Green Bank Telescope Performance

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1 Green Bank Telescope Performance Dana S. Balser GBT Performance July 2007 Pune, NCRA

2 Telescope Structure

3 Unblocked Aperture

4 Frequency Coverage

5 Telescope Control Focus Surface Pointing

6 Pointing Requirements + = = θ σ σ σ σ ρ ν θ θ ρ ρ 2 2 El 2 Az GHZ 740 arcsec 4ln 2 exp ) ( f g Condon (2003) %) ( Usable %) ( Good s s = = f f σ σ

7 Focus Requirements Δy g exp 4ln 2 a = θ a θ 4λ a Good ( g Usable ( g a a 2 > 0.99) Δy > 0.95) Δy s s s Axial < θ /16 < λ / 4 a < θ / 8 < λ / 2 a Δx s g exp 4ln 2 l = θl θ 6λ l Good ( g l > 0.99) Δx 2 s Lateral < θ /16 < λ / 3 l Plate Scale 3.7 / mm Q - band : λ = 7 mm Δx " s θ = 17.3 < 2.3 mm " f = 0.5 Srikanth (1990) Condon (2003)

8 Surface Requirements 2 4πε ηs exp λ η is the aperture efficiency for the surface. s ε is the rms surface error. S ν 2kT = η A a ' A g S ν k is Boltzmann's constant. T η is the aperture efficiency. a A ' A is the flux density. g is the antenna temperature corrected for the atmosphere. is the geometric primary area. Good : ε < λ /16 η 0.54 Usable : ε < λ / 4π η 0.37 s s Ruze (1966) Condon (2003)

9 Repeatable Errors Pointing Telescope misalignments: Azimuth track tilt Horizontal collimation Elevation axle collimation Encoder offsets Gravity: assume linear elastic structure ΔA Cos(E) = d b 0,0 1,1 + b 0,1 Sin(E) + Cos(A)Sin(E) d + 0,1 a Cos(E) 1,1 + Sin(A)Sin(E) ΔE = d 0,0 + c 1,0 Sin(A) + d 1,0 Cos(A) + b 0,1 Sin(E) + d 0,1 Cos(E)

10 Repeatable Errors Focus Gravity: assume linear elastic structure X = A Y = A Z = A x y z B B B z x y Cos(E) + Cos(E) + Cos(E) + C C C z x y Sin(E) Sin(E) Sin(E)

11 Repeatable Errors Surface Gravity: Homologous design (almost) Photogrammetry (50.3 deg) Zero-point Finite Element Model (FEM) Best Fit Parabola (BFP) Active Surface: 2004 Panels 2209 Actuators

12 Point Source Calibrators PCALS 4.0: 7108 sources Two-dimensional rms error < 0.2 arcsec 3 mm pointing calibrators Condon & Yin (2005)

13 Pointing Model Azimuth Series ΔA Cos(E) Elevation Series ΔE Balser et al. (2002)

14 Focus Model Axial Focus X = Y = Z = Cos(E) Sin(E) mm Cos(E) Sin(E) mm Cos(E) Sin(E) mm Ghigo et al. (2001)

15 Finite Element Model Gain Elevation Curve K-band (20 GHZ)

16 Finite Element Model Sidelobes O EL =12

17 Non-repeatable Errors Thermal 30 mm 3λ at 30 GHz 30 mm λ/3 at a frequency of 3 GHz 30 mm 3λ at a frequency of 30 GHz Usable ( g a > 0.95) Δy s < θ a / 8 < λ / 2

18 Non-repeatable Errors Wind 2 s σ (wind) m s 1 σ (wind) 2 '' 8 ( wind) arcsec 2 σ 1 at s = 6 m s 1 f = 0.22 at 20 GHz Usable ( σ s = 10%) f 0.20

