adjusting the gbt surface: towards 100 ghz operation
DESCRIPTION
Adjusting the GBT Surface: Towards 100 GHz operation. Richard Prestage, Bojan Nikolic, Dana Balser 18 th August 2006. How to make a 100m telescope work at 50 GHz. … on the way to 115 GHz Pointing and surface accuracy are equally challenging - PowerPoint PPT PresentationTRANSCRIPT
April 8/9, 2003 Green BankGBT PTCS Conceptual Design Review
Richard Prestage, Bojan Nikolic, Dana Balser
18th August 2006
Adjusting the GBT Surface: Towards 100 GHz operation
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
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
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
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
Image quality and efficiency
Theoretical beam pattern (point spread function) defined by Geometric Theory of Diffraction
Aperture efficiency:
Power incident on antennaPower collected by feedη =
Max. value: η = 1
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
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
Fourier transform relationship
Far-field beam pattern is Fourier transform of aperture plane electric field distribution
10
Aperture plane
Losses:• Blockage efficiency: ηb • Taper efficiency: ηt • Spillover efficiency: ηs
• Phase efficiency: ηp
Ideal telescope:ηa = 1 . 1 . 1 . 1
Real telescope:ηa = ηbηt ηs ηp
0.8 x 0.8 x 0.8 x 0.8 = 0.41
11
Blockage efficiency
Effelsberg 100 m NRAO 140 Foot
Conventional Telescope: ηb = 0.85 – 0.9
GBT: ηb = 1.0
13
blue = taper loss, red = spillover loss
Gaussian-illuminated zero phase error unblocked circular antenna:
ηa = ηt ηs = 0.815 (maximum) for 11dB edge taperηa = ηt ηs = ~ 0.7 for ~15dB edge taper (GBT)
Illumination efficiency – taper and spillover
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
real telescope with phase losses
Ruze formula:
ε = rms surface error
ηp = exp[(-4πε/λ)2]
“pedestal” θp ~ Dθ/L
ηa down by 3dB for ε = λ/16
“acceptable” performanceε = λ/4π
Error distribution modeled by Ruze
17
Summary
• Maximum aperture efficiency ηt ηs (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
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 21/4 football fields ?
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
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
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
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
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
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
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
“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
Some mathematics
• Consider the combination of a perfect parabolic antenna with aperture function A0, and phase errors Q(k).
• If Q small, A A0(1+ iQ), and the far-field electric field pattern is
E = FT [A0(1+ iQ)]
= E0 + i[E0 FT (Q)] = E0 + iF
(defining F = E0 FT (Q); F contains all the information about Q)
• Power pattern of the antenna is then
P = |E0|2 + |F|2 + 2[(E0)(F) (E0)(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
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
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
53
Application: Gravity
• Make measurements over a range of elevations
• Assume linear elastic structure:
zi(θ) = a sin(θ) + b cos(θ) + c
• Make measurements under benign night-time conditions (low wind, minimize thermal gradients)
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: ηS = 0.67 ηA = 0.47
90 GHz: ηS = 0.2 ηA = 0.15
• Now dominated by panel-panel errors (night-time), thermal gradients (day-time)
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
63
Daytime thermal variations
12th January 2006
8:00am (top left) 6:00pm (bottom right)
Sunny, temperatures: -3.4C (start)14C (middle)2.5C (end)
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
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: ηS = 0.67 ηA = 0.4790 GHz: ηS = 0.2 ηA = 0.15 (W-band rx, better for Penn Array)
• Now dominated by panel-panel errors (night-time), thermal gradients (day-time)
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?