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

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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-of-focus”) 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:

Power incident on antennaPower collected by feedη =

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: 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

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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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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

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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

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

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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

• 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

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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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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

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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 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

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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

m300 rms m220 rms

m220 rms

rms ~ 330µm

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 = 0.4790 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)

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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?