The M13 experiment: using PEC for unguided imaging

The usual recommendation to a beginner is to get a sturdy mount and a small refractor. Countless threads on Cloudy Nights go more or less like this:

Pro: "Spend as much as you can on the mount but on the other hand do not buy a cheap telescope."
Noob: "That's over my planned budget but I pulled the trigger anyway. Now I have no money left for food."
Pro: "You definitely want to use auto guiding."
Pro: "Hm, well, you might try unguided. Try 1 min subs."

One important hint is missing. I recommend to train the mount's Periodic Error Correction (PEC) and turn it on for unguided imaging. The procedure is to follow a bright star near the celestial equator and watch it in a cross hair eye piece or on the camera screen. The task is to keep the star centered using the hand controllers arrow keys. After a painstaking 20 minutes the mount as saved correction data that can be used for every imaging night from now on. Some low priced mounts do not have this feature or cannot store the data permanently. Thus I recommend to double check that the mount does keep them permanently. Some brands call this function permanent PEC or PPEC. Others just call it PEC and it is permanent.

The open question is this: does it work? Two answer this question I made an experiment. The experiment is to put up a simple setup comprising an entry level mount with PEC trained, a small refractor and an unmodified DSLR. The object is M13, the Great Cluster in Hercules. Imaging time is roughly two hours, something that everyone can do at a weekday and still get enough sleep. Here is what I did:

Data Acquisiton and Calibration Frames

I put up the tripod level, put my Skywatcher EQ6-R on top. Polar alignment was done using the polar scope with the common clock dial reticle. Next I put my small refractor on top, the well known 65mm quad sold by Astro Tech, Telescope Service and others a few years ago. Focal length is 420mm. The camera was an unmodified Canon T7i (800D in Europe). Please mind: no guider, of course. It is meant to be an unguided experiment. Neither did I use electronic helpers for polar alignment nor did I do a drift alignment (also known as the Scheiner method). All simple and straight forward as a beginner would probably do. No computer was used, no plate solving was done. Just a 3 star alignment using the mounts hand controller. Focus was done in live view with a self made Bahtinov mask. I plugged in a simple cable type $20 intervalometer and set it to 1 minute. Camera settings were ISO 400, mirror lock active, raw of course. I selected M13 from the hand controllers Messier list and made no corrections. After almost an hour of 1 min shots the temperature had dropped so dramatically that I interrupted the capture, slewed to Vega and focused again using the B-mask. Back to M13 and a another hour of data. Although I usually do and recommend I did not take any flats this time. Since I have the T7i I stopped using darks because they really do not make a difference for my amount of light pollution and sub exposure length. I did use the master bias I have for this camera, though. I guess this is what a beginner would be able to do for the first light.


