PE Measurement

Oh geeze….   PE.   Now this is a horrid subject.  Here’s an introductory guide.

This discussion will refer to errors in the drive systems of  German Equatorial Mounts (GEMs) and particularly to those that are driven by a worm gear arrangement.  The basics and principles will of course also apply to other drive systems, but the analysis has to be done in relation to the specific drive type and configuration.

What is PE? Periodic Error…  virtually all mechanical drive systems have error, they are not perfectly smooth.  Some of the errors in motion are “periodic”, meaning the error repeats at a regular interval or period, hence the name.  Usually, the largest periodic error in a GEM mount  is due to the rotational period of the worm drive of the RA axis.  This is because the machining of the worm is not perfect.  There are surface defects on the contact face of the worm, and there will be some deviation from a geometrically perfect worm shape.  As such, there will be tracking errors that will cycle and repeat with every rotation of the worm.  It’s worth noting that one rotation of the worm advances the worm-wheel one tooth, from that you can see why we don’t talk about the periodic error of the big wheel (since its period of rotation is one sidereal day ;)).  It is possible to see periodic errors at 2 or 3 times the worm rotation rate due to miss-machining (like miss-spacing) of the teeth on the wheel.  I’ve seen this on other machinery, but never heard it mentioned for a scope mount….  doubt I ever will.

Often folks refer to PE as PEC which is actually Periodic Error Correction.  PEC is typically a software routine built into the mount control software.  When PEC is enabled, the control software tries to counteract/correct the PE of the mount by using a “map” of the mount’s natural PE which is recorded and stored in the control memory.  We’ll talk a little more about that later.

The amount of PE your mount has may or may not be important to you.  If you’re a visual observer, and objects don’t wander in you eyepiece too much, then why worry?   However, if you’re doing long exposure photography, then having a low PE and controlling it well is very important.

Measuring PE

Measuring the PE of your mount is not hard and there is software freely available to help you analyze the results of the measurement.  I’ll caution here that there are a lot of variables that effect PE so don’t make decisions (like deciding to tear down and rebuild your mount) based on only one night’s measurements.  Get several runs of data and look for trends and common traits.

The easiest way to measure PE (or to record PEC curves) is to use an imager suitable as a guide camera along with guide software to create guide logs.  This is usually done with everything working just like you’re guiding, except the correction signals are not actually sent to the mount.  What this does is records how far the guide star moves around it’s original position.  As example you might let the mount track for about an hour (guider up and running, tracking a guide star, but not sending corrections) to get data for several rotations of the worm into the guide log.  Then the data in the log would be graphed and analyzed.

It doesn’t really matter what scope is used, most any should work although I’d avoid long FLs so you can keep the guide star on the chip.

Software: There are some free programs available to analyze the log data.  Two notable ones are PEAS and PecPrep.  Which program you use will depend somewhat on what guide program you have, which in turn determines how your guide log data is formated.  I usually use PEAS.  Two reasons:  1) it uses templates to read the guide logs, so it’s easy to update it for different versions of guide software and, 2) I like the simple FFT results shown on the same graph.

Here’s a sample:

This is not an actual PE measurement, but is representative of what you might see.  This shows about 4 worm cycles on my GM8 mount where each cycle takes 480 seconds.  Note that the “Smooth data” block is checked and the “Raw data” is not.  The raw data shows the position as captured, and adds a lot of “noise” to the graph.  Here’s the same data showing the Raw data:

The jagged noise seen in the raw data is a combination of the Seeing and small vibrations in the drive system.  It’s good to try and lower the amount magnitude of the noise, but how to analyze and correct for this is more than I should put in this post.  It involves identifying what parts of the drive system are causing the largest problems by using the FFT information, then finding ways to correct the issues.   I’ll write a post on the subject and review my experiences chasing these issues another time.

A small issue to overcome is getting the guider log file ready to be read by the analysis software.  Typically, when you get your guider up and running, there will be several starts and stops as you calibrate; maybe to change targets, readjust the camera, or balance, or something…  as a result your log file will have many short sections that you don’t care about.  Additionally, you may have two or three sections that you do care about or want to compare.  An easy way to deal with it is to just copy the areas of interest into individual files that contain just the data (no run info or column headers) and name the files to help identify what’s what.  For example, lets say I did some PE measurement first, then trained PEC, then shot images of M33 for the rest of the night.  I might cut up the logs and save the data of interest as:  PHD_CGE_PEraw.txt  PHD_CGE_PECTrng.txt, and PHD_CGE_M33.txt.  The content of the files would look something like this:
_________________________________________________
1,3.746,-0.17,1.32,1.7,450.1,1.19,0.0,-0.19,123518.54
2,7.772,-0.20,1.19,1.7,449.3,1.19,0.0,-0.22,128314.44
3,11.787,-0.18,1.80,1.7,655.3,1.73,81.9,-0.21,127999.39
4,23.334,-0.15,1.83,1.7,686.3,1.82,70.8,-0.18,128122.90
5,27.350,-0.03,1.62,1.6,620.9,1.64,0.0,-0.05,124805.48
6,31.346,-0.29,1.64,1.7,619.4,1.64,125.1,-0.31,126909.70
7,35.812,-0.25,1.55,1.7,587.5,1.55,110.2,-0.28,125283.11
8,39.828,-0.16,1.66,1.7,622.5,1.65,73.7,-0.18,49266.85
…..  and so on for hundreds/thousands of lines…
________________________________________________

(You’ll of course already figured out if the format can be read by your software, or set up a template so it can.)

Evaluating PE:

When evaluating the PE of your mount, compare it to what others get on that model or class of mount and to previous data runs on your mount.  For example, you might be wanting to know if your mount is behaving badly compared to others, or if some work you did made it better, or if setting the balance just so had an effect, etc.

There are two main things to look for in the PE curve:

1. The magnitude of the PE curve.  Such as  +4/-2 arcsecs (that’s 6 arcsecs peak-to-peak) in the fake example above.
2. How smooth the curve is.  E.g., whats the magnitude of the noise (which looks to me like 10 arcsecs p-p in the example above), and are there any big jumps that might indicate a serious problem with the worm.

The main thing is that mounts with pretty big PE may still be able to be guided well if the curve is regular and pretty smooth (by the way the mount in the example above guides just fine, even with that amount of noise).   Don’t panic just because you mount’s PE is larger than you’d like as long as there aren’t sharp changes in the curve that would disrupt guiding .  If the PE is much bigger than what other folks are getting on that mount, then it’s time to look into it.  The first place to look would be checking the mesh/alignment of the worm to worm-wheel.

Last topic… PEC.  Your mount may or may not be able to do PEC.  As I stated, PEC is a way the mount controller reduces a mount’s PE by making little corrections based on a map (a PEC curve) that’s input into the controller by the user.  The PEC curve can be generated different ways, and typically the curve will be an average of several PE curves indexed and added together.  Again, the PEC curves are usually generated using a guide camera, but they can be done with a reticule eyepiece.  Anyway, if your mount supports it, how to build the curves should be well covered in the manual.  BTW, I’ve used the batch training mode of PECTool a program made to do the training on some Celestron mounts, and it is very easy to use.  Very Sweet.

I think that’s enough for this post.  If you have questions or comments just ask here or send me and email and I’ll do my best to answer up.

al