Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.mrao.cam.ac.uk/~bn204/almasim08/papers/ALMASim08.pdf Дата изменения: Tue Dec 2 15:00:10 2008 Дата индексирования: Tue Oct 2 11:07:12 2012 Кодировка: Поисковые слова: m 103

Simulating Atmospheric Phase Errors, Phase Correction and the Impact on ALMA Science
B. Nikolic1 J. S. Richer1 R. E. Hills2
1

Cavendish Laborator y, University of Cambridge 2 Joint ALMA Office, Santiago, Chile

10th September 2008, IRAM, Grenoble

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

1 / 41


Outline
1 2

Introduction Simulations method Framework Simulating a turbulent volume 2d projections and steepening of structure fn Results Results without phase correction Fast-switching phase calibration WVR + Fast-switching Summar y/Links

3

4

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

2 / 41


Introduction

Outline
1 2

Introduction Simulations method Framework Simulating a turbulent volume 2d projections and steepening of structure fn Results Results without phase correction Fast-switching phase calibration WVR + Fast-switching Summar y/Links

3

4

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

3 / 41


Introduction

Atmospheric Phase errors
Observed path fluctuation at the SMA while tracking a quasar for one hour (p = 207 µm)
750

500

250

p (µm)

0

-250

-500

-750 16.8

17

17.2

17.4 t (hours UT)

17.6

17.8

18

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

4 / 41


Introduction

Atmospheric Phase errors vs baseline
Phase fluctuation measured at 22 GHz at the VLA by observing a quasar for about thir ty minutes. Correlations along one arm of the VLA only shown.
100

Phase fluctuation (deg)

50

20

10 1 · 102

2 · 102

5 · 102

1 · 10

3

2 · 103

5 · 103

1 · 104

baseline length (m)

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

5 / 41


Introduction

Why Simulate Phase Errors?
ALMA phase correction/calibration/mitigation strategies Fast switching 183 GHz Water Vapour Radiometry Self-calibration Scheduling

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

6 / 41


Introduction

Why Simulate Phase Errors?
ALMA phase correction/calibration/mitigation strategies Fast switching 183 GHz Water Vapour Radiometry Self-calibration Scheduling The science end-user : Interested only in residual phase errors after calibration/correction

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

6 / 41


Introduction

Why Simulate Phase Errors?
ALMA phase correction/calibration/mitigation strategies Fast switching 183 GHz Water Vapour Radiometry Self-calibration Scheduling The science end-user : Interested only in residual phase errors after calibration/correction Algorithm design, scheduling, hardware design: Need to understand the phase errors in detail, and how each of the correction techniques can be used to its best potential
B. Nikolic, et al (University of Cambridge) Simulating Atmospheric Phase Errors September 2008 6 / 41


Simulations method

Outline
1 2

Introduction Simulations method Framework Simulating a turbulent volume 2d projections and steepening of structure fn Results Results without phase correction Fast-switching phase calibration WVR + Fast-switching Summar y/Links

3

4

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

7 / 41


Simulations method

Framework

Outline
1 2

Introduction Simulations method Framework Simulating a turbulent volume 2d projections and steepening of structure fn Results Results without phase correction Fast-switching phase calibration WVR + Fast-switching Summar y/Links

3

4

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

8 / 41


Simulations method

Framework

Simulation Flowchar t
Star t Generate uv tracks, samples Geometry only, use CASA Calculate visibilities Corrupt visibility phases Simulate phase correction Make and analyse image Stop Trivial for point sources Use custom C++ and Python Use custom Python CASA or Obit

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

9 / 41


Simulations method

Framework

Simulations Framework

A very straightforward flowchar t! Factors cleanly into distinct steps The FITS format ties all of these steps together very well Not considering thermal noise at any stage Develop own modules separately:
Minimise dependencies Maximise re-usability for other projects Ever ything driven from Python (using SWIG when necessar y)

Can be incor porated into user-orientated simulators or used for algorithm development

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

10 / 41


Simulations method

Framework

Simulations Framework

A very straightforward flowchar t! Factors cleanly into distinct steps The FITS format ties all of these steps together very well Not considering thermal noise at any stage
Not required for our goals, so keeping it simple

Develop own modules separately:
Minimise dependencies Maximise re-usability for other projects Ever ything driven from Python (using SWIG when necessar y)

