1. April 8/9, 2003 Green Bank GBT PTCS Conceptual Design Review Richard Prestage, Bojan Nikolic, Dana Balser 18 th August 2006 Adjusting the GBT Surface: Towards 100 GHz operation

2. 2 How to make a 100m telescope work at 50 GHz … on the way to 115 GHz Pointing and surface accuracy are equally challenging I will only talk about surface accuracy today, pointing is a whole other story

3. 3 Overview of talk 1.Review basic theory / causes of loss of telescope efficiency 2.Briefly describe basic “Phase I” GBT solutions 3.Describe the technique of phase retrieval (“out-of- focus”) holography and its application to the GBT

4. 4 Acknowledgements Everyone who has worked on the active surface (most recently Jason Ray, J.D. Nelson, Melinda Mello, Fred Schwab). Richard Hills and colleagues who developed the analysis approach we use here Bill Saxton for the line graphics for this talk

5. 5 Performance Metrics Telescope performance can be quantified by two main quantities: 1. Image quality / efficiency: –PSF / Strehl ratio (optical) –Beam shape / aperture efficiency (radio) 2. Ability to point it in the right direction Image quality is determined by accuracy and alignment of the optics

6. 6 Image quality and efficiency Theoretical beam pattern (point spread function) defined by Geometric Theory of Diffraction Aperture efficiency: Power incident on antenna Power collected by feed η = Max. value: η = 1

7. 7 Quantifying telescope performance Two theorems: –Reciprocity Theorem: Angular response of a radio telescope when used as a transmitting antenna is the same as when it is used as a receiving antenna –Fourier Transform theorem: Far field electric field pattern is the Fourier transform of the aperture plane distribution Two main causes of loss: –Losses related to the amplitude of the electric field –Losses due to the phase of the electric field See Goldsmith Single-Dish Summer School Lecture for excellent overview of these topics

8. 8 Reciprocity Theorem Performance of the antenna when collecting radiation from a point source at infinity may be studied by considering its properties as a transmitter

9. 9 Fourier transform relationship Far-field beam pattern is Fourier transform of aperture plane electric field distribution

10. 10 Aperture plane Losses: Blockage efficiency: η b Taper efficiency: η t Spillover efficiency: η s Phase efficiency: η p Ideal telescope: η a = 1. 1. 1. 1 Real telescope: η a = η b η t η s η p 0.8 x 0.8 x 0.8 x 0.8 = 0.41

11. 11 Blockage efficiency Effelsberg 100 mNRAO 140 Foot Conventional Telescope: η b = 0.85 – 0.9 GBT: η b = 1.0

12. 12 Illumination efficiency – taper and spillover Idealized uniform illumination

13. 13 blue = taper loss, red = spillover loss Gaussian-illuminated zero phase error unblocked circular antenna: η a = η t η s = 0.815 (maximum) for 11dB edge taper η a = η t η s = ~ 0.7 for ~15dB edge taper (GBT ) Illumination efficiency – taper and spillover

14. 14 ideal telescope with edge taper

15. 15 real telescope with phase losses Amplitude of electric field is largely unchanged Irregularities (deformations) in mirrors and misalignments cause phase errors => phase losses. Large scale errors (mis-alignments) may have predictable effects on beam pattern (e.g. astigmatism) Distribution of small-scale errors is generally unknown

16. 16 real telescope with phase losses Ruze formula: ε = rms surface error η p = exp[(-4πε/λ) 2 ] “pedestal” θ p ~ Dθ/L η a down by 3dB for ε = λ/16 “acceptable” performance ε = λ/4π Error distribution modeled by Ruze

17. 17 Summary Maximum aperture efficiency η t η s (feed illumination) ~ 0.7 Large-scale phase errors (e.g. misalignment of secondary) affect main beam and near-in side lobes Random surface errors cause loss of efficiency and large scale error pedestal Can use Ruze formula to define equivalent wavefront error

18. 18 Scientific Requirements (GHz)

19. 19 Challenges for large telescope design How do you achieve 200 µm accuracy – the thickness of two human hairs – over a 100m diameter surface – an area equal to 2 1 / 4 football fields ?

21. 21 What is possible? The Astronomical Journal, February 1967

22. 22 Solutions… The Astronomical Journal, February 1967

23. 23 GBT Solutions… Innovative design/construction Careful initial alignment Active surface / FE model Calibration measurements of residuals (OOF holography) Real-time monitoring/dynamic adjustments (OOF holography) (Potential alternative: use laser rangefinders to measure absolute position of all optical elements and correct appropriately.) <= Original <= Now <= Future

24. 24 Phase I – Static alignment and use of Finite Element Model

25. 25 Homologous design

26. 26 Homologous design

27. 27 Focus Tracking Changing parabola causes change in location of prime focus (focal length changes, parabola “slides downhill”) Feedarm also flexes under gravity Six degree of freedom (Stewart platform) subreflector mount relocates subreflector to correct position

28. 28 Subreflector focus tracking X,Y,Z = A + B cos(el) + C sin(el) Xt, Zt = Const

29. 29 GBT active surface system Surface has 2004 panels –average panel rms: 68 µm 2209 precision actuators Operates in open loop from look-up table generated from Finite Element Model + OOF corrections

30. 30 One of 2209 actuators. Actuators are located under each set of surface panel corners Actuator Control Room 26,508 control and supply wires terminated in this room Surface Panel Actuators

31. 31 Photogrammetry Basis for setting actuator zero-points at “rigging angle” (~ 50 degrees) Sets lower-limit on small-scale (panel to panel) error of around ~ 250 µm

32. 32 Mechanical adjustment of the panels

33. 33 Finite Element Model Predictions

34. 34 FE Model - Efficiency and Beam Shape Focus tracking and FE Model: Acceptable surface to 20GHz

