Generalities on Metrology and Microwave Holography

Transcription

1 Generalities on Metrology and Microwave Holography Richard Prestage National Radio Astronomy Observatory Second Sardinian Summer School on Radio Astronomy and Radio Science

2 Outline of Talk Part I: General Metrology largely aimed at telescope pointing Types of antenna Quantities which affect telescope performance Stability criteria Approaches to metrology and instrumentation Part II: Microwave Holography measuring and setting the telescope surface Traditional (with phase, satellite) holography Near-field (with phase, beacon) holography Phase retrieval ( out-of-focus ) holography Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 2

3 Antenna Types long wavelength arrays centimeter transit cm/mm wave antenna millimeter antenna This talk will focus on the metrology requirements for antenna types 3 and 4 Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 3

4 Quantities to be Controlled Most telescopes perform as an ideal telescope at the low end of their frequency range. To observe at high frequencies, we need to measure and correct for departures of the telescope from ideal behavior: Pointing Collimation (focus) Surface Accuracy (wavefront phase errors) Path Length In the presence of: Gravity Temperature Wind Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 4

5 Departures from Ideal (I) [Refraction] Misalignment of the antenna structure (e.g. non-perpendicularity of the Az and El axes) May change (slowly) with time e.g. effects due to non-flatness of azimuth track. Deformations due to gravity (affects all four components). Most well behaved deformation; depends only on elevation angle. Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 5

6 Departures from Ideal (II) The effect of temperature change over time and location in the structure is to distort the optical alignment. Although telescopes are designed to minimize these effects, they can still be substantial. While temperature effects are repeatable, the state of the structure (distribution of temperatures, whether the structure is in thermodynamic equilibrium) is not well known. Wind loading can cause structural loads that significantly distort the telescope (i.e. cause the optical properties to change). Again, the effects are repeatable, but the flow field will not be well known. Structural vibrations can be excited by wind or servo system drives. For the GBT these vibrations can be significant, and have modal frequencies from 0.6Hz and up. The largest magnitude motions are in the feedarm assembly. Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 6

7 Stability Criteria Pointing Errors The normalized power gain g can be written as: ρ g( ρ) = exp 4ln(2) θ where ρ is the angular displacement from the beam center. In most cases the sensitivity lost through the reduction of mean gain <g> can be recovered by additional integration. fluctuations in gain have much worse consequences than the mean gain loss, both in terms of data quality and operational efficiency (Condon, 2003). 2 σ θ 10% flux errors: 5% flux errors: σ θ Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 7

8 Stability Criteria Focus Errors variation of relative power gain g a resulting from axial defocusing is given by: g A = exp f 4ln(2) θ A 2 Where θ A is the FWHM beamwidth in axial focus. g A > 0.99 for good focusing: axial focusing error < λ/16 (GBT) For a typical Cassegrain telescope f < λ/10. Axial focusing beamwidth in wavelengths is roughly proportional to (f/d) 2 and independent of D. Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 8

9 Stability Criteria - Wavefront Phase Error If the rms deviation from the ideal aperture is ε and the error correlation length is much smaller than the aperture diameter, the aperture efficiency is multiplied by the factor (Ruze 1966): η S exp 4πε λ 2 The traditional requirement for the efficiency η s of a good aperture is: ε < λ/16, so η s 0.54 A looser criterion for usable performance is that the forward gain, which is proportional to η s / λ 2, not decline as wavelength decreases. This implies: ε < λ/4π, so η s 0.37 Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 9

10 Typical Values Pointing accuracy λ/d Surface accuracy λ Tel. λ D θ θ ε GBT 3mm 100m µm SRT 3mm 65m µm ALMA 1.3mm 12m µm ALMA 350µm 12m µm Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 10

11 Error Budget Pointing (LMT) Source and Type of Error Uncorr. ( ) Corr. ( ) Method Environmental influences(quasi-static) a) Gravity Deformation Foundation << << Azimuth Rotation Structure << << Elevation Rotation Structure < LUT b) Wind Deformation (10 m/sec) Foundation << << Elevation FBC Cross Elevation FBC c) Thermal Deformation Foundation << << Azimuth Rotation Structure < FBC Elevation Rotation Structure < FBC Environmental Influences (Dynamic) Gusts on Servo Gusts on Structure Mechanical Alignment FBC Servo 0.3 Margin 0.3 Overall Pointing Error 0.75 Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 11

12 Error Budget Surface (LMT) Source and Type of Error Uncorr. (µm) Corr. (µm) Method Environmental influences(steady-state) a) Gravity Deformation BUS LUT Panels b) Wind Deformation (10 m/sec) BUS PANELS 6 6 Subreflector Lateral Offset Subreflector Defocus 6 6 c) Thermal Deformation BUS FBC PANELS Reflector Manufacturing Panels Subreflector Mechanical Alignment Panels Subreflector Margin 25 Overall Surface Error Budget 69 Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 12

