Create PE Curve

Important: the curve-fitting calculations are CPU intensive and could take seconds or even tens of seconds to calculate the best-fitting Fourier-series. A small pop-up dialog appears and an hour-glass cursor appears while processing so you know calculations are going on. Everything is recalculated if you change RA Axis, Interpolate Points, or change the drift fitting polynomial.

 

Most of the calculations and fit optimizations are hidden and occur automatically. This dialog is separated into three sections. The top is the graph area which will display the PE curve and data points.

Note that there is a scroll bar below the graph which allows you to scroll across the data to see how it matches the all of the PE data you are analyzing. There are also buttons on the left and right of the scroll bar that allow you to jump exactly one worm period ahead or behind (unless you have reached the beginning or end of the data). Also, as you move the mouse over the graph the current relative time of the data (X-Axis) and the arc-seconds (Y-axis) are displayed above the graph.


Graph Type

There are four graph types: Periodic Error, Error Histogram, Frequency Spectrum, and Frequency Spectrum(secs).

Periodic Error: Shows the fitted curve that PEMPro created against the original data. This is the default display when this dialog opens. Moving the cursor over the graph window will show the phase of the mount (x-axis) and arc-seconds (y-axis).

Error Histogram: When selected the graph will show the histogram plot of the errors (last column in the Data Points Table). This histogram plot shows the distribution of these errors. If the distribution is broad then the PE curve is not likely very accurate. If it is asymmetrical that might signal a physical problem.

Moving the mouse over the graph will display the error value and the number of instances found for it. The blue line is the center-point (0 arc-sec error). The buttons to the left and right of the scroll bar on the bottom allow you to increase or decrease the resolution of the histogram.

Moving the cursor over the graph window will show the arc-seconds error (x-axis) and the number of instances in the data where this amount of error occurred (y-axis).

Frequency Spectrum: Shows the periodic error components in inverse units of "worm periods".

In almost all mounts are a number of spinning gears that ultimately allow the mount to track at nearly perfect sidereal rate. Because there are always very slight errors in the manufacturing process, every one of those gears is not perfectly round. They are shaped more like an ellipse, but the error is so small you might not be able to actually tell that the gears are not perfectly circular.

Now because each gear is an ellipse it causes the mount to move faster when on the longest diameter of the ellipse and slower on the shortest edge. If you where to chart the motion produced by the gear it would look like a sine wave with a specific duration. Most often the gears also rotate an exact integral number of times in one worm period. This ratio, whether it is an integral or not, is sometimes called a fundamental.

So, if the worm period were exactly 480 seconds and a gear rotates 10 times in each 480 second interval it has a Fundamental of "10" because it would produce a sine wave that repeats 10 times in 480 seconds. In actual time that would mean each rotation of the gear takes 480/10 = 48 seconds.

For example in the picture below there are major fundamentals at 1, 2, and smaller fundamentals at about 0.5 and 10.

In physical terms this means that this mount, which has a worm period of 382.95 seconds has repeating errors at:

382.95 / 1 = 382.95 seconds (Worm period divided by 1.)

382.95 / 2 = 191.48 seconds (Worm period divided by 2.)

382.95 / 10 = 38.29 seconds (worm period divided by 10

382.95 / 0.5 = 765.9 seconds (this could be real harmonic but is probably just drift fitting error)

Once you note the fundamentals you can customize PEMPro to look at only those fundamentals with the menu option: File | Edit Fundamentals. which is described below.

Moving the cursor over the graph window will show the frequency in multiples of worm period error (x-axis) and the arc-seconds error (y-axis) of this component. The amplitude of of the data peaks may not match the amplitudes in the FFT Waveform Analysis table because the peaks have a non-zero width and the actual amplitude is related to the area under the peak.

Frequency Spectrum(secs): Shows the periodic error components in units of seconds. Moving the cursor over the graph window will show the frequency in seconds (x-axis) and the arc-seconds error (y-axis) of this component. The amplitude of of the data peaks may not match the amplitudes in the FFT Waveform Analysis table because the peaks have a non-zero width and the actual amplitude is related to the area under the peak.


FFT Waveform Analysis: This table has the fundamental waveforms of the period of the worm gear. PEMPro automatically calculates the optimized values for each fundamental and displays the amplitude and phase.

You can check or uncheck each fundamental to see how the waveform changes. As you do this watch the Total RMS Error in the upper right. This is a measure of “goodness of fit” of the curve to the data. The lower the RMS Error, the better the fit. That shows the root-mean square error in arc-seconds of the fitted PE curve to the data.

Below this is the Periodic Error of your mount in arc-seconds as calculated by the terms in use. Important: be sure that the Image Scale value in the lower left corner is correct for your camera. If it is not you need to Cancel this dialog, change the image scale in the Analyze page and come back to this dialog.

If you are not sure which axis is the RA axis you can switch between axes with the RA Axis combo box.

Drift Fitting is the most important user-controllable parameter. You want to set this to the lowest order that makes a minimal impact on the Total RMS error. If you set it too low any drift (very likely) will skew the FFT curve fitting. If you set it too high, especially if you only have a couple worm periods of data will start to artificially remove the periodic error. Usually linear or as most, quadratic, is best. When this dialog opens PEMPro makes a guess on the order to use.

A good rule of thumb is that you never want to initially set it to a higher order than Quadratic. Start from there and try lowering the drift order while watching the RMS error and how the curve matches the data. Sometimes dropping the order will actually lower the RMS error (that is good). Do your best to eyeball the best match.

The last section is the imported data. At any moment you can see the value calculated by the FFT analysis and the fit error.

RA Axis: PEMPro will by default select the axis it thinks is the Right Ascension (RA) Axis. Usually you can tell the declination axis from the right ascension axis because the declination axis will have a very low periodic error because it is just drifting. If the data looks too flat or the periodic error is less than an arc-second then you may be looking at the Declination axis instead of the RA Axis. You can change it with this control.

Note that it is very important that you select the correct axis for proper correction of periodic error. Use the Setup/Calibration Wizard to find the correct axis if you are unsure you have this parameter set correctly.

Cancel: Exit without creating a curve.

Export Data: Exports the data points and FFT parameters for analysis in an external program like Excel.

Create PE Profile and Close : Press this after you are satisfied that you have an optimum periodic error curve. This will close this dialog and display the Program Mount Page.


Menu Options

Export Data: Exports the data points and FFT parameters for analysis in an external program like Excel.

Create PE Profile and Close : Press this after you are satisfied that you have an optimum periodic error curve. This will close this dialog and display the Program Mount Page.

Edit Fundamentals: Use this option to edit the fundamentals. This is usually used in conjunction with the Frequency Spectrum graph.

New Fundamental: Enter a number here and press Add to add it to the fundamentals list.

Add: pressing this will add the fundamental you entered to the list on the right.

Delete: Click on an item in the Fundamentals list and this button will activate. Click it to delete the fundamental.

Apply: Activates when you have added or deleted a fundamental. Pressing it will cause the Create PE Curve dialog to recalculate and display the periodic error curve. The Edit PE Fundamental Frequency dialog will remain open.

OK: Pressing it will cause the Create PE Curve dialog to recalculate and display the periodic error curve. The Edit PE Fundamental Frequency dialog will close.

Cancel: Pressing will exit without applying any changes made to the Fundamental list. Note that any previous changes to the Fundamentals list that have been applied are not canceled.