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Is my poor guiding the result of flex?

Q: My guiding doesn't seem great and I get stars that aren't round. How can I tell if this is flex in my guide setup?

Unless you're using an SBIG camera with two sensors that both get the light from the same OTA, you're bound to have some differential flex between your main imaging camera and your guide camera. Let's say the main OTA is solidly locked onto the mount and the guide scope is attached by rubber bands to the top of the main scope. Since gravity tends to always pull down, as the whole rig rotates, the deflection of the guide scope relative to the main scope changes. With the guide scope atop the main scope, the guide scope will aim a bit too far down. Rotate the whole rig so that the guide scope is now to one side but keep the cameras fixed and the flex in the guide rig makes it aim "left" or "right" on the image (i.e., gravity is now "camera-left" or "camera-right" rather than "camera-down").

All rigs will have some flex. The question is, how much? Is it a big enough factor to hurt your imaging?

Here's a simple way to measure and hopefully rule out flex. Let's assume that PHD (or whatever package you use) isn't loosing the star and that it's guiding somewhere between perfectly and off by, oh, 3-5 arcsec. So, your mount has some error it just can't keep up with, it overshoots, etc (settings being off, mount being crud, etc.). If that is the case, over time, the star should wobble back and forth but on average be in the same place. We overshoot, we undershoot, we oscillate back and forth past the star - whatever. On average, the star is in the right place, but we have line segments instead of points.

Go out some nice, still night (please don't attempt this with 40 MPH gusts...) and shoot, say an hour of anything at something less than say 1 min exposures. We want something short enough that your mount isn't coughing up furballs during the exposure. Be guiding of course during this.

Now, take those images and do two stacks of them:

1) Do an Align and Combine without any aligning (i.e., fixed alignment). Do this for say 1 min worth of shots, 5 min worth of shots, and for the whole shebang. Does the 1 min stack look pretty clean? How much worse is the 5 min? Now, the big question - how much worse is the whole shebang? If the big stack is a lot worse than the 1-5 min stack, you've got flex. Why? The guide scope kept the guide star on target, plus or minus a few arcsec. That error may show up in the 1-5 min (which can show flex too) but if an hour is a lot longer trail, the only explanation is flex (assuming PHD kept a good lock). A 50 arcsec trail there isn't PHD wobbling.

Note, you can use the Measure Distance tool in Nebulosity to see just how many pixels long your trail is. See how wide a star is in a single shot and see how long the trail is, subtract the two (e.g. 117 pixels - 5 pixels = 112 pixels per hour = 1.8 pixels per minute = you'll not be exposing for 10 minutes with clean stars).

2) Do an Align and Combine with Translation (or Translation + Rotation) in Nebulosity. You'll find in your directory an align.txt file with the dx and dy (shifts in x and y) needed to bring that frame into alignment. You can open this up in something like Excel and plot the total distance the stars moved. Ideally, dx and dy would always be 0. If you're having issues, they won't. Use good old Pythagorus to determine the total distance the stars moved: sqrt(dx*dx + dy*dy). If this is a horizontal line on average with some bumps up and down / some noise, you've got no flex. If there is a real drift component, you've got flex.

Now, how bad is it? The easiest way to check is to fit a straight line to your plot. If you're in Excel, you can just have it add a "trend line". Make sure to have it put the equation on the graph if you do this. That equation will tell you just how bad things are. If you're not in Excel and can't automatically add a trend line, print out your plot and just put a ruler on there and draw a line. Your eye is amazingly good at this fit.

The key number that you need is the slope. In Excel, you'll see an equation like "y = 0.4683x - 1.0786" or some such thing. That 0.4683 is what you need. If doing by hand, the slope is the "rise over the run". That is, how much do you move up on the y axis (pixels) over some amount on the x-axis (time). You may find that your line goes up 10 pixels in 15 minutes, making your slope 10/15 or 0.667 pixels per minute.

Here is a sample from two guide rigs I used:

The first slope of 0.4683 pixels per minute means that if I want a max of 1 pixel worth of extra elongation, I can go for about 2.1 minutes in the first setup and 17 minutes in the second. 1 pixel is pretty harsh, so if we double that to 2 pixels (which will still seem pretty round), I'm talking ~4 minutes and over 30 minutes that I can go before differential flex has become an issue for me.