Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://www.mrao.cam.ac.uk/~bn204/mk2/publications/2009/NikolicURSI09.pdf Äàòà èçìåíåíèÿ: Wed Nov 25 23:20:19 2009 Äàòà èíäåêñèðîâàíèÿ: Thu Apr 8 12:29:11 2010 Êîäèðîâêà:

Atmospheric phase correction for ALMA with water-vapour radiometers
B. Nikolic
Cavendish Laborator y, University of Cambridge

January 2009 NA URSI, Boulder, CO

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

1 / 40


Outline
1

Introduction Goals for this talk Atmospheric Phase Fluctuations at mm/sub-mm wavelengths Review of ALMA Phase Correction/Calibration Strategy Fast-switching Phase correction with WVRs Water Vapour Radiometry Algorithms Summar y

2

3

4

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

2 / 40


Introduction

Outline
1

Introduction Goals for this talk Atmospheric Phase Fluctuations at mm/sub-mm wavelengths Review of ALMA Phase Correction/Calibration Strategy Fast-switching Phase correction with WVRs Water Vapour Radiometry Algorithms Summar y

2

3

4

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

3 / 40


Introduction

Goals for this talk

Outline
1

Introduction Goals for this talk Atmospheric Phase Fluctuations at mm/sub-mm wavelengths Review of ALMA Phase Correction/Calibration Strategy Fast-switching Phase correction with WVRs Water Vapour Radiometry Algorithms Summar y

2

3

4

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

4 / 40


Introduction

Goals for this talk

Goals for this talk

Introduce the work in Cambridge on algorithms for WVR phase corrections
Why this is interesting Where we are heading

Very briefly present some simulations Also briefly review results of prototype testing at the SMA

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

5 / 40


Introduction

Atmospheric Phase Fluctuations at mm/sub-mm wavelengths

Outline
1

Introduction Goals for this talk Atmospheric Phase Fluctuations at mm/sub-mm wavelengths Review of ALMA Phase Correction/Calibration Strategy Fast-switching Phase correction with WVRs Water Vapour Radiometry Algorithms Summar y

2

3

4

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

6 / 40


Introduction

Atmospheric Phase Fluctuations at mm/sub-mm wavelengths

Causes of Phase Errors at mm/sub-mm wavelengths
Atmospheric ­ Tropospheric Instrumental Sources: Mechanical/ Optical/ Electronic Two sources: Fluctuating quantity of water-vapour along line of sight (`wet')

Fluctuating temperature of dry air Timescales: from about 30 along line of sight (`dry') minutes to ver y long Two relevant timescales: timescales (e.g., the Inner: Set by the smoothing effect diurnal cycle) of the D = 12 m telescope beam: Mitigation: Stable designs D /v 1 s and astronomical phase Outer: Determined by the calibration baseline length B : 5 s B /v 20 minutes
WVR phase correction for ALMA January 2009 7 / 40

B. Nikolic (University of Cambridge)


Introduction

Atmospheric Phase Fluctuations at mm/sub-mm wavelengths

Example of observed path fluctuations
SMA, Mauna Kea, Hawaii
750

500

250

p (µm)

0

Measured path fluctuation while observing a quasar 200 m baseline About 3.5 mm line-of-sight water
17 17.2 17.4 t (hours UT) 17.6 17.8 18

-250

-500

-750 16.8

= 207 µm.

This and all other data from the SMA were collected by the ALMA WVR prototype collaboration: for full list of people involved and more details see http://www.mrao.cam.ac.uk/~bn204/alma/smat.html
B. Nikolic (University of Cambridge) WVR phase correction for ALMA January 2009 8 / 40


Introduction

Atmospheric Phase Fluctuations at mm/sub-mm wavelengths

Simulated ALMA phase errors
Details of simulations at http://www.mrao.cam.ac.uk/~bn204/alma/
50 1.5 1 40 0.5 antenna # 30 (rad) 20 10 -1.5 0 0 20 40 60 80 time (integration #) 50 100 120 140 0 1 40 30 (rad) 20 -1 10 0 0 20 40 60 80 time (integration #) 100 120 140 0 1 0 0 -0.5 -1