13 Approaches to Metrology - Pointing Astronomically-defined pointing models, and offset pointing/focus calibration observations Temperature sensors to measure and compensate for thermal deformations Inclinometers to measure tilts / antenna deformations Quadrant Detector to measure relative location of subreflector [Use of laser rangefinders to measure absolute position of optical elements GBT] Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 13

14 Approaches to Metrology - Surface Use of passive means (insulation; homology) Photogrammetry for initial panel setting Microwave holography for static actuator zero-point measurements Use of FEA models / LUT for repeatable gravitational deformations Phase-retrieval holography to correct for residual gravitational deformations, and measure real-time thermal deformations Use of temperature sensors and FEA model to predict thermal deformations Direct measurement of relative actuator positions prototype, SRT [ Use of laser rangefinders for closed-loop control of actuators GBT] Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 14

15 Flexible Body Control Use auxiliary sensors in addition to main axes encoders. Modify indicated position to correct as well as possible for deformations in the structure Include these corrections into position loop. Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 15

16 Current State of the Art Conventional (astronomically derived) pointing models; offset pointing with calibration measurements Aided by thermal models and (real-time) inclinometry Open-loop control of actuators based on FEA models and LUTs Microwave holography to set actuator zero-points Residual gravitational terms and slowly varying large-scale thermal errors measured via out-of-focus holography SRT aiming for close-loop control with localized actuator displacement sensors Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 16

17 Structural/Air Temperature Sensors - GBT YSI 083 thermistors YSI 4800LC Thermistor Linearizing Circuit 0.15 C accuracy, -35 to 40 C 0.05 C interchangable accuracy 0.01 C resolution, 1 sec sampling 19 structure sensors 5 air sensors (forced convection cells, ~ 5 sec time constant) Structure thermal distortions Vertical air lapse Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 17

18 Temperature Sensors BUS R.Side EL Bearing Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 18

19 Structural Temperatures Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 19

20 Elevation Model Results Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 20

21 Inclinometers / Linear Sensors - ALMA Linear sensors measure to ends of CFRP encoder mount reference structure Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 21

22 Inclinometers - ALMA Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 22

23 Inclinometers - GBT AG gas-damped capacitive readout type from Wyler Zeromatic 2-axis (horizontal plane), both elevation bearings 0.1 short-term accuracy, 0.01 resolution ~1 sec damping, 17 Hz resonance 5 Hz sampling rate, 0.3 noise at 5 Hz Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 23

24 Inclinometers - GBT Accelerometer Cube Elevation Bearing Casting Three Point, Spherical Washer and Shim Leveled Mount Y Inclinometer X Inclinometer Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 24

25 Before and After Track Repair Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 25

26 Part II: Microwave Holography for Antenna Surface Measurements Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 26

27 Homologous Design Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 27

28 Homologous Design Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 28

29 Surface Adjustment Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 29

30 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 Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 30

31 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 Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 31

32 Fourier Transform Relationship A(x,y) B(u,v) Far-field beam pattern is Fourier transform of aperture plane electric field distribution Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 32

33 Illumination efficiency taper and spillover Idealized uniform illumination 33

34 Illumination efficiency taper and spillover blue = taper loss, red = spillover loss Gaussian-illuminated zero phase error unblocked circular antenna: η a = η t η s = (maximum) for 11dB edge taper η a = η t η s = ~ 0.7 for ~15dB edge taper (GBT) 34

35 Ideal Telescope with Edge Taper Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 35

36 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 Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 36

37 Surface Irregularities Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 37

38 Phase Errors Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 38

39 Phase Losses Error distribution modeled by Ruze 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 Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 39

40 Far Field Beam Pattern 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 Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 40

41 Traditional (phase-reference) holography Dedicated receiver to look at a geostationary satellite Second dish (or reference antenna) provides phase reference Measure amplitude and phase of far-field beam pattern Fourier transform to determine amplitude and phase of aperture illumination Standard Technique which has been in use for ~ 35 years (see e.g. Bennett et al. 1976). These examples from the GBT (Hunter et al. 2011). Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 41

42 B(u,v) = ΣA(x,y) exp[2πj(xu+yv)] where B = beam, A = aperture u,v are angles; x,y are distances Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 42

43 Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 43

44 Phase Reference Holography Advantages: Can be performed at reasonable elevation angles. High spatial resolution over the dish. High accuracy (~60µm for GBT system). Disadvantages: Generally can only be performed at one elevation. Long (hours) data acquisition time. Requires dedicated hardware Receiver requires unusually high dynamic range (70dB). Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 44

45 Phase Reference Holography Basic method: Measure complex beam pattern via interferometry Fourier transform to get phase and amplitude of E-field Convert phase to surface error GBT Ku-band holography system re-commissioned (December 2008): Two room-temp. LNBs, 10 khz filter and digital correlator New DROs with Digital PLLs (stability) Linux backend, sample rate = 28 Hz Allows 200-column, 2 x2 maps in 3 hours Reference signal path Main signal path Reference horn at top of feedarm Main receiver in Gregorian turret Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 45

