Out-of-focus (OOF) holography at the Effelsberg telescope Effelsberg - - PowerPoint PPT Presentation

Out-of-focus (OOF) holography at the Effelsberg telescope

Effelsberg Science Workshop Tomas Cassanelli

Max-Planck-Institut f¨ ur Radioastronomie University of Toronto 21 February 2018

• Prof. Dr. K. Menten
• Dr. A. Kraus
• Dr. U. Bach
• Dr. B. Winkel

This presentation has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 730562 [RadioNet] Cassanelli (MPIfR) OOF holography at Effelsberg 21 February 2018 1 / 14

Outline

1 Introduction 2 OOF holography theory 3 OOF holography observations 4 pyoof package 5 Analysis 6 Conclusions S9mm α

Cassanelli (MPIfR) OOF holography at Effelsberg 21 February 2018 2 / 14

Introduction Motivation

Motivation: Optimize the surface accuracy

20 40 60 80 α degress 0.80 0.85 0.90 0.95 1.00 Gnorm(α)

Normalized gain-elevation 9-mm receiver

Sensitivity can be improved Γ =

Ae 2kB = π 8kB εaperD2 p

Γ ≈ 0.75 K/Jy @ λ = 9 mm εaper = εrad εtaperεspill

• εi

εcrεbk εrsεϕrεϕf

• εph

Cassanelli (MPIfR) OOF holography at Effelsberg 21 February 2018 3 / 14

Introduction Motivation

Motivation: Optimize the surface accuracy

20 40 60 80 α degress 0.80 0.85 0.90 0.95 1.00 Gnorm(α)

Normalized gain-elevation 9-mm receiver

Sensitivity can be improved Γ =

Ae 2kB = π 8kB εaperD2 p

Γ ≈ 0.75 K/Jy @ λ = 9 mm εaper = εrad εtaperεspill

• εi

εcrεbk εrsεϕrεϕf

• εph

Surface accuracy optimization Increases Gain Decreases P obs(u, v) error Deformation sources gravity, thermal, wind mis-collimations phase error receiver Random-surface-error efficiency εrs = e−(4πλ−1δrms)2 Surface error is elevation dependent

Cassanelli (MPIfR) OOF holography at Effelsberg 21 February 2018 3 / 14

Introduction Effelsberg telescope

Effelsberg and its active surface

Gregorian geometry Sub-reflector equipped with active surface control system 96 actuators → displacement ⊥ aperture plane Active surface corrects deformation in primary dish ⊥ displacement ±5000 µm Modeled by a FEM look-up table

Ds Fp Receiver Vp xf zf

Sub-reflector 6.5-m

Ds xf yf

Cassanelli (MPIfR) OOF holography at Effelsberg 21 February 2018 4 / 14

Introduction Holography

Optimize surface accuracy → Holography

What is holography?

P obs(u, v) → Ea(x, y) → ϕ(x, y)

Cassanelli (MPIfR) OOF holography at Effelsberg 21 February 2018 5 / 14

Introduction Holography

Optimize surface accuracy → Holography

What is holography?

P obs(u, v) → Ea(x, y) → ϕ(x, y)

Holography at the Effelsberg telescope Phase-coherent holography OOF holography Geostationary satellite 11.7 GHz Compact source

• S

N > 200

• Elevation restriction

Complete elevation range Needs a reference antenna No extra equipment Time consuming (∼ 7 h) ∼ 45 min High accuracy (panel-to-panel) Large-scale error

Cassanelli (MPIfR) OOF holography at Effelsberg 21 February 2018 5 / 14

Introduction OOF holography

Aperture distribution Ea(x, y)

Why do we need the aperture distribution? Aperture related to the phase error Ea(x, y) → ϕ(x, y) Phase error has the aberration of an

• ptical system

How do we obtain the aperture from the beam pattern P (u, v) =

• F
• Ea(x, y)
• 2

in-focus power pattern under-determines the aperture distribution

1 in-focus and 2 out-of-focus beam maps to break degeneracy

Cassanelli (MPIfR) OOF holography at Effelsberg 21 February 2018 6 / 14

Introduction OOF holography

Aperture distribution Ea(x, y)

Why do we need the aperture distribution? Aperture related to the phase error Ea(x, y) → ϕ(x, y) Phase error has the aberration of an

• ptical system

How do we obtain the aperture from the beam pattern P (u, v) =

• F
• Ea(x, y)
• 2

in-focus power pattern under-determines the aperture distribution

1 in-focus and 2 out-of-focus beam maps to break degeneracy

The aperture distribution is a collection of sub-functions

Ea(x, y) = B(x, y) · Ea(x, y) · ei{ϕ(x,y)+ 2π

λ δ(x,y; dz)}

Aperture distribution Blockage Illumination function Phase error Optical path difference

Cassanelli (MPIfR) OOF holography at Effelsberg 21 February 2018 6 / 14

OOF holography theory Phase error

Phase error ϕ(x, y)

Ea(x, y), d−

z

Ea(x, y) Ea(x, y), d+

z

−40 −20 20 40 −40 −20 20 40

Phase error ϕ(x, y) pyoof package P obs(u, v), d−

z

P obs(u, v) P obs(u, v), d+

z

Zernike circle polynomials ϕ(x, y) = 2π

n,ℓ KnℓUℓ n(x, y)