1

B. Nikolic (University of Cambridge)

antenna #

WVR phase correction for ALMA

January 2009

9 / 40


Introduction

Atmospheric Phase Fluctuations at mm/sub-mm wavelengths

Impact of poorly corrected phase errors
General impact on science Phase errors increase with baseline length = limit on maximum usable baseline length = limit on possible resolution Loss of sensitivity due to de-correlation Impact on snapshot + mosaics Fur ther effects due to time-variance of phase fluctuations Amplitude calibration Astrometric accuracy Top level specification for ALMA w pcorrected 1 + 1 mm
B. Nikolic (University of Cambridge)

10 µm + 0.02 â praw
January 2009

(1)
10 / 40

WVR phase correction for ALMA


Review of ALMA Phase Correction/Calibration Strategy

Outline
1

Introduction Goals for this talk Atmospheric Phase Fluctuations at mm/sub-mm wavelengths Review of ALMA Phase Correction/Calibration Strategy Fast-switching Phase correction with WVRs Water Vapour Radiometry Algorithms Summar y

2

3

4

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

11 / 40


Review of ALMA Phase Correction/Calibration Strategy

ALMA phase correction strategy
Fast-switching Observe nearby quasars Calculate antenna phase errors Calibration cycle down to 10­15 s (fast antennas!) Expect calibrators about two degrees from science target Can calibrate at 90 GHz and transfer up to 950 GHz Water Vapour Radiometry Measure atmospheric proper ties along the line of sight of each telescope

+

Use dedicated 183 GHz radiometers on each telescope Measurements at about 1 Hz Infer excess path Correct either in correlator or in post-processing

+ Self-Calibration in a very limited number of cases
B. Nikolic (University of Cambridge) WVR phase correction for ALMA January 2009 12 / 40


Review of ALMA Phase Correction/Calibration Strategy

Fast-switching

Outline
1

Introduction Goals for this talk Atmospheric Phase Fluctuations at mm/sub-mm wavelengths Review of ALMA Phase Correction/Calibration Strategy Fast-switching Phase correction with WVRs Water Vapour Radiometry Algorithms Summar y

2

3

4

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

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Review of ALMA Phase Correction/Calibration Strategy

Fast-switching

Fast-Switching offset calibration
Astronomical source Phase calibration source (typically 2 degrees away)

Turbulent layer w 250 m

h 750 m

Ant. #1

Ant. #2

Illustration of the geometry of the turbulent layer and the directions to astronomical and calibration sources.

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

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Review of ALMA Phase Correction/Calibration Strategy

Fast-switching

Simulated fast-switching phase calibration
Medium configuration, 15 s cycle (http://www.mrao.cam.ac.uk/~bn204/alma/)
50

40

1

antenna #

30 (rad) 20 -1 10 0 0 50 1 40 0.5 20 40 60 80 time (integration #) 100 120 140 0 1 30 (rad) 20 -0.5 10 -1 0 0 20 40 60 80 time (integration #) 100 120 140 0 1 0 0

B. Nikolic (University of Cambridge)

antenna #

WVR phase correction for ALMA

January 2009

15 / 40


Review of ALMA Phase Correction/Calibration Strategy

Fast-switching

Fast-switching phase calibration
Use standard algorithms to determine antenna phase errors from observed visibilities Phase transfer from = 3 mm to the observing frequency. Benefits:
Quasars are much brighter at = 3 mm than in the sub-mm Phase errors are unlikely to be large enough to cause phase wraps

Potential challenges:
Atmosphere is dispersive in the sub-mm so the transfer of gain solution requires modelling or itself needs calibration Instrumental phase stability between = 3 mm and obser ving bands needs to be good

Residual phase errors depend on the atmospheric conditions and the calibration cycle, but not on the baseline length

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

16 / 40


Phase correction with WVRs

Outline
1

Introduction Goals for this talk Atmospheric Phase Fluctuations at mm/sub-mm wavelengths Review of ALMA Phase Correction/Calibration Strategy Fast-switching Phase correction with WVRs Water Vapour Radiometry Algorithms Summar y

2

3

4

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

17 / 40


Phase correction with WVRs

Water Vapour Radiometry

Outline
1

Introduction Goals for this talk Atmospheric Phase Fluctuations at mm/sub-mm wavelengths Review of ALMA Phase Correction/Calibration Strategy Fast-switching Phase correction with WVRs Water Vapour Radiometry Algorithms Summar y