35. 35 Phase II – “Out of focus” holography

36. 36 Reminder – what we are trying to measure

37. 37 Holography

38. 38 Traditional (phase-reference) holography Dedicated receiver to look at (usually) a terrestrial transmitter (at low elevation) or geostationary satellite Second dish (or reference antenna) provides phase reference Measure amplitude and phase of (near or far)-field beam pattern Fourier transform to determine amplitude and phase of aperture illumination

39. 39 Alternative – phase-retrieval holography There are many advantages to traditional holography, but also some disadvantages: –Needs extra instrumentation –Reference antenna needs to be close by so that atmospheric phase fluctuations are not a problem –S/N ratio required limits sources to geostationary satellites, which are at limited elevation ranges for the GBT (35  -45  ) Alternative: measure power (instead of phase and amplitude) only, recover phase by modeling

40. 40 “out-of-focus” holography Hills, Richer, & Nikolic (Cavendish Astrophysics, Cambridge) have proposed a new technique for phase-retrieval holography. It differs from “traditional” phase-retrieval holography in three ways: –It describes the antenna surface in terms of Zernike polynomials and solves for their coefficients, thus reducing the number of free parameters –It uses modern minimization algorithms to fit for the coefficients –It recognizes that defocusing can be used to lower the S/N requirements for the beam maps

41. 41 Some mathematics Consider the combination of a perfect parabolic antenna with aperture function A 0, and phase errors Q(k). If Q small, A  A 0 (1+ i Q), and the far-field electric field pattern is E = FT [A 0 (1+ i Q)] = E 0 + i [E 0  FT (Q)] = E 0 + i F (defining F = E 0  FT (Q); F contains all the information about Q) Power pattern of the antenna is then P = |E 0 | 2 + |F| 2 + 2[  (E 0 )  (F)  (E 0 )  (F)] Small defocus  last term is negligible, and Q is derived from fitting for |F| 2 Large defocus  end term dominates and different defocus values weight  (F) and  (F) differently to obtain independent information about F

42. 42 Technique Make three Nyquist-sampled beam maps, one in focus, one each ~ five wavelengths radial defocus Model surface errors (phase errors) as combinations of low-order Zernike polynomials. Perform forward transform to predict observed beam maps (correctly accounting for phase effects of defocus) Sample model map at locations of actual maps (no need for regridding) Adjust coefficients to minimize difference between model and actual beam maps.

43. 43 Technique Typically work at Q-band (43 GHz in continuum) Some tests done at Ka-band Observe brightest calibrators in sky (e.g. 3C273), sources ~10 Jy Data acquisition takes ~ 30 minutes Data analysis takes ~ 10 minutes

44. 44 Zernike polynomials z2: phase gradient (pointing shift) z5: astigmatismz8: coma aperture plane

45. 45 Zernike examples

46. 46 Zernike examples

47. 47 Zernike examples

48. 48 Scanning pattern

49. 49 Typical data Q-band (43 GHz)

50. 50 Typical data

51. 51 Closure: before (wrms = 370 µm)

52. 52 Closure: after (wrms = 80 µm)

53. 53 Application: Gravity Make measurements over a range of elevations Assume linear elastic structure: z i (θ) = a sin(θ) + b cos(θ) + c Make measurements under benign night-time conditions (low wind, minimize thermal gradients )

54. 54 Gravitational Deformations

55. 55 Gravity model

56. 56 Gravity Model

57. 57 Gravity Results: Summary OOF technique can easily measure large-scale wavefront errors with accuracy ~ 100µm Large scale gravitational errors corrected via OOF look-up table Benign night-time rms ~ 350µm Efficiencies: 43 GHz: η S = 0.67 η A = 0.47 90 GHz: η S = 0.2 η A = 0.15 Now dominated by panel-panel errors (night-time), thermal gradients (day-time)

58. 58 Application: Thermal gradients We know that thermal effects in the feed-arm displace the subreflector from the nominal position This mis-collimation primarily appears astigmatism- like, and also affects the pointing Use the measured pointing offsets to deduce and correct for the subreflector displacement Improve pointing and efficiency simultaneously

59. 59 Effect of subreflector displacement

60. 60 Thermal effects – 2 nd and 5 th order fits

61. 61 Azimuth LPC versus astigmatism

62. 62 Elevation LPC versus astigmatism

63. 63 Daytime thermal variations 12 th January 2006 8:00am (top left) 6:00pm (bottom right) Sunny, temperatures: - 3.4C (start) 14C (middle) 2.5C (end)

64. 64 Thermal Effects – “real-time” correction rms ~ 330µm rms ~ 220µm

65. 65 Thermal Results: Summary Some correlation between azimuth LPC and x-type astigmatism, less clear for elevation Astigmatism is caused by a combination of factors rather than simple mis-positioning of the subreflector Daytime thermal aberrations are large-scale and slowly varying, and so can be removed by “real-time” measurements.

66. 66 Conclusions GBT surface performance delivered by combination of approaches: –Homologous design + focus tracking + FE Model => 20 GHz –OOF holography for gravitational corrections => 50 GHz Large scale gravitational errors corrected via OOF look-up table: –Benign night-time rms ~ 350µm Efficiencies: 43 GHz: η S = 0.67 η A = 0.47 90 GHz: η S = 0.2 η A = 0.15 (W-band rx, better for Penn Array) Now dominated by panel-panel errors (night-time), thermal gradients (day-time)

67. 67 Future work…. Extend current technique using Penn Array (8x8 element bolometer array working at 90GHz) Potential collaboration with JWST Wavefront Sensing and Controls Group (more sophisticated techniques) Concentrate for now on small-scale errors – actuator zero-point setting. Photogrammetry and/or traditional holography?