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Phase Calibration/Correction for ALMA
B. Nikolic
Cavendish Laborator y, University of Cambridge

1st December 2008 Algorithms 2008 Workshop, Oxford

B. Nikolic (University of Cambridge)

Phase calibration for ALMA

December 2008

1 / 27

Outline

1

Phase errors in the mm/sub-mm ALMA Phase Correction Plan Fast-switching WVR Phase Correction Algorithms!

2

3

4

B. Nikolic (University of Cambridge)

Phase calibration for ALMA

December 2008

2 / 27

Phase errors in the mm/sub-mm

Outline

1

Phase errors in the mm/sub-mm ALMA Phase Correction Plan Fast-switching WVR Phase Correction Algorithms!

2

3

4

B. Nikolic (University of Cambridge)

Phase calibration for ALMA

December 2008

3 / 27

Phase errors in the mm/sub-mm

Causes of Phase Errors at mm/sub-mm wavelengths
Instrumental

Possible sources: Electronic Mechanical/optical Timescales: Hopefully from about 30 minutes to very long timescales (e.g., diurnal cycle) Mitigation: Stable designs Phase calibration using astronomical sources

B. Nikolic (University of Cambridge)

Phase calibration for ALMA

December 2008

4 / 27

Phase errors in the mm/sub-mm

Causes of Phase Errors at mm/sub-mm wavelengths
Atmospheric (tropospheric)

Two sources (both only impor tant in first km of atmosphere): Fluctuating quantity of water-vapour along line of sight (`wet') Fluctuating temperature of dry air along line of sight (`dry') Two characteristic timescales: Inner: Set by the smoothing effect of the D = 12 m telescope beam: D /v 1 s Outer: Determined by the baseline length B : 5s B /v 20 minutes

B. Nikolic (University of Cambridge)

Phase calibration for ALMA

December 2008

5 / 27

Phase errors in the mm/sub-mm

Atmospheric Phase Fluctuations

B. Nikolic (University of Cambridge)

Phase calibration for ALMA

December 2008

6 / 27

Phase errors in the mm/sub-mm

Atmospheric Phase Fluctuations

B. Nikolic (University of Cambridge)

Phase calibration for ALMA

December 2008

6 / 27

Phase errors in the mm/sub-mm

Atmospheric Phase Fluctuations

B. Nikolic (University of Cambridge)

Phase calibration for ALMA

December 2008

6 / 27

Phase errors in the mm/sub-mm

Atmospheric Phase Fluctuations

B. Nikolic (University of Cambridge)

Phase calibration for ALMA

December 2008

6 / 27

Phase errors in the mm/sub-mm

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.

B. Nikolic (University of Cambridge)

Phase calibration for ALMA

December 2008

7 / 27

Phase errors in the mm/sub-mm

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 #

Phase calibration for ALMA

December 2008

8 / 27

Phase errors in the mm/sub-mm

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 Not so much a worr y at sub-mm Small field of view + Small dynamic range of sky less dynamic range problems due to phase errors
B. Nikolic (University of Cambridge) Phase calibration for ALMA December 2008 9 / 27

ALMA Phase Correction Plan

Outline

1

Phase errors in the mm/sub-mm ALMA Phase Correction Plan Fast-switching WVR Phase Correction Algorithms!

2

3

4

B. Nikolic (University of Cambridge)

Phase calibration for ALMA

December 2008

10 / 27

ALMA Phase Correction Plan

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) Phase calibration for ALMA December 2008 11 / 27

ALMA Phase Correction Plan

Fast-switching

Outline

1

Phase errors in the mm/sub-mm ALMA Phase Correction Plan Fast-switching WVR Phase Correction Algorithms!

2

3

4

B. Nikolic (University of Cambridge)

Phase calibration for ALMA

December 2008

12 / 27

ALMA Phase Correction Plan

Fast-switching

Fast-switching phase calibration
Use standard algorithms to determine antenna phase errors from observed visibilities Phase transfer from = 3 mm to theobserving 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 dispersive in 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)

Phase calibration for ALMA

December 2008

13 / 27

ALMA Phase Correction Plan

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 #

Phase calibration for ALMA

December 2008

14 / 27

WVR Phase Correction

Outline

1

Phase errors in the mm/sub-mm ALMA Phase Correction Plan Fast-switching WVR Phase Correction Algorithms!

2

3

4

B. Nikolic (University of Cambridge)

Phase calibration for ALMA

December 2008

15 / 27

WVR Phase Correction

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) Phase calibration for ALMA December 2008 16 / 27

600

800

1000

WVR Phase Correction

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) Phase calibration for ALMA December 2008 17 / 27

185

187.5

190

WVR Phase Correction

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)

Phase calibration for ALMA

December 2008

18 / 27

WVR Phase Correction

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

(1)

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)

Phase calibration for ALMA

December 2008

19 / 27

WVR Phase Correction

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)

Phase calibration for ALMA

December 2008

20 / 27

Algorithms!

Outline

1

Phase errors in the mm/sub-mm ALMA Phase Correction Plan Fast-switching WVR Phase Correction Algorithms!

2

3

4

B. Nikolic (University of Cambridge)

Phase calibration for ALMA

December 2008

21 / 27

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 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) Phase calibration for ALMA December 2008 22 / 27

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) Phase calibration for ALMA December 2008 23 / 27

Algorithms!

Example: Prediction of
Pressure variation
250

dL dTB

,i

from WVR data only
Temperature variation

Single, thin layer; non-dispersive water vapour delay only; prototype filter set
250

200

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)

Phase calibration for ALMA

December 2008

24 / 27

Algorithms!

Example: Prediction of
n
0.04
277.5 275

dL dTB

,i

from WVR data only
P
605
3 · 10
4

Model parameters retrieval with priors

T
600 595
2 · 104 270 267.5 272.5

2 · 104

0.03
T (K)

1.5 · 10

4

P (mbar)

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) Phase calibration for ALMA

610

December 2008

25 / 27

Algorithms!

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

dL dTB

dL dTB,i

,i

from WVR data only
0.03 0.025 0.02 0.015 0.01 0.005 0 13.5 f

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)

Phase calibration for ALMA

December 2008

26 / 27

Algorithms!

Challenges

15 km baselines, 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 Understanding of atmospheric physics and models

B. Nikolic (University of Cambridge)

Phase calibration for ALMA

December 2008

27 / 27