What is Periodic Error and How Can It Be Corrected?
Telescope mounts most commonly have two axes at right angles to each other. There are two main types, Altitude-Azimuth (or AltAz) and Equatorial. The telescope at Thanet Observatory is mounted on a German Equatorial Mount, sometimes known as a GEM.
In equatorial mounts, one of the axes, the Right Ascension axis, points directly at the North Celestial Pole (NCP). The NCP is quite close to Polaris, the north star, often called the Pole Star for that reason. As you may know, this is the point in the sky that all the other stars seem to revolve around. So, by having one axis pointed there, the telescope is able to track any star just by slowly moving that one axis. It is much harder to track a star accurately when two or more axes have to be moved, so equatorial mounts are the ones normally used by most serious astronomers and especially astrophotographers.
The axes are driven by something called a Worm Gear which meshes with a Worm Wheel, which turns the telescope axis. An example of a worm gear and worm wheel is shown in the animation to the right. This method of gearing allows for a high gear ratio while being very accurate. Many telescopes are able to position themselves (or ‘point’) to within a few arc seconds. Remember there are 360 degrees in a circle (or a full rotation of the telescope axis), there are 60 arc minutes in every degree and there are 60 arc seconds in every minute. That’s a total of 1, 296, 000 arc seconds in a full circle!
When using a camera to take photographs through the telescope, it is very important to track the stars very accurately otherwise they will become smudged and the image will be ruined. Getting a telescope to track accurately enough can be quite a challenge. There are a few main things that affect the tracking accuracy:
- The speed of the drive motor, which must run at a constant speed and at exactly the right rate. At Monkton, we have a sophisticated drive system that takes care of this for us, so we can assume this is correct.
- The polar alignment, or how accurately the right ascension axis points at the north celestial pole. Polar alignment can be measured and adjusted quite accurately so we can assume this source of errors has been eliminated too.
- The final major source of error is known as Periodic Error
Periodic error comes from slight inaccuracies in the drive system but mostly from the worm gear (the purple gear in the animation). If the worm gear axle is not quite straight, or there is some play in the bearings, or it is worn or the teeth are not quite regularly spaced then stars in the image may appear to wander back and forth slightly as the telescope tracks. A very small amount of movement is enough to spoil an image! If we plot a graph of a star position over time, then we will usually see something like this:
In this graph, time is along the bottom and the vertical axis is ‘error’ (the distance from where a star should be to where it actually is). So when the line is above zero, the star is slightly ahead (or the telescope is lagging slightly behind) and vice versa. This particular graph shows an error of about plus or minus 15 arc seconds measured over a period of 27 minutes.
In an ideal telescope, the star should be as close as possible to zero all the time, but this is never possible in practice. As you can see, the error oscillates back and forth and repeats over a period of time – hence the name Periodic Error. A close inspection will reveal that the time it takes for the error to repeat is exactly the same time it takes for the worm gear to rotate once, confirming that the worm gear is the main source of the error. In this graph (which is not from the Monkton telescope) we might deduce that the worm rotation takes about 8 minutes (540 seconds).
Periodic Error Correction (PEC)
Since periodic error behaves very predictably, repeating exactly once for each worm revolution, then in theory we should be able to compensate for it by slightly speeding up and slowing down the drive motor at exactly the right times. We can see from the graph when we need to do this. All we would need to know is what position the worm gear is in at any given moment.
For the telescope at Monkton, the worm gear takes exactly 5 minutes and 0.22 seconds for each revolution. So if we know the starting position and how long it has been since the worm gear was in that position, we know what position the worm gear is in and therefore how much we need to speed up or slow down. So how do we know what the starting position is?
The photo above shows the actual right ascension drive on the Monkton telescope. On the right is the worm wheel that turns the telescope. On the left we can only see the end of the worm gear axle poking out, with a brass disc attached to it. In that brass disc you may be able to see a thin slot, just wide enought to allow a beam of light to pass through.
In this next photo, you can see that we have mounted a little sensor over the brass disc. Part of the sensor is behind the disk and part of it is in front. The sensor shines a light at the disc and as the worm turns, the slot passes across the sensor, letting the light shine through to the detector, causing it to generate an electrical ‘pulse’ which marks the start position of the worm rotation. The white cable carries this signal back to the drive box under the floor, so we are able to know very accurately when the worm gear is in the starting position.
Armed with this information, we can measure the periodic error very accurately and automatically using our computer and the CCD camera.The computer can then calculate how much to speed up or slow down the drive motor to compensate for the periodic error. This information can be permanently recorded into the drive system, so that periodic error should be almost completely eliminated.
The recording of the periodic error correction curve is one of our main goals over the next few visits to the observatory and we will try to publish graphs of the data we collect to demonstrate how effective the technique is.