1. January 6, 2005 URSI Nation Radio Science Meeting, Boulder, CO. Pointing and Focusing the GBT K. T. Constantikes NRAO Green Bank

2. URSI National Radio Science Meeting, Boulder, CO. 2 January 6, 2005 Telescope Structure and Optics

3. URSI National Radio Science Meeting, Boulder, CO. 3 January 6, 2005 PTCS / High Frequency Environmental Envelope ss

4. URSI National Radio Science Meeting, Boulder, CO. 4 January 6, 2005 Scientific Requirements: ½ to 1 Hour Stability

5. URSI National Radio Science Meeting, Boulder, CO. 5 January 6, 2005 Pointing Coefficients Entire pointing error budget is: 0.32 mm subreflector X translation, or 0.41 mm subreflector Y translation, etc. Entire pointing error budget is: 0.32 mm subreflector X translation, or 0.41 mm subreflector Y translation, etc. Feed arm tip moves ~ 400mm as elevation changes from horizon to zenith: ~ 250 arcsec of elevation pointing ~ 140 mm of focus shift > 2 orders of magnitude improvement needed! Feed arm tip moves ~ 400mm as elevation changes from horizon to zenith: ~ 250 arcsec of elevation pointing ~ 140 mm of focus shift > 2 orders of magnitude improvement needed!

6. URSI National Radio Science Meeting, Boulder, CO. 6 January 6, 2005 Effects and Current Best Performance Gravity: Model Fit Temp Gradient: With and W/O Linear Model Track/Alidade: Astronomy, Inclinometers Wind: Estimated from Astronomical Data, Inclinometers Vibration: Wind gusting, Max ~ 20 MPH Servo: Tracking Error per Axis Inertial: Prelim from QD “Hysteretic”, Inertial, Bearing, Encoder, etc. Model Residuals from All-Sky and Single Source Tracking, 10/03 to 11/04 Includes Symmetric Thermal Model, Azimuth Dependent Wind, Non-Parametric Astronomical Estimates of Track Effects SourceFocusAzEl Gravity~140mm~8”~250” Temp Gradient ~25mm~20”~40” Track~7” Wind~0”.3/(m/s)^2 Vibration~3” Servo~1”.5 to 2.5 Etc…2”? Conditions68 th 95 th 24 Hrs, 20-80 El, < 5 m/s: Focus1.9mm5.1mm Azimuth2”.77”.3 Elevation3”.99”.8 0000-0800, 3.5 m/s: Focus1.0mm2.8mm Azimuth2”.35”.4 Elevation2”.77”.7

7. URSI National Radio Science Meeting, Boulder, CO. 7 January 6, 2005 Gravity, Structure Temperature Gradient, and Wind Model Gravity terms, linear combinations of structure temperatures, and alidade-relative wind transformed to linearized space (T). 23 temperature sensors… Linear combinations of temperatures enforce symmetry conditions, e.g., mirroring about plane of telescope symmetry Robust least-squares fitting to linear model (m) Subsequent non-parametric estimate of residuals as a function of azimuth and elevation (f, g) Dataset contains ~ 11000 separate astronomical observations from “jack-scans” in all-sky or single- source track modes

8. URSI National Radio Science Meeting, Boulder, CO. 8 January 6, 2005 Confidence and Significance of Gravity, Thermal, Wind Model Coefficients (Bootstrap) Large contribution of HFA thermal gradient to focus X wind V 2 term (elevation) is significant and stable… Agrees with inclinometer T 3 F ~ N(6.8, 0.3) V x 2 Term ~ N(0.25, 0.03) Track tilt (Cos) contribution to elevation error Cos(Az) Term ~ N(3.4, 0.2) Large alidade thermal term for elevation. 0.1° C sensor accuracy is on the edge… T 4 E ~ N(29.3, 1.2)

9. URSI National Radio Science Meeting, Boulder, CO. 9 January 6, 2005 Correcting Focus for Thermal Distortions Corrected via robust linear regression of linearized features: Temperature differences Gravity model Wind velocities in alidade-relative frame Include k-nearest neighbor estimates of az, el anomalies Current best model has 68% at < 2mm Corrected via robust linear regression of linearized features: Temperature differences Gravity model Wind velocities in alidade-relative frame Include k-nearest neighbor estimates of az, el anomalies Current best model has 68% at < 2mm

10. URSI National Radio Science Meeting, Boulder, CO. 10 January 6, 2005 Azimuth Track Effect on Elevation Axle Pose: Side to Side Motions El Bearing Casting X2 Y2 Y1 X1 Vertex X (Alidade) Y (Alidade) Acceleration in X direction, rotations around Y Measurement  = 0”.6 Blue and Red are same data, symmetry condition applied Mean wind V 2 in alidade frame Acceleration in Y direction, rotations around X

11. URSI National Radio Science Meeting, Boulder, CO. 11 January 6, 2005 Azimuth Track Effect on Elevation Axle Pose: Torsional Motions 1  difference is 1”.4 1  measurement 1”.0 Measurement  = 0”.6  0 : Inclinometer level,  1 : tempco of angle, P x, P y are alidade relative V 2 wind,  4 and  5 are track tilt coefficients. Bootstrap estimates of tilt coefficient uncertainty ~0”.2. El encoder is in X2 frame! “Jaggies” are real (repeatable). 11/28/04 Data, low wind 12/12/04 Data, windy and gusty

12. URSI National Radio Science Meeting, Boulder, CO. 12 January 6, 2005 Comparison to Astronomical Estimate, Tilt Stability over Time Azimuth Elevation Track tilt has changed over 2 days…

13. URSI National Radio Science Meeting, Boulder, CO. 13 January 6, 2005 Wind Pumped Vibration of Feed Arm WRT Elevation Axle High Q structure rejects wind gusts except over narrow range of frequencies, mitigates wind pumping.

14. URSI National Radio Science Meeting, Boulder, CO. 14 January 6, 2005 Servo Resonances From Half Power Track Experiment Structural vibration at start of scan ~ 0.04 (Limit cycle?) and ~0.30 Hz (Position Loop Peaking?) RMS < 1”… Substantial track degradation since this? “Good” track interval?

15. URSI National Radio Science Meeting, Boulder, CO. 15 January 6, 2005 Predicting Tracking Error From Inclinometers Samples (10 Hz) 8500 data points fit by linear combination of two measurements (smoothed X2 and Y2 inclinometers) ! Time scales and direction (elevation) suggest track bumps.

16. URSI National Radio Science Meeting, Boulder, CO. 16 January 6, 2005 Vibration, Estimating Positions from Acceleration Inclinometer 1” apparent rotation = 4.8  G = 3  m motion @ 0.6 Hz 5 Hz sampling BW noise ~ 0.3”, 30 sec random walk ~ 100  m. Accelerometer ~ 2  G/root-Hertz, or 10 sec random walk ~ 400  m (5 Hz BW) Limiting BW to structural freqs extends interval x 5 (50 sec 100  m with inclinometer), disciplining with other constraints even better (e.g., QD, LRF) Currently no servos capable of correcting for 0.6 Hz (lowest structural mode) and higher vibrations – post- processing for actual position on sky Structural health monitoring via modal analysis ~ 60 micron motions

17. URSI National Radio Science Meeting, Boulder, CO. 17 January 6, 2005 Acknowledgements, Etc. Prestage and Balser: Astronomical data collections and reduction to pointing offsets Condon: Scientific requirements on pointing, focus Much more info on instruments in next presentation…