Obviously, this entire area can be treated much more technically (and turn more novices off). Based on factors such as your focal length and amount of movement in the guide star over a period of time, the exact correction to azimuth and altitude can be determined mathematically (just as programs such as Gemini do). The point of this exercise is to lend a natural understanding of the fundamental process/geometry at work and provide a simple method for achieving very accurate polar alignment based on the very problem it is meant to cure - drifting stars.
William J. Shaheen
Superstition Mountain Astronomical League
Gold Canyon, AZ USA
http://www.pbase.com/wjshaheen/superstition_mountain_astronomical_league
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