19 Thermal Pointing and Focus Corrections Constantikes (2003)

20 Data Collection and Quality All-sky Observations Single Source Track Up-Down at Night Gravity NCP Source Temperature Gaussian Fits (Az, El, Focus) Polarization (LCP RCP) Direction (Forward Backward) Jack Scan

21 Thermal Model Focus Constantikes (2003) Term Coefficient Min-Max Significance Parameter M SR-Pri M VFA-Pri M HFA M BUS V1 M BUS V2 M BUS F M Offset M sin term M cos term

22 Thermal Model Azimuth Constantikes (2003) Term Coefficient Min-Max Significance Parameter M Alidade M HFA M BUS M VFA M CA, d(0,0) M NPAE, b(0,1) M IA, d(0,1) M AW, b(1,1) M AN, a(1,1)

23 Thermal Model Elevation Constantikes (2003) Term Coefficient Min-Max Significance Parameter M BUS M HFA M VFA M Alidade M IE,d(0,0) M HZCZ,b(0,1) M HZSZ,d(0,1) M AW,c(1,0) M AN,d(1,0)

24 Performance Blind Pointing

25 Pointing Data Quality Polarization [LCP - RCP] = ± 0.57 arcsec

26 Pointing Data Quality Direction [F - B] [F - B] Az El = arcsec = 2.3 arcsec

27 Cross-Elevation Uncertainty σ[ ΔA Cos(E)] = 2.7 arcsec

28 Elevation Uncertainty σ[ ΔE] = 4.8 arcsec

29 Focus Data Quality Polarization [LCP - RCP] = ± 0.81 mm

30 Focus Uncertainty σ[ Δf ] = 2.1mm

31 Performance Offset Pointing

32 Offset Pointing Uncertainty σ arcsec

33 Offset Focus Uncertainty σ 1.2 mm σ 1.2 mm

(Az, El) o (99, 37 ( ΔAz, ΔEl) (3.6 ΔAz ΔEl, Δt Δt ), 3.9 o o ) (10.8'/ m,11.

34 Performance Tracking Half-power in Azimuth Half-power in Elevation σ 2 = 1.2 arcsec o o ( Az, El) (290, 58 ) o o ( ΔAz, ΔEl) (1, 5 ) ΔAz ΔEl, Δt Δt (2'/ m,10' / m) (Az, El) o (99, 37 ( ΔAz, ΔEl) (3.6 ΔAz ΔEl, Δt Δt ), 3.9 o o ) (10.8'/ m,11.7 '/ o m) σ arcsec (Az, El) o o ( ΔAz, ΔEl) (4.0, 3.8 ) ΔAz ΔEl, Δt Δt o o (105, 43 ) (12.0'/ m,11.4' / m)

35 Power Spectrum Servo resonance 0.28 Hz

36 Servo Error

37 Performance Summary Benign Conditions: (1) Exclude 10:00 18:00 (2) Wind < 3.0 m/s Blind Pointing: (1 point/focus) σ 1(pointing) 5 arcsec σ (focus) 2.5 mm Offset Pointing: (90 min) σ 2(pointing) 2.7 arcsec σ (focus) 1.5 mm Continuous Tracking: (30 min) σ 2 1arcsec

38 Surface Improvements Holography Traditional Holography (Phase Coherent Holography) Maddalena Out-of-Focus Holography (Phase Retrieval Holography) Nikolic et al. (2006)

39 Zernike Polynomials Zernike (1934) Maeda (2003)

40 OOF Holography Gravity z i (E) = a Sin(E) + b Cos(E) + c Nikolic et al. (2006)

41 Gain-Elevation Curve FEM only FEM + OOF Nikolic et al. (2006)

42 OOF Holography Thermal Effects rms 300μm rms 330μm rms 220μm rms 220μm rms 220μm

43 Summary Surface Performance

Generalities on Metrology and Microwave Holography

Generalities on Metrology and Microwave Holography Richard Prestage National Radio Astronomy Observatory Second Sardinian Summer School on Radio Astronomy and Radio Science Outline of Talk Part I: General