For the mount in the example above, a value of x0 = -5 arcseconds placed the curve in the center of the graph, a value of v = 0.45 arcseconds per image corrected the slow drift of the star, and a value of a - 0.0008 arcseconds per image removed the slowly increasing drift rate. Since images were taken every 15 sec-

onds, the v value shows that during the test the drive was falling behind the sky at an average rate of 0.03 arcseconds per second, or 1 arcsecond every 33 seconds.

However, the really interesting result is the periodic error with an amplitude of 10 arcseconds. The drive was tested under three conditions: with the telescope perfectly balanced, loaded so that the imbalance pushed the telescope in the direction the drive was running, and loaded so that the imbalance opposed the drive, retarding it. You will probably find that when you run your drive against a light load, you get significantly better and more consistent tracking. This is particularly important with periodic error correction, which relies on a consistent periodic error.

If your telescope has a fork mounting with a short polar axis, examine the declination error by plotting the y-axis data. In these instruments, the pressure of the worm on the drive gear can force the polar axis to wobble in declination so that the star traces a cyclical path across the CCD. A mounting with a long polar axis shaft resists wobbling more effectively than a short-axis one.

If unbalancing the telescope does not improve drive performance, examine its mechanical parts. It is not uncommon to find that the worm assembly fits loosely or is lightly held in place by weak springs. Check that none of the components have worn or slipped out of place. Consultation with the dealer or manufacturer may help and should precede any work, to avoid invalidating the warranty. If the drive is supposed to track within 5 arcseconds and you measure a peak-to-peak tracking error of 30 seconds, at the very least the dealer owes you a polite response.

If you suspect that your telescope tracks poorly, your CCD can help you assess the performance of the drive. You may find that what you thought the drive was doing and what it really does are not the same. Armed with information instead of hunches, you can optimize the drive and your tracking strategy.

4.5.4 Periodic Error Correction (PEC) Drives

Commercial telescopes may have periodic error correction (PEC) circuits in their drive electronics; that is, a programmable microprocessor that the observer can "train" to run at a rate calculated to offset a periodic error in the drive system. Typically, after training the PEC, the circuit eliminates about 90% of the periodic error. Although PEC is often used as an inexpensive way to produce marginally acceptable tracking from a poor drive gear, when PEC is applied to a drive that is already good, it produces superb correction.

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