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

Adjusting the GBT Surface:
Towards 100 GHz operation
Richard Prestage, Bojan Nikolic, Dana Balser
18th August 2006
GBT PTCS Conceptual Design Review
April 8/9, 2003 Green Bank
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
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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-offocus”) holography and its application to the GBT
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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
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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
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Image quality and efficiency
Theoretical beam pattern
(point spread function)
defined by Geometric
Theory of Diffraction
Aperture efficiency:
η=
Power collected by feed
Power incident on antenna
Max. value: η = 1
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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
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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
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Fourier transform relationship
Far-field beam pattern is Fourier transform of aperture
plane electric field distribution
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Aperture plane
Losses:
• Blockage efficiency:
• Taper efficiency:
• Spillover efficiency:
• Phase efficiency:
ηb
ηt
ηs
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
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Blockage efficiency
Effelsberg 100 m
NRAO 140 Foot
Conventional Telescope: ηb = 0.85 – 0.9
GBT: ηb = 1.0
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Illumination efficiency – taper and spillover
Idealized uniform illumination
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Illumination efficiency – taper and spillover
blue = taper loss, red = spillover loss
Gaussian-illuminated zero phase error unblocked circular
antenna:
ηa = ηt ηs = 0.815 (maximum) for 11dB edge taper
ηa = ηt ηs = ~ 0.7 for ~15dB edge taper (GBT)
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ideal telescope with edge taper
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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
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real telescope with phase losses
Error distribution
modeled by Ruze
Ruze formula:
ε = rms surface error
ηp = exp[(-4πε/λ)2]
“pedestal” θp ~ Dθ/L
ηa down by 3dB for
ε = λ/16
“acceptable” performance
ε = λ/4π
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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
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Scientific Requirements
(GHz)
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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 ?
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What is possible?
The Astronomical Journal, February 1967
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Solutions…
The Astronomical Journal, February 1967
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GBT Solutions…
• Innovative design/construction
• Careful initial alignment
• Active surface / FE model
<= Original
• Calibration measurements of residuals
(OOF holography)
<= Now
• Real-time monitoring/dynamic
adjustments (OOF holography)
<= Future
(Potential alternative: use laser rangefinders to measure
absolute position of all optical elements and correct
appropriately.)
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Phase I – Static alignment and
use of Finite Element Model
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Homologous design
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Homologous design
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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
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Subreflector focus tracking
X,Y,Z = A + B cos(el) + C sin(el)
Xt, Zt = Const
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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
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Surface Panel Actuators
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
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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
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Mechanical adjustment of the panels
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Finite Element Model Predictions
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FE Model - Efficiency and Beam Shape
Focus tracking and FE Model:
Acceptable surface to 20GHz
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Phase II –
“Out of focus” holography
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Reminder – what we are trying to measure
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Holography
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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
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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
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“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
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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
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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.
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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
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Zernike polynomials
z2: phase gradient
(pointing shift)
z5: astigmatism
z8: coma
aperture plane
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Zernike examples
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Zernike examples
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Zernike examples
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Scanning pattern
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Typical data
Q-band (43 GHz)
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Typical data
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Closure: before (wrms = 370 µm)
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Closure: after (wrms = 80 µm)
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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)
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Gravitational Deformations
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Gravity model
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Gravity Model
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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)
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Application: Thermal gradients
• We know that thermal effects in the feed-arm
displace the subreflector from the nominal position
• This mis-collimation primarily appears astigmatismlike, and also affects the pointing
• Use the measured pointing offsets to deduce and
correct for the subreflector displacement
• Improve pointing and efficiency simultaneously
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Effect of subreflector displacement
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Thermal effects – 2nd and 5th order fits
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Azimuth LPC versus astigmatism
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Elevation LPC versus astigmatism
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Daytime thermal variations
12th January 2006
8:00am (top left)
6:00pm (bottom right)
Sunny, temperatures: 3.4C (start)
14C (middle)
2.5C (end)
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Thermal Effects – “real-time” correction
rms  300m
rms  220m
rms ~ 330µm
rms  220m
rms ~ 220µm
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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.
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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 = 0.47
90 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)
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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?
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