Wednesday, May 3, 2017

PoleMaster--A Quantative Estimate of Accuracy

It's one thing to say how nice a PoleMaster works based on a practice run indoors, but the real measure of its usefulness is the accuracy of its polar alignment (PA). A practical measure of PA accuracy can be found by examining images of either long exposure time or a sequence of short exposures taken a considerable time apart. The other night I was able to do the latter by taking 4 minute exposures during the course of about 1.7 hours.

To get an estimate of PA error one needs to know the declination drift rate and the declination of the target.  A good reference for how this is done is an article by Frank Barrett, "Determining Polar Alignment Accuracy."
I shot 15 light frames using autoguiding and then aligned the first and last in the sequence using ImagesPlus. A nice feature of IP is that it tells you the field rotation it had to apply during frame alignment; when aligning two frames, it tells you the rotation it performed to bring the second frame into alignment with the first.  In my test case the rotation was 0.02 degrees (72 arcseconds); the elapsed time between the start of the two frames was 65.3 minutes.

Given the above data (and the declination of my field of view) Barrett's Equation 1 yields a polar alignment error of 4.4 arcminutes, which is almost 9 times the maximum accuracy suggested by QHY, the maker of Polemaster. Some caveats are in order:
  • This was the first time I used PoleMaster. As with most things, I expect the quality of my alignments will improve. I did use the rough and fine polar alignment methods.
  • The coarse reporting of rotation angle by IP means the estimate could be between 3.3 and 5.5 arcminutes.
  • The rotation reported by IP is sensitive to the choice of alignment points, and will vary substantially when close to zero like it is here.
Should I be disappointed that the accuracy was not what QHY suggested it might be? Not at all--it's actually quite good if you're autoguiding!

Consider what happens when you guide. The guide star is held motionless in or near the field of view. An error in the polar alignment will cause the FOV to rotate around the guide star. The distance the stars rotate will be proportional to the alignment error and the distance from the guide star. A guide star at the center of the FOV will cause the greatest distortion of star shapes at the four corners of the field.

Since this will get highly mathematical quickly, I'll try to make a worst-case example and see how bad it can be. I'm going to assume that the guide star is within the FOV (as it was for my test case) and located at one of the corners.That star will remain fixed thanks to guiding, but the image will rotate slowly around it because of PA error. In a long exposure this motion will result in oblong or streaked stars, with the worst effect at the greatest distance from the guide star. This will be at the corner opposite the guide star.

Let's set an arbitrary limit of a star being oblong by one pixel. Any more than that and we won't be happy.

The distance between opposite corners is calculated from sensor dimensions in pixels; for my DSLR it's 6,230 pixels. The rotation rate calculated above (0.02 degrees in 65.3m) corresponds to 0.0000053 radians per minute.  The tangential star movement is therefore R * 0.0000053 pixels per minute, which equals 0.033 pixels per minute. Take the inverse of this to find the time it would take for the star to move one pixel: 30 minutes. Therefore one can expect to be able to use 30 minute exposures and have only a one pixel of star elongation at worst when the PA error is around 4 or 5 arcminutes.

Keep in mind that this is only a very rough estimate, and it ignores how the effect varies with the parto of the sky being imaged.  To minimize field rotation effects, follow a couple of rules:
  • Keep your autoguiding scope reasonably well aligned with the axis of your imaging optics; if possible choose a guide star near the center of your image
  • Always align light frames with both translation and rotation
The idea that a 4 to 5 arcminute PA accuracy is good matches my impression from the images I collected. My polar alignment is usually obtained using an impatient application of the drift method assisted by PHD2 guiding. It's rarely ever the case that stack of subs doesn't need some minor cropping to get rid of field rotation effects at the edges of the FOV.

My first time imaging with PoleMaster produced no edge effects. That's a huge improvement over my usual polar alignment. Combine that with the ease of using PoleMaster and it's clear to me that it represents a great innovation for astrophotography.

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