2

3

4

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

18 / 40


Phase correction with WVRs

Water Vapour Radiometry

Water Vapour cm/mm/sub-mm lines
1 mm water vapour
300 250 200 Tb (K) 150 100 50 0 200 400 ( GHz )
B. Nikolic (University of Cambridge) WVR phase correction for ALMA January 2009 19 / 40

600

800

1000


Phase correction with WVRs

Water Vapour Radiometry

The 183 GHz Water Vapour Line
Blue rectangles are the production WVR filters

250

200

150 Tb (K) 100 50 0 175 177.5 180 182.5 (GHz)
B. Nikolic (University of Cambridge) WVR phase correction for ALMA January 2009 20 / 40

185

187.5

190


Phase correction with WVRs

Water Vapour Radiometry

The 183 GHz Water Vapour Radiometers
Un-cooled mixer, double-sideband, with 1000 K receiver noise Total bandwidth 18 GHz split into four DSB channels Dicke-switched with a chopper wheel against loads at two temperatures allowing continuous calibration Specifications:
Sensitivity: 0.08­0.1 K per channel RMS Stability: 0.1 K peak-to-peak over 10 minutes + 10 degree tilts Absolute accuracy: 2 K maximum error

Prototypes designed and built by Onsala and Cambridge Simplified design for production and the manufacture of 60 units by industr y par tners Deliver y of first production units to Chile expected toward end Q1­2009
B. Nikolic (University of Cambridge) WVR phase correction for ALMA January 2009 21 / 40


Phase correction with WVRs

Water Vapour Radiometry

Signal from two prototype WVRs mounted on SMA antennas
From the ALMA WVR prototype testing campaign in 2006
210

205

200

300 250

TB (K)

Tb (K)

195

200 150 100 50

190

175

180

185 (GHz)

190

195

185

180 17.3

17.325

17.35

17.375

17.4 t (hours UT)

17.425

17.45

17.475

17.5

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

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Phase correction with WVRs

Water Vapour Radiometry

Interferometer path vs. radiometer difference
2.5 0

-2.5

TB (K)

-5

-7.5

-10

July 18 2006 test at the SMA with the ALMA prototype WVRs Black line: difference between channels 2 on the two radiometers Red line: interferometric path fluctuation

-12.5 1000

500

p (µ m)

0

-500

-1000 4

4.5

5

5.5 t (hours UT)

6

6.5

7

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

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Phase correction with WVRs

Water Vapour Radiometry

Algorithms for WVR phase correction
L change in excess path to antenna T
B,i

change in i -th channel sky brightness observed by a WVR

wi weight of i -th channel L
i

wi

dL TB, dTB,i
dL dTB,i

i

(2)

TB : WVR hardware design Low noise High bandwidth High stability

wi

: (primarily) algorithm design

Optimal use of information Atmospheric models+physics Experience at the site `Ancillary' information

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

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Phase correction with WVRs

Water Vapour Radiometry

Will this work? Optimise w
1000

dL i dTB,i

directly as a test

SMA test data, total fluctuations: L reduced from 271 to 75 µm

500

p (µm)

0

-500

-1000

4

4.5

5 t (hours UT)

5.5

6

6.5

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

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Phase correction with WVRs

Water Vapour Radiometry

More SMA prototype test observations
750
500

500
250

250

p (µ m)

0

p (µ m)

0

-250
-250

-500

-750 16.8

17

17.2

17.4 t (hours UT)

17.6

17.8

-500

18

7.2

7.4

7.6

7.8 t (hours UT)

8

8.2

8.4

200

500

100

250

0 p (µ m)

p (µ m)

0

-100

-250
-200

-300 5.25

-500
5.5 5.75 6 t (hours UT) 6.25 6.5 6.75

5.5

6

6.5

7 t (hours UT)

7.5

8

8.5

9

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

26 / 40


Phase correction with WVRs

Algorithms

Outline
1

Introduction Goals for this talk Atmospheric Phase Fluctuations at mm/sub-mm wavelengths Review of ALMA Phase Correction/Calibration Strategy Fast-switching Phase correction with WVRs Water Vapour Radiometry Algorithms Summar y

2

3

4

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

27 / 40


Phase correction with WVRs

Algorithms

WVR algorithms: available information
Four absolute measurements of sky brightness: i.e., TB,i rather than TB,i The obser ved correlation between L and T
B

