Periodic Error Correction (PEC) Data Analysis with CCD

The purpose of this note is to analyze and adjust PEC data by examining CCD image data. We hope that we will be able to make good PEC data by using CCD camera. My equipments are Meade LX200GPS 12 ” on polar mount (permanent pier) with firmware 1.6b with 1g6B patch being applied and SBIG ST9XE CCD camera. (I live in the Northern Hemisphere.)
First of all, let's examine the relation between PEC data and the periodic error movement of the telescope with PEC off by using CCD. I have already done PEC train and 3 updates by using CCD camera and I am satisfied with the PEC data because the periodic error is reduced. Some data, which is my note, is here.
To manipulate PEC data, we use software PEC Viewer or PEC Editor ( new one ) in addition to Autostar update client application ASU . See also useful links for more information.
By using PEC Viewer or PEC Editor, you can get PEC numbers over 200 segments. By comparing the PEC data with the CCD autoguider's tracking log, it is found that the order of segment number from 1 to 200 is a reversal of the time direction. Therefore, adding the PEC data from 200 to 1, you will get the movement of the telescope with PEC being off. Whether it is well trained PEC data or not will be seen later.
PEC sum

As is seen from the figure, the sum of my PEC data is not zero but -20. The reason is as follows: My telescope with PEC off has a drift to the west. It is about 0.12 degrees during 8 hours. Thus, to get rid of this RA drift, we have to set Custom Tracking Rate to -1 (unit is in tenths of a percentage of sidereal rate) when PEC is off. However, when PEC is on with above PEC data and the telescope's tracking is at sidereal rate, PEC sum -20 compensates for the drift and now there is no (very small) RA drift at sidereal rate without setting Custom Tracking Rate. In this way, the positive and negative directions of vertical axis shows that the telescope moves to the west and the east, respectively, to compensate for the telescope's periodic error in opposite directions.
Next, let's take a look at the periodic error of the telescope when PEC is off by examining the CCD image data. It is very important to take images during more than 8*3 = 24 minutes, as will be seen later. Here and hereafter, the star near the celestial equator is picked up when the images are taken. The weather condition might not be so good as will be seen in the figure. However, it will be enough for our analysis.
Scope's Periodic Error

Here CCD images are taken, with PEC off, in about 2.4 second (lower is better) periods, which include time to download images . In the figure, x-axis denotes Hour Angle (= Local Sidereal Time - Right Ascension) in units of degree and y-axis is in units of arcsecond. Hence, 2 degrees in Hour Angle is equivalent to 8 minutes, which is the time for one PEC cycle. Here RA is taken to be the current RA of the center on the CCD image. LST is calculated here. It should be emphasized that the unit of horizontal axis of the graph is taken to be hour angle (degree). The positive and negative directions of vertical axis shows that the telescope moves to the east and the west, respectively. The reference point on vertical axis is not important here since it is just chosen for my convenience.
We can easily find that the curve on the graph is roughly the same as the one obtained from the sum of PEC data. At this stage, one can tweak the PEC data by the editor so as to fit into the curve obtained from telescope's periodic error movement.
In my telescope, there are about 30 arcseconds periodic errors. Comparing two graphs, it is assumed that the one PEC unit is equivalent to about 0.28 arcseconds. It is interesting to see a superimposing of the CCD image data upon the PEC data when one PEC unit is chosen to be 0.28 arcseconds, where about +/- 0.02 would be within the errors. Here, y=a*x+b is added to PEC data graph. (Note added: It is known that PEC value 128 is equivalent to 15 arcsec/sec. Hence one PEC unit (for 2.4sec) = 15*2.4/128 = 0.28125 arcseconds.)
CCD data vs PEC sum

Next, let's examine residual periodic error when PEC is on. The following figure shows the data when PEC is on-off-on. PEC was off during the period between -16 and -14 hour angle and it is easily seen in the figure. When PEC is off, custom tracking rate -1 is also set.
PEC on-off-on
Here is another data in different hour angle region with PEC on.
PEC on
By looking at these figures, it seems to be a difficult task to find a residual periodic error. However, we can find out three different types of periodic errors by examining the data for more larger region in hour angle.
We have obtained the data during hour angle between 0 and 30 degrees. By analyzing the residual periodic error, it turns out that 24 minutes (6 degrees) periods exist and hence there are three categories in different 8 minutes (2 degrees) hour angle region. We will call them Type A, B, and C depending on the hour angle region [0+6*n,2+6*n], [2+6*n,4+6*n], and [4+6*n,6+6*n], respectively. Although we restrict ourselves to the case of n=0,1,2,3, and 4 in our analysis, it is easy to extend the regions to other value of n and also negative hour angle. These 8 minutes and 24 minutes periodic error will also be found from the analysis of the periodic error data obtained when PEC is off.
The following figure shows that the residual periodic error in the case of Type A (hour angle [0+6*n, 2+6*n] with n=0,1,2,3,4).
Type A
In the figure, 5 small circles with different colors plot all of the data for 5 different hour angle regions in Type A, i.e. [0+6*n,2+6*n] with n=0,1,2,3,4. Since it includes not only periodic error but also some other errors, it should be averaged out. The red dots with line denote the average of them. Apparently, it turns out that there exists some residual error, which should be eliminated by adjusting the PEC data.
In the same way, the following figures are in the case of Type B (hour angle [2+6*n, 4+6*n])
Type B
and Type C (hour angle [4+6*n, 6+6*n]) with n=0,1,2,3,4.
Type C
If you are interested in only 8 minutes tracking during 24 minutes, in other words probability 1/3, you can adjust PEC data by considering one of the data Type A, B, and C. However, you can get good tracking at only 1/3 of total time.
Averaging over all of the Types A, B, and C, we can get the average residual periodic error. In the figure, the red dots with line are the average of Types A, B, and C. One might think that red dots are within the errors because they are within +/- 2 arcseconds.
Converting arcseconds to PEC units by using our previous relation that one PEC unit equals to 0.28 arcseconds, we can adjust PEC data by adding the above average residual periodic error to the original PEC data obtained from PEC train and updates.
Finally, let's take images by using the adjusted PEC data. To compare the effect of the adjusted PEC with previous PEC data, images are taken in the same hour angle region as the one shown above. Here is an example for [-18,-12] hour angle (see for some other data).
To ensure that it is a well-adjusted PEC data, we have to repeat the above method and examine whether average residual periodic error exists. It is necessary to do some statistical analysis by examining average, standard deviation, and so on. Further analysis is under consideration.
Any comments and suggestions are welcome. Please send mail to
If RA anti-backlash percentage has non-zero value, there is a small jump ( about 1 arcminute or less ) after the end of PEC train and updates. If you do not like this jump, please try to set RA anti-backlash percentage to zero and train PEC.
Last Update: Oct. 1, 2004