Mount periodic error

If you already have the motorized mount or you plan to purchase one, then probably you are already familiar with this term. Some claim that periodic error is the root cause of all evil, others say it is not a big problem that can be completely handled with guiding or corrections. I believe that after reading this article you will figure it out by yourself.

What is the periodic error?

Almost every motorized telescope mount contains some transmission gears with reduction. There are toothed gearboxes, belt drives, and very many mounts contain large worm gears at both axes. All gears have some finite precision, so they are not perfect. For example, a toothed gear can be a little eccentric, and when it rotates the effective ratio will differ a little at different positions. The same may apply to worm in the worm drive. Since the worm and toothed gear rotate, then imperfections they introduce changes with the rotation angle. That is why it is called a periodic error because this error amount varies but repeats with every rotation. Usually, astronomy amateurs are most concerned with the periodic error of the main worm drive. Periodic errors that originate in other transmission parts are relatively low.

What are the periodic error values?

It is obvious that periodic error value depends on the gears manufacturing accuracy. And that accuracy is unfortunately related to the mount price. There are two parameters that describe periodic error – its value and period. The periodic error value is expressed in arcseconds. The period is measured in seconds. Entry-level small mounts may have a periodic error in the range from 30 to 120 arcseconds. Popular SW mounts, like HEQ5 or EQ6, have PE in the range 10-30 arcseconds. The newer SW mounts (like EQ6-R) seem to have lower PE values. Premium grade mounts have low and consistent PE lower than 10 arc seconds.

The actual period of the periodic error equals to worm rotation period and usually, it is around ten minutes (600 seconds). So if you are told that periodic error is 20 arc seconds, it just means that mount tracking deviates by this amount from ideal tracking during the given period. 20 arc seconds during ten minutes does not seem to be a large value, but the actual impact on the final image depends also on periodic error changes rate.

How periodic error affects mount tracking?

It depends on the way you use the telescope. If you are a visual observer then even if you have a narrow field of view orthoscopic eyepiece and large magnification, then 30 or 60 arc seconds do not make much difference. If you do planetary work with small chip camera at long focal length, then periodic error value may equal for example Jupiter apparent diameter. And that can be a problem. It is also a serious problem for long-exposure astrophotography.

Take a look at the example synthetic periodic error curve above. The vertical scale is tracking error in arc seconds, and the horizontal line is time in seconds. In this example, we assumed that the worm period is 600 seconds.  The orange line indicates ideal tracking – error equals zero. The green line shows an example of a periodic error curve with peak to peak value of 30 arc seconds. It does not change evenly during the time. It raises quickly at the beginning and then lowers slowly till half of the period. The second half of the curve has a similar shape, but a negative sign. If you do long exposure frames, let’s say 60 seconds long, and start exposure at the beginning of the curve, then during 60 seconds accumulated error will be around 14 arc seconds. But when you for example start exposure at the 100s at horizontal line, then during the next 60s the error will be about 7 arc seconds. It is of course too much for all but short focal imaging setups.

But if you have a premium grade mound with a uniform periodic error curve with peak to peak value of 4 arc seconds (blue plot), then 30 or 60 seconds exposure is not a problem even for setups with pixel scale 2px/”. However, if you would like to shot longer exposures, then that periodic error value may still be a problem. What can we do then?

How to fight periodic error?

There are two ways. The first is periodic error correction. The second one is guiding. Both are independent and can be used at the same time.

Period error correction (PEC or PPEC) is a functionality available in several mounts or drivers (like EQASCOM). The idea behind is to measure the periodic error value during the time, and then calculate the periodic error curve. Having that data mount driver may apply corrections to the tracking that will compensate periodic error of the mount. Measuring periodic error is usually done by recording short exposed star images over a longer time. The position of the star in the frames is then calculated and converted into the tracking error – periodic error curve. PEC is a convenient way of fighting with periodic error and should be used all the time if it is available because it compensates for the tracking error before it actually happens (in contrast to guiding, that corrects errors that already occurred).

There are also some mounts available with high-resolution encoders in one or both axes – for example, iOptron EC version mounts. These mounts may apply real-time corrections to the tracking rate basing on position data given by encoder. This way effective periodic error can be limited to one arc second or even less. Such mounts for long focal length imaging may still require guiding (to compensate drift or setup elements bending), but tracking in RA axis alone is very accurate.

Guiding is another way of correcting periodic and other tracking errors. Guiding requires an additional camera that records star image (via main optical train or auxiliary guiding scope), measures its position, and then applies a calculated correction to the mount position. Guiding may compensate for periodic error and other errors (see How good guiding can be), but it has some drawbacks. And the main drawback is that guiding compensates for errors that already happened. So guiding must be adjusted in a way that it detects errors that are not yet visible in the recorded image. And this is usually possible, except for some extreme cases, when periodic error changes very fast (like several arc seconds during a few seconds of time).

So the recommended approach for long exposure astrophotography is to use both periodic error correction and guiding. The first functionality will be applied before the actual error occurs, so the periodic error curve will be significantly flattened. And then guiding should deal with remaining slow changes with ease.

The image below was made in my backyard observatory using Meade ACF 10″ telescope and EQ6 mount. I have used both periodic error correction in EQASCOM driver and guiding to achieve low tracking error. This was quite a demanding target because at my location it never raises high in the sky (see details in this post).

Clear skies!

Cover photo by Bill Oxford on Unsplash