Ground-level temperature, pressure, humidity, wind-speed Information on the profile of atmospheric temperature with height from a single 60 GHz O2 sounder at the centre of the array Library of radio-sonde measurements Shor t-term meso-scale meteorological forecast Will we need all of this information? We are aiming for very challenging 2% accuracy in
i

wi

dL dTB,i

For operational efficiency impor tant to understand how well phase correction will work (also the opacity too of course)
B. Nikolic (University of Cambridge) WVR phase correction for ALMA January 2009 28 / 40


Phase correction with WVRs

Algorithms

Algorithm framework: Bayesian
We are developing a Bayesian framework to optimally combine all available information together with models of the atmosphere Why Bayesian? We are not interested in model parameters such as pressure, temperature, lapse rate, turbulent layer height, etc. dL All we want are the dTB,i Marginalise all model parameters, get probability distributions for dL dTB,i . Framework features A model for accuracy of absolute measurements T Incorporate empirical
dL dTB,i

B,i

as observation

Other information naturally fit in as priors
B. Nikolic (University of Cambridge) WVR phase correction for ALMA January 2009 29 / 40


Phase correction with WVRs

Algorithms

Shor t adver tisement & request: ATM

The work presented here is based only on the 183 GHz line and non-dispersive delay: these are both trivial model For predicting dispersive effects and also for absolute calibration, ALMA will use Juan Pardo's ATM This version is now available for everybody to download and use under the open-source GPL licence:
http://www.mrao.cam.ac.uk/~bn204/alma/atmomodel.html

Any comments on accuracy of this code would be greatly appreciated by the project

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

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Phase correction with WVRs

Algorithms

Prediction of
250

dL dTB,

i

from T

B,i

only
Temperature variation
250 200

Single, thin layer; non-dispersive water vapour delay only; prototype filter set

Pressure variation
200

150 Tb (K) Tb (K) 100

150

100

50

50

0 175 177.5 180 182.5 (GHz) 185 187.5 190

0 175 177.5 180 182.5 (GHz) 185 187.5 190

Amount of Water
250
250

Filters
200

200

150 Tb (K)
Tb (K)

150

100

100

50

50

0 175 177.5 180 182.5 (GHz) 185 187.5 190

0 175 177.5 180 182.5 (GHz) 185 187.5 190

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

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Phase correction with WVRs

Algorithms

Prediction of
n

dL dTB,

i

from T

B,i

only
P
8 · 104 800 8 · 104 750 6 · 104 700 6 · 104 P (mbar)

Model parameters retrieval without priors

T
340 320 T (K) 300 4 · 104

0.02

0.015

0.01

650

4 · 104

f

280

0.005
260

2 · 104

600

2 · 104

n

0 0.975

1

1.025

1.05 c (mm)

1.075

1.1

1.125

0 1 1.025 1.05 c (mm) 1.075 1.1 0 1

550 1 1.025 1.05 c (mm) 800 1.075 1.1

0 0 1

0.025
750

1 · 105

0.02 0.015 f 0.01 0.005
600 2.5 · 10
4

P (mbar)

700

7.5 · 10

4

650

5 · 104

T

0 240 260 280 300 T (K) 320 340 360

550 260 280 300 T (K) 320 340

0 0 1

0.04

0.03

0.02

f

0.01

P
B. Nikolic (University of Cambridge) WVR phase correction for ALMA

0 500 600 700 P (mbar) 800 900

January 2009

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Phase correction with WVRs

Algorithms

Prediction of
n
0.04

dL dTB,

i

from T

B,i

only
P
605
3 · 10
4

Model parameters retrieval with priors

T
277.5 275

2 · 104

600 595
2 · 104

0.03
T (K)

272.5

1.5 · 10

4

P (mbar)

270 267.5

590 1 · 104 585

0.02

f

0.01

265 262.5

1 · 104

580 575

5 · 103

n

0 0.97

0.98

0.99

1 c (mm)

1.01

1.02

1.03

0 0.98 0.99 1 c (mm) 1.01 1.02 0 1

0 0.98 0.99 1 c (mm) 1.01 1.02 0 1

0.025 0.02

605 600 595

3 · 104 2.5 · 10
4

0.015 f 0.01 0.005

P (mbar)

