Visualizing Tracking Errors

In the seemingly never ending quest to get my telescope to track better, I've delved into countless articles on guiding and poured over many track logs trying to get a handle on what really is happening during a guided exposure. Although the articles have helped a great deal, analyzing the track logs has been a different matter. This because track logs are linear and it is very hard for me to translate these linear logs into a visual representation of what the guider is doing. There are additional problems such as orthogonality. Rarely is the camera perfectly square with the telescope mount. This further complicates things because corrections shown in one axis on the track log might be related to the opposite axis and this taints the results for any particular axis. In addition, the final image is the product of all the tracking log points over the length of a single exposure and so these points have to be looked at, not individually but as a whole. The image of a star is composed of a number of pixels that again do not correlate directly with any individual points on the track log. Or do they?

I have come up with a way of visualizing a track log in a way that includes all the track points for a particular exposure, and it's pretty simple. It dawned on me that instead of using a linear chart with all the points neatly arranged in a time-sequential order, what I really wanted to see is the track log's representation of an "artificial star". By looking at this artificial star I could see exactly how the guiding is affecting the shapes of real stars in the final image. A very easy way to do this is with a scatter plot.

I set out by isolating a single exposure from my track log and charting both the X and Y axes into a single scatter plot chart. The image below shows this scatter plot after the axes have been normalized and the chart made square. This must be done to get an accurate "image".

SCATTER PLOT 1

The next question was - Does this scatter plot correlate accurately with the actual image? To help visualize this I needed to place this scatter plot next to an actual image of a star in the image that corresponded to this track log. The first step was to change the appearance of the track log. I changed the points to square "pixels" and increased the size of them to better match those of a star in the image. The next image shows this step:

SCATTER PLOT 2

The scatter plot now started looking more like a star and I could already see that there was some elongation in the X-axis as compared to the y-axis. For the next step, I brought the scatter plot into PhotoShop and Lassoed the main area of the plot with a 30 pixel feather. The next image shows this:

SCATTER PLOT 3

The next step was to shrink the size of the scatter plot to match the size of a star in the corresponding star image. This is shown in the next image:

SCATTER PLOT 4

The scatter plot has now been reduced in size and can be seen in the upper left-hand corner of the chart as a selection. The final step was to create a new image and to copy and paste a real star along with the scatter plot's "artificial star", as well as another artificial star with perfect round dimensions for comparison. The next image shows the result:

STAR IMAGES COMPARISON

The artificial star from the track log very closely matches the image of the real star. This result gives me confidence that the track log scatter plot is indeed a match with the star shapes in the actual CCD image. I now have a way to visualize track-logs that corresponds directly to the results on the CCD image.

All these steps are not necessary. I just did them to make sure that the scatter plot is a faithful representation of what is in the actual CCD image. In reality, I can quickly detect not only the elongation but also the amount in the X-axis from the second "modified" scatter plot. In this particular case, the X-axis is roughly 27% longer than the Y axis. To start making corrections, I could either increase the calibration speed or reduce the aggressiveness in the x-axis by 27%. The calibration speed adjustment must be used in guiding software that does not allow a change in aggressiveness for each individual axis independently. For example. if my calibration speed for the x-axis was 5.34 pixels/second, I would start by increasing this number to 6.78. In the case where the aggressiveness can be adjusted independently, if my aggressiveness was set at 8 then I would set it to 6.