Can be incor porated into user-orientated simulators or used for algorithm development

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

10 / 41


Simulations method

Simulating a turbulent volume

Outline
1 2

Introduction Simulations method Framework Simulating a turbulent volume 2d projections and steepening of structure fn Results Results without phase correction Fast-switching phase calibration WVR + Fast-switching Summar y/Links

3

4

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

11 / 41


Simulations method

Simulating a turbulent volume

The method and Kolmogorov hypothesis
Assume a frozen atmospheric volume translated across the array

y -direction b = 128 m

x-direction Wind direction

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

12 / 41


Simulations method

Simulating a turbulent volume

The method and Kolmogorov hypothesis
Assume a frozen atmospheric volume translated across the array Wind-speed 10­15 m s- Kolmogorov turbulence: q (r ) - q (r + r)
2 1

= Dq (|r|) = Dq (r ) = 6.88

r r0



In two-dimensional approaches, exponent depends on geometry of the turbulent volume
For a thin sheet 2/3 For a thick sheet 5/3

In our approach, directly simulate the three dimensional volume

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

12 / 41


Simulations method

Simulating a turbulent volume

Generating large 3D Kolmogorov volumes
Array size 15km в 15 km Wind: 1 hour в 10 ms
-1

= 36 km

Need to generate volumes with > 109 elements, aliasing makes FFT-based methods inefficient See: http://www.mrao.cam.ac.uk/~bn204/alma/

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

13 / 41


Simulations method

Simulating a turbulent volume

Generating large 3D Kolmogorov volumes
Array size 15km в 15 km Wind: 1 hour в 10 ms
-1

= 36 km

Need to generate volumes with > 109 elements, aliasing makes FFT-based methods inefficient

z

z

z

x

y

x y

x y

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

13 / 41


Simulations method

Simulating a turbulent volume

Alternative: Large-eddy simulation

Alison Stirling's memos Much more physics, more input parameters likely to be much more accurate Computationally very expensive Not feasible to LES a large enough volume, at sufficient resolution, but a hybrid technique probably possible

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

14 / 41


Simulations method

2d projections and steepening of structure fn

Outline
1 2

Introduction Simulations method Framework Simulating a turbulent volume 2d projections and steepening of structure fn Results Results without phase correction Fast-switching phase calibration WVR + Fast-switching Summar y/Links

3

4

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

15 / 41


Simulations method

2d projections and steepening of structure fn

Two-dimensional Kolmogorov screen
0 0 200 400 600 800 1000 50

100

150

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

16 / 41


Simulations method

2d projections and steepening of structure fn

Two-dimensional Kolmogorov screen + two adjacent screens
0 0 200 400 600 800 1000 50

100

150

0 0

200

400

600

800

1000

50

100

150

0 0

200

400

600

800

1000

50

100

150

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

16 / 41


Simulations method

2d projections and steepening of structure fn

Adding slices produces steepening
0 0 200 400 600 800 1000 50

100

150

1st slice
0 0 200 400 600 800 1000 50 100

150

2nd slice
0 0 200 400 600 800 1000 50 100

150

3rd slice
0 0 200 400 600 800 1000 50 100

150

1st­10th slices
B. Nikolic, et al (University of Cambridge) Simulating Atmospheric Phase Errors September 2008 17 / 41


Simulations method

2d projections and steepening of structure fn

Adding slices produces steepening II
0 0 200 400 600 800 1000 50

100

150

1st­10th slices
0 0 200 400 600 800 1000 50 100

150

10th­20th slices
0 0 200 400 600 800 1000 50 100

150

20th­30th slices
0 0 200 400 600 800 1000 50 100

150

1st­100th slices
B. Nikolic, et al (University of Cambridge) Simulating Atmospheric Phase Errors September 2008 18 / 41


Simulations method

2d projections and steepening of structure fn

Line of sight effect
50 40 30 y 20 10 0 100 50 0 150

0

25

50

75

100 x

125

150

175

200

0

1

At zenith

50 40

150 100

30 y 20 10 0 50 0

0

25

50

75

100 x

125

150

175

200

0

1

10 from zenith

50 20 40 10 30 20 10 0 0 -10 -20 0 25 50 75 100 x 125 150 175 200 0 1 y

difference
September 2008 19 / 41

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors


Results

Outline
1 2

Introduction Simulations method Framework Simulating a turbulent volume 2d projections and steepening of structure fn Results Results without phase correction Fast-switching phase calibration WVR + Fast-switching Summar y/Links

