Tape circumference = 105.866 x 25.4 x pi = 8477.5 mm, so 1 arc sec = 6.54 um movement
Heidenhain or Renishaw? Renishaw RG2 system looks good and is much cheaper. Some comparisons:
Heidenhain:
Renishaw:
Ellipticity and Eccentricity: The ellipticity and eccentricity of the track will cause measurement errors. Drawing 17-00-2 specifies the scanning gap to be 0.8 +/- 0.1 mm (0.032 +/- 0.004 inches). This corresponds to a worst case error of +/- 15 arc sec. Multiple read heads can be used to help correct for this. PMAC can make a simple sum of encoder inputs to control a given axis.
Backlash: Azimuth axis is driven through a reducer with 10 minute backlash. The drive wheel is 8 inch in diameter, track diameter is 110.3 inch (mid-point). Hence the telescope backlash is 10/(110.3/8) = 44 arc sec. A twin motor antibacklash configuration will be used.
RON285 gives 1 Vpp output with 18,000 lines/rev. The recommended measuring step is 1.8 arc sec, corresponding to 10-fold interpolation. Stated accuracy is +/- 5 arc sec. Price approx $3K (+ interpolator approx $500).
RON287 gives 1 Vpp output with 18,000 lines/rev. The recommended measuring step is 0.36 arc sec, corresponding to 50-fold interpolation. Stated accuracy is +/- 2.5 arc sec. Price approx $5K (+ interpolator approx $900).
Backlash: Elevation is also driven through a reducer with 10 minute backlash. Rack and pinion reduction ratio is approx 10, and the telescope backlash is 1 arc minute. Twin motor drive will again be used.
We will almost certainly use the Renishaw tape on the theta axis which has a less demanding accuracy requirement.