2 · 104 1.5 · 10
4

590 585

1 · 104 580 575 5 · 103 0

T

0 260 265 270 T (K)
0.015 0.0125 0.01 0.0075 0.005 0.0025 0 570 580 590 P (mbar) 600 f

275

280

265

270 T (K)

275

0

1

P
B. Nikolic (University of Cambridge) WVR phase correction for ALMA

610

January 2009

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Phase correction with WVRs

Algorithms

Prediction of
Retrieved
0.03 0.025 0.02 0.015 0.01 0.005 0 12.5 f

dL dTB,i

dL dTB,

i

from T

B,i

only
0.03 0.025 0.02 0.015 0.01 0.005 0 13.5 f

(with priors)

13

13.5

14

14.5

15

15.5

16

14

14.5 d TB,2 /d L (K/mm)

15

15.5

d TB,1 /d L (K/mm)
0.025 0.02 0.015 f

0.025 0.02 0.015 f 0.01 0.005

0.01 0.005

0 10.8

0
11 11.2 11.4 11.6 11.8

6.4

6.5

6.6

6.7

6.8

6.9

d TB,3 /d L (K/mm)

d TB,4 /d L (K/mm)

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

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Phase correction with WVRs

Algorithms

Including the empirical correlation between L and TB

Observed correlation between L and TB gives us directly the information we need to do phase correction But, must minimise time spent on this observation instead of science = Use the obser ved correlation, and a physical model for dL atmosphere to allow inference of wi dTB,i at:
Different airmass Different total water column ...

This approach naturally fits into the Bayesian framework

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

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Phase correction with WVRs

Algorithms

Prediction of
0.04 0.03

dL dTB,

i

from T

B,i

and correlation L vs T
0.04 0.03

B

0.02

0.02

f

0.01

f 14.4 14.5 14.6 d TB,1 /d L (K/mm) 14.7 14.8 14.9

0.01

0 14.3 0.04

0 14.4 0.04

14.5

14.6 d TB,2 /d L (K/mm)

14.7

14.8

0.03

0.03

0.02

0.02

f

0.01

f 11.3 11.35 11.4 11.45 11.5

0.01

0 11.25

0 6.65

6.7

6.75 d TB,4 /d L (K/mm)

6.8

6.85

d TB,3 /d L (K/mm)

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

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Phase correction with WVRs

Algorithms

Prediction of
0.04

dL dTB,

i

from T

B,i

and correlation L vs T
0.04

B

Transferred to an airmass 25% higher

0.03

0.03

0.02

0.02

f

0.01

f

0.01

0 10.3

10.4

10.5

10.6 d TB,1 /d L (K/mm)

10.7

10.8

10.9

0 11.8

11.9

12

12.1

12.2

12.3

d TB,2 /d L (K/mm)

0.04

0.04

0.03

0.03

0.02

0.02

f

f

0.01

0.01

0 10.05

10.1

10.15

10.2

10.25

10.3

0 6.25

6.3

6.35

6.4

6.45

6.5

d TB,3 /d L (K/mm)

d TB,4 /d L (K/mm)

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

37 / 40


Summary

Outline
1

Introduction Goals for this talk Atmospheric Phase Fluctuations at mm/sub-mm wavelengths Review of ALMA Phase Correction/Calibration Strategy Fast-switching Phase correction with WVRs Water Vapour Radiometry Algorithms Summar y

2

3

4

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

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Summary

Summary

WVRs phase correction has an impor tant role in ALMA phase correction plan Initial results from SMA promising The algorithm design is challenging but hopefully tractable But need to : Get ALMA phase-stable and observing at sub-mm frequencies at the AOS (the high site) Get the WVRs commissioned, integrated into the ALMA system, and the obser vation and data recording software systems working And then the real challenges for phase correction star t...

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

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Summary

Challenges
15 km baselines with substantial elevation difference between par ts of the array dL need different set of dTB,i for each antenna In some correlator modes, need to apply correction in semi-real-time dL need to get the dTB,i right `dry' fluctuations: very little direct information, need to rely on correlation with `wet' fluctuations Optimisation of fast-switching and phase transfer calibration stages Understanding of atmospheric physics and models

B. Nikolic (University of Cambridge)

WVR phase correction for ALMA

January 2009

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