46 Satellite Target Galaxy 28 = geostationary TV satellite Elevation = 44 o, well-behaved diurnal path GHz beacon (stable to < 1 khz) Typical phase stability (system + atmosphere) <2 rms in 36ms integrations Galaxy MHz Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 46

47 Holography Map Showing Panel Locations Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 47

48 Progression of Surface Adjustments Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 48

49 Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 49

50 Comparison to known panel errors Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 50

51 Recent (not ideal) Results Non-repaired actuators (due to structural inspections) Patch of 128 bad actuators (now fixed power supply problem) Ice damage

52 Near-Field (Beacon) Holography Similar to traditional with-phase holography. Use a radio beacon in the near-field (Fresnel region) of the antenna under test. Use of near field causes a rapid variation of phase across the aperture (Baars et al. 2007). Largely corrected for by displacing the feed from the primary focus. Residual correction applied to the aperture phase distribution after the Fourier transform. Higher order terms collected into a variable ε: A( x, y) B( u, v)exp{ ik( ux + vy) e ikε The terms in ε modify the direct Fourier transform dudv Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 52

53 Near-Field(Beacon) Holography Advantages: Nearby beacon allows high S/N, high-resolution maps Maps can be obtained relatively quickly (less than one hour) Beacon can be chosen to have convenient frequency/location Disadvantages: Maps obtained at a single, low elevation Requires dedicated hardware Possibility of multiple reflections from ground or near-by structures Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 53

54 Near-Field (Beacon) Holography - ALMA Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 54

55 Near-field (Beacon) Holography Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 55

56 Phase Retrieval (Out of Focus) Holography Measure power only (instead of amplitude and phase) of far-field beam pattern on bright astronomical calibrator Without the amplitude/phase, cannot do the inverse Fourier transform to get aperture plane values. Instead assume aperture amplitude and phase; do forward transform to predict beam pattern. Iteratively adjust aperture phase, varying phase until predicted beam map is in good agreement with observed map. Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 56

57 B(u,v) = ΣA(x,y) exp[2πj(xu+yv)] where B = beam, A = aperture u,v are angles; x,y are distances Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 57

58 Phase Retrieval (Out of Focus) Holography Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 58

59 Phase Retrieval (Out of Focus) Holography Advantages: Uses same receiver as used for astronomical measurements Measure the complete optical aberrations in the telescope Rapid maps (< five minutes) As a function of elevation As a function of time Disadvantages: Low spatial resolution (cannot resolve individual actuators) Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 59

60 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. Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 60

61 Typical data Q-band (43 GHz)

62 Typical data: before (rms = 370 µm)

63 OOF technique Measure power only (instead of phase and amplitude), recover phase by modeling A classic non-linear inverse problem: The forward model Conceptually relatively simple: only requires an FFT Beam switching, non-point like sources, atmospheric effects, off-axis pixels, etc., make it complex Parametrisation of surface errors Zernike polynomials Likelihood of data given model Take normally distributed errors Pointing errors, residual atmospheric emission, gain fluctuation can also be important Solver algorithm Levenberg-Marquardt maximum-likelihood 63

64 The OOF holography algorithm 64

65 Zernike Polynomials n = 1 Vertical pointing Horizontal pointing Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 65

66 Zernike Polynomials n = 2 X Astigmatism Focus + Astigmatism Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 66

67 Zernike Polynomials n = 5 Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 67

68 Approximate by adding higher Zernikes

69 Typical Data Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 69

70 Switch to Astrid Here Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 70

71 Recovered Phase Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 71

72 AutoOOF display Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 72

73 AutoOOF display Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 73

74 AutoOOF display Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 74

75 Gravity Model Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 75

76 Gravity Model Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 76

77 Thermal Distortions due to Solar Heating Time Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 77

78 Example Daytime AutoOOF Correction Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 78

79 How Long is it Good For? About 2 hours But probably depends on many factors including observing mode: Tracking a single source All-sky survey, etc. 3 Scans on OOF 25 min old (3C273) OOF 90 min old (J ) OOF 200 min old (J ) Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 79

80 Estimated error budget Small-scale errors: panel manufacturing plus gravity error: 127 µm residual actuator error: 80 µm panel corner setting error: 80 µm panel-scale thermal errors: 100 µm subreflector: 75 µm total small-scale error: = 211 µm Large-scale thermal error: 100 µm Total error: = 235 µm 80

81 Acknowledgements Bojan Nikolic (OOF holography) Todd Hunter, Fred Schwab, Steve White (with-phase holography) GBT Engineering Staff (temperature sensors, inclinometers ) Second Sardinian Summer School on Single-Dish Radio Astronomy and Radio Science 81