Polar Drift Alignment
By Steve Walters, 2004.
For a long time, I used the "cookbook" method of drift alignment. Somewhere on the Internet, I found an article similar to the following:
"Using high magnification, observe a star to the south. Make adjustments to azimuth until it stays on the crosshairs for 10 minutes. Repeat with a star to the east but now adjust elevation."
I used this method successfully for several years. But when I started using medium format film and a new off-axis guider, field rotation crept into my photos. This puzzled me since I was doing exactly the same thing. But then I started thinking, what constitutes "high magnificaton" and why is 10 minutes adequate? This led me to the following two questions about the drift method of polar alignment which will be answered in this article. Namely:
1. How accurately must you align the polar axis?
2. How do you know it's aligned at the necessary accuracy?
While researching these questions, I stumbled onto an excellent article written by R. N. Hook titled “Polar Axis Alignment Requirements for Astrophotography”. This was published in the Journal of the British Astronomical Association, Feb 1989.
What Accuracy is Needed?
Hook calculates the degree of misalignment that will produce 30 micron trails on images. His result is easily generalized to:
E = 45000 * S * cos ( D ) / ( T * F * A)
E = maximum allowable polar misalignment in arcminutes
S = worst case length of trails in microns
D = declination of the object in degrees
T = duration of the exposure in minutes
F = focal length in mm
A = angle in degrees between guide star and object
So, given the parameters S, D, T, F and A, this equation will tell you how closely you need to align your polar axis to the true pole. For example, my BRC-250 and OAG have F = 1268 mm and A = 3.5 degrees. If I want 6 microns or less trailing (S) and want to photograph objects up to 60 degrees declination (D) for up to 30 minutes, then I need to be aligned within 1 arcminute of the pole (E). If I want to use 60 minute exposures, I need to be aligned with 30 arcseconds.
This gives the answer to question one; we can now determine how accurately we must be aligned for any given trailing. Incidentally, I selected 6 micron trails because my smallest stars are around 20 microns. On these stars, even 6 micron trails are difficult to detect; on larger ones, it is impossible. Depending on your particular optical system, you may need to allow either larger or smaller trails. For example, on my 12" SCT operating at f/6.3 with a compressor, my smallest stars are around 60 microns. Here, trailing of as much as 20 microns might be acceptable.
How Do You Know You're Aligned ?
Hook's article also holds the answer to question two. He calculates how much a star drifts in declination during an interval of time when no guiding is performed. His result is easily converted into drift rate.
R = 0.262 * E
R = drift rate in arcseconds per minute
E = the degree of misalignment in arcminutes
This means that if the polar axis is aligned to within 1 arcminute of the true pole, then a star will drift in declination by 0.262 arcseconds per minute or less. In one minute, it will drift 0.262 arcseconds, in two minutes it will drift 0.52 arcseconds, in 3 minutes it will drift .79 arcseconds and so on.
We can calculate the time for a star to drift 1 arcsecond by simply inverting the drift rate.So, if the drift rate is 0.262 arcseconds per minute and we wait for 3.8 minutes, it will move by 1 arcsecond. An STV can measure changes in the position of a star by as little as 1 arcsecond. This allows us to tell when we have reached an accurate alignment.
Here's an example. Suppose we need to be aligned to within 2.54 arcminutes of the true pole. Then we are adequately aligned when the drift rate is 0.67 arcseconds per minute or less. That means that a star will drift 1 arcsecond in 1.5 minutes. So, using our STV, if we drift for 1.5 minutes and see 1 arcsecond or less of movement, we are done.
The STV is a powerful tool for doing drift alignment. It is like an extremely high magnification eyepiece that allows you to quickly detect very small changes in the position of a star. Because it displays changes in the position of a star in arcseconds, you can accurately measure the drift rate using a timer. If a reasonable focal length is used, this measurement is quite accurate.
First, let's consider what focal length should be used. This determines the resolution of the STV. An STV calculates a star's position to within 1/30th of a pixel. The TC237 CCD chip in the STV uses 7.4 micron pixels. The number of arcseconds subtended by a pixel in the STV depends on the focal length of the optical system in front of the STV. In particular:
A = 0.206 * I / F
A = angle subtended in arcseconds
I = pixel size in microns
F = focal length in meters
So, for my BRC-250 with a focal length of 1268 mm (1.268 meters), each pixel in my STV covers 1.2 arcseconds of sky. Since the STV calculates stellar centroids to 1/30th of a pixel, the resolution of the STV on my BRC-250 is 0.04 arcseconds. But suppose we are using the ever-popular eFinder which has a focal length of 100 mm (0.1 meters). Then each pixel subtends 15.2 arcseconds and centroids are only resolved to within 0.5 arcseconds. If we are trying to detect drift rates of 1 or 2 arcseconds per minute, this is a bit coarse but for many applications such as CCD imaging using short exposures where polar alignment is not so critical, this may be adequate. Remember that no matter what focal length you use, the STV will display values in arcseconds. But you will notice that the resolution (when using an eFinder) is +/- 0.5 arcseconds. This can be seen by watching the values and noticing that they change by increments of 0.5 arcseconds.
Here's the procedure to drift align using the STV. First, use "Drive Test (slow)" mode to get an approximate alignment. In this mode, the STV displays errors on an axis that is 50 arcseconds full scale. When the mount is badly aligned, this is sensitive enough to see which way the star is drifting. Use this mode on a southern star around 0 degrees declination and again on an eastern star at about 45 degrees declination to get the mount roughly aligned.
Next, select a star to the south, train the STV normally and start tracking . In this mode, the STV full scale display is only 4 arcseconds so it is much easier to see drift. Because we wish to avoid the effects of seeing, program the STV to average the maximum number of frames (10) and select a star that requires exposures of around a 1 second.. Once the STV is tracking the star, reduce the Yaggressiveness value to ZERO so no corrections are applied to the declination axis. Now, start tracking, note the initial error and see if it increases or decreases. If seeing is being averaged out, you should be able to see changes of 1 arcsecond. Make adjustments to azimuth until the drift rate is less than you require for your alignment. Repeat this using a star to the east but now adjust elevation.
I recommend that you figure out which direction corrections must be made when the star drifts up or down in the display to move towards the pole. This will depend on your specific mount and optical arrangement. Always set up the STV so its X axis corresponds to right ascension. Make sure you set up the STV in the same way each time out. I keep a table with my STV that tells me which way to adjust azimuth and elevation for up/down drifts of a star to the south and east. I consult the table before every adjustment. Otherwise, I'm sure to make a wrong adjustment.
Hopefully, this method will allow you to become more quantative in your drift alignment. You can save time through the use of an STV rather than an eyepiece because of its greater sensitivity. Also you may be getting greater alignment than is needed. This means wasted time in drifting.. By calculating the needed alignment and using the STV method, you can get the alignment you need in the least amount of time.