The over all number of sub exposures was 123 subs. I sorted out the first few frames because I started a bit too early and the sky was not really dark. I also sorted out a bunch that was out of focus caused by the temperature drop. The star diameter is usually measured as the Full Width at Half Maximum. Here is a plot in chronological order, the removed subs marked by an X:
The first half of the graph clearly shows the increase of star diameter that is caused by the temperature change. After the new focus the temperature no longer dropped that fast so that the star diameter remains constant. It happened to be 100 subs left for stacking. The key question for me was if my estimated 1 minute exposure time was right. There are two reasons to keep unguided exposures short. The first one is star drift that is caused by polar alignment error. My mount gives a feedback how much off the pole it is according to it's internal calculation. It cannot know how precisely I centered the stars during the 3-star alignment so the numbers must be taken with a grain of salt. I usually achieve values below 10 arc minutes with my polar scope. Although the mount displayed only 4 arc seconds in this particular night I recommend to use a higher value for planning just to be on the safe side. There are calculators available online to translate the polar error into the number of pixels a star drifts for a given time. This is one of them: link to celestialwonders. Despite the measured 4 arc minutes which I doubt for the reasons given before, I entered 10 arc minutes for the polar error. Next 1 minute for the exposure time and the declination of M13 is 36°. The result is a drift of 2.1 arc seconds during the 1 minute exposure. The image scale of the system used is 1.8 arc seconds per pixel so the drift is 1.17 pixels. You can hardly call this a star trail. But wait, there is a second mechanism to be considered and that is the periodic error of the mount. I trained PEC when I received the mount and of course I checked if it improves the situation. The image below is an inverted and slightly processed trail of an actual star near the celestial equator. The strong drift from left to right is caused by an intentional polar error of about one degree. The star does not drift a long a straight line but it follows as sinusoidal curve. This curve is the mount's periodic error. During one turn of the worm, 8 minutes for this mount, it is sometimes a bit too fast and sometimes a bit too slow. The graphs represent a single 25 minutes exposure so about 3 turns of the worm are shown. The graph is scaled to 1 arc second per pixel and I added the red lines to show the limits. Without PEC the deviation is 53 arc seconds peak to peak.
A one minute exposure taken during a maximum or minimum of the curve may show as little as 4 arc seconds of drift. But an exposure of the same length taken at the steepest part of the slope suffers from almost 20 arc seconds of drift. That is the reason why there are some very sharp shots and some shots with extreme trailing. Now let's look at the drift curve with PEC enabled:
The periodic error correction obviously is a dramatic improvement. At almost all times a one minute sub will come away with less than 3 arc seconds of drift. The 2.1 arc seconds caused by polar error and the 3 or less arc seconds caused by periodic error may be in the same direction or in opposite direction or perpendicular to each other or anything else depending on the direction of the polar error. So all we can tell is that we expect some 5 arc seconds worst case but very likely much less for almost all subs. Can we see what really happened during that night? Yes, we can. Hot pixels are the sort of thing we do not want in our images. In this case we can use them as indicators for the drift. During the stacking the single frames are aligned to each other so that the stars match. Normally we would use average or median as the combination method and sort out outliers. If maximum is used instead and if pixel correction is disabled the hot pixels mark the path of the drift in the image. Let's look at this red one:
The image is magnified 5 times. The thin white line is a satellite that happened to cross this portion of the image. Just ignore it and look at the red trace. As described in the Image Acquisition section above I interrupted the capture after one hour to correct focus. The time it took to focus and the sub frames I sorted out caused a gap in the trace. The lines are not straight and that is because the polar error and the periodic error are unlikely to be in the same direction. I measured one line and checked the time code of the corresponding files. The drift was 54 pixels in 72 minutes (real time, not 72 subs). The image scale is 1.8 arc seconds per pixel. So I have 1.35 arc seconds drift in on minute. This is well below the estimated worst case scenario of polar error and periodic error adding up. Looking at the FWHM chart we find the star diameter is between 3 and 5 arc seconds. So the elongation caused by drift is small compared to the star diameter. On a close inspection the stars are not perfectly round but they to not look like eggs either. Under exceptional calm skies with an FWHM of 2 arc seconds the drift is a bit too large. For my poor conditions the 1 minutes subs are a good compromise.


As the object is small compared to the field of view the image was cropped from it's original 6000 x 4000 pixels to 2720 x 1530 pixels. As the idea of this experiment was to figure out what a beginner can expect from an unguided session only a basic processing was applied. I intentionally did not do a deconvolution as this would not be within a beginner reach. Here is a small version of the result. For native resolution click the link below.
full resolution


The standard advice "sturdy mount, small refractor, 1 min subs" works well. In addition I recommend to train PEC for unguided imaging. Please note that a flat field astrograph with a triplet lens including one FPL53 element was used for this test. A doublet should be an FPL53/lanthan type at least. Comparing an FPL53 triplet and FPL53 doublet the doublet will come up with a slightly greater star diameter. Any lower quality glass will bloat the stars and add colored halos to the stars. I have seen images where the blue halo was several times the star diameter. There are only very few camera lenses that can be used for astro photography and most of them are prime lenses. With good glass decent images can be taken without guiding but the technique is limited to brighter and larger objects.


Yes, the gentleman up there. Beg your pardon, what did you say? Ah, how the image compares to a guided image from a large telescope and longer subs? Well, there is always room for improvement, but see yourself. Here is a toggle image showing a tight crop of the above vs. 2 hours and 40 minutes taken with an 8'' Ritchey–Chrétien telescope at 1100 mm focal length using guided 2 minute subs.

Yes, over there! Ah, no. No, I do not recommend to start with such a big telescope. First it needs a larger and more expensive mount. Second finding the alignment stars in such a small field of view can be tricky. Third some of the longer scopes need off axis guiding that was used here. This is nothing a beginner can handle. I recommend to keep the first setup small and the workflow as simple as possible. You can update step by step as your skills improve.

Thank you!

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