Phase determined by Knℓ coefficients ϕ(x, y) → Active surface system

Cassanelli (MPIfR) OOF holography at Effelsberg 21 February 2018 7 / 14

OOF holography observations

Observed power pattern example

−0.05 0.00 0.05 u degrees −0.04 −0.02 0.00 0.02 0.04 v degrees

P obs

norm(u, v), dz = −0.022 m

−0.05 0.00 0.05 u degrees −0.04 −0.02 0.00 0.02 0.04 v degrees

P obs

norm(u, v), dz = 0.0 m

−0.05 0.00 0.05 u degrees −0.04 −0.02 0.00 0.02 0.04 v degrees

P obs

norm(u, v), dz = 0.022 m

Observation Mean elevation α = 53 deg. δrms = 15.1 mJy

S N = 1285 > 200

• bs time ∼ 45 min

Radial offset ↑ / ↓ sub-reflector movement Order of dz ∼ 2 cm ϕ(x, y) + δ(x, y; dz) → change in phase

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pyoof package Least squares optimization

Python package: pyoof

START input data: Pobs, λ, dz resolution mesh:

• [x], [y]
• iteration counter: j = 0

initial parameters: θ(j) Aperture evaluation [Ea] = [B] · [Ea] · e

i

• [ϕ]+ 2π

λ [δ]

• Power pattern: [Pnorm]

Residual [P obs

norm] − [Pnorm]

Least squares θ(j+1) Optimality Estimated solution

• θ = θ(j)

j = j + 1 END FFT2 interpolation yes no GitHub Repository https://github.com/tcassanelli/pyoof

Cassanelli (MPIfR) OOF holography at Effelsberg 21 February 2018 9 / 14

pyoof package Least squares optimization

Least squares minimization n = 7

θ = cdB K1 −1 K1 1 K2 −2 · · · K7 7 ⊺

−0.05 0.00 0.05 u degrees −0.04 −0.02 0.00 0.02 0.04 v degrees

P obs

norm(u, v), dz = −0.022 m

−0.05 0.00 0.05 u degrees −0.04 −0.02 0.00 0.02 0.04 v degrees

P obs

norm(u, v), dz = 0.0 m

−0.05 0.00 0.05 u degrees −0.04 −0.02 0.00 0.02 0.04 v degrees

P obs

norm(u, v), dz = 0.022 m

−0.05 0.00 0.05 u degrees −0.04 −0.02 0.00 0.02 0.04 v degrees

Pnorm(u, v) dz = −0.022 m

−0.05 0.00 0.05 u degrees −0.04 −0.02 0.00 0.02 0.04 v degrees

Pnorm(u, v) dz = 0.0 m

−0.05 0.00 0.05 u degrees −0.04 −0.02 0.00 0.02 0.04 v degrees

Pnorm(u, v) dz = 0.022 m

Cassanelli (MPIfR) OOF holography at Effelsberg 21 February 2018 10 / 14

pyoof package Phase error construction

Phase error (computed)

ϕ(x, y) n = 1 ϕ(x, y) n = 2 ϕ(x, y) n = 3 ϕ(x, y) n = 4 ϕ(x, y) n = 5 ϕ(x, y) n = 6 ϕ(x, y) n = 7 ϕ(x, y) n = 8 ϕ(x, y) n = 9 ϕ(x, y) n = 10

Phase error primary reflector nmax = 10 ⇒ 65 coefficients lines between -2 and 2 radians Optimum 5 ≤ n < 10 Correlation + Polynomial properties

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Analysis Convention in sub-reflector

Adding an offset

The convention problem Coordinate system Numbering Uℓ

n polynomials

Labeling in actuators Angle of view sub-reflector Offset amplitude of 1500 µm Same amplitude obtained in ϕ⊥ calculated

−2 2 x m −3 −2 −1 1 2 3 y m

Look-up table α = 40 deg

−2 2 x m −3 −2 −1 1 2 3 y m

Phase error α = 42 deg

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Conclusions Summary

Project summary

Development of a OOF holography software: pyoof package Individual function selection and testing Interval Zernike circle polynomial order, 5 ≤ n < 10 Residual optimization, covariance and correlation ↓ orders → optical aberrations + orthogonality pyoof package and observations Added offset to active surface → observed in phase error

Cassanelli (MPIfR) OOF holography at Effelsberg 21 February 2018 13 / 14

Conclusions Summary

Project summary

Development of a OOF holography software: pyoof package Individual function selection and testing Interval Zernike circle polynomial order, 5 ≤ n < 10 Residual optimization, covariance and correlation ↓ orders → optical aberrations + orthogonality pyoof package and observations Added offset to active surface → observed in phase error It is possible to make an OOF holography look-up table and improve the current model!

Cassanelli (MPIfR) OOF holography at Effelsberg 21 February 2018 13 / 14

Conclusions Future OOF holography campaigns

Project continuation

More observations active surface off OOF holography look-up table → interpolation or gravity Knℓ(α) = G1

nℓ sin α + G2 nℓ cos α + G3 nℓ

Find weighted factor residual

• P obs

norm

• i − (Pnorm)i

wi Improve pre-calibration routine + pyoof → pipeline Different OOF holography observations Extended sources from planets → higher flux

Cassanelli (MPIfR) OOF holography at Effelsberg 21 February 2018 14 / 14

Conclusions Future OOF holography campaigns

Project continuation

More observations active surface off OOF holography look-up table → interpolation or gravity Knℓ(α) = G1

nℓ sin α + G2 nℓ cos α + G3 nℓ

Find weighted factor residual

• P obs

norm

• i − (Pnorm)i

wi Improve pre-calibration routine + pyoof → pipeline Different OOF holography observations Extended sources from planets → higher flux Thank you for listening GitHub: https://github.com/tcassanelli/pyoof cassanelli@astro.utoronto.ca

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