3

4

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

20 / 41


Results

Results without phase correction

Outline
1 2

Introduction Simulations method Framework Simulating a turbulent volume 2d projections and steepening of structure fn Results Results without phase correction Fast-switching phase calibration WVR + Fast-switching Summar y/Links

3

4

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

21 / 41


Results

Results without phase correction

No phase correction, long integration
Increasing magnitude of phase-fluctuations

Peak: 2 Jy

Peak: 1.66 Jy

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

22 / 41


Results

Results without phase correction

No phase correction, long integration
Increasing magnitude of phase-fluctuations

Peak: 0.98 Jy

Peak: 0.45 Jy

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

22 / 41


Results

Results without phase correction

No phase correction, snapshots
Sequence of snapshots separated by about 3 minutes in time

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

23 / 41


Results

Results without phase correction

No phase correction, snapshots
Sequence of snapshots separated by about 3 minutes in time

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

23 / 41


Results

Results without phase correction

No phase correction, snapshots
Sequence of snapshots separated by about 3 minutes in time

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

23 / 41


Results

Results without phase correction

No phase correction, snapshots
Sequence of snapshots separated by about 3 minutes in time

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

23 / 41


Results

Results without phase correction

No phase correction, snapshots
Sequence of snapshots separated by about 3 minutes in time

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

23 / 41


Results

Results without phase correction

No phase correction, snapshots
Sequence of snapshots separated by about 3 minutes in time

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

23 / 41


Results

Results without phase correction

Parametrisation of magnitude of phase fluctuation

Have to specify somewhere how good/bad the atmospheric stability is Chose to do this by specifying the phase fluctuation RMS on a 300 m baseline
300 m baseline to be able to relate directly to the site-testing interferometer data Parametrisation in terms of phase to make clear the wavelength dependence

The thickness of the turbulent layer is probably around 200 m ­ several values shown in the plots below

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

24 / 41


Results

Results without phase correction

Uncalibrated: point source sensitivity
Compact configuration
1

0.5

S 0.2 0.1 0.05

0.1

0.2

0.5 rms (rad)

1

2

5

Point source sensitivity (relative to no atmospheric phase fluctuations) as function of phase rms on a 300 m baseline, for four thicknesses of the turbulent layer and no phase correction.
B. Nikolic, et al (University of Cambridge) Simulating Atmospheric Phase Errors September 2008 25 / 41


Results

Results without phase correction

Uncalibrated: point source sensitivity
Medium configuration
1

0.5

S 0.2 0.1 0.05

0.1

0.2

0.5 rms (rad)

1

2

5

Point source sensitivity (relative to no atmospheric phase fluctuations) as function of phase rms on a 300 m baseline, for four thicknesses of the turbulent layer and no phase correction.
B. Nikolic, et al (University of Cambridge) Simulating Atmospheric Phase Errors September 2008 25 / 41


Results

Results without phase correction

Uncalibrated: point source sensitivity
Extended configuration
1

0.5

S 0.2 0.1 0.01

0.02

0.05

0.1

0.2 rms (rad)

0.5

1

2

5

Point source sensitivity (relative to no atmospheric phase fluctuations) as function of phase rms on a 300 m baseline, for four thicknesses of the turbulent layer and no phase correction.
B. Nikolic, et al (University of Cambridge) Simulating Atmospheric Phase Errors September 2008 25 / 41


Results

Results without phase correction

No phase correction: beam size
Medium configuration

Point-source sensitivity
1
1

Gaussian beam size

0.5
D (arcsecs)

0.5

S 0.2

0.2

0.1 0.05

0.1

0.2

0.5 rms (rad)

1

2

5

0.1 0.05

0.1

0.2

0.5 rms (rad)

1

2

5

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

26 / 41


Results

Results without phase correction

No phase correction: snapshot errors
Medium configuration

Positional error
1
1

Fractional flux error

(arcsecs)

P

0.01

S

2

-S /S

0.1

0.1

2

2

0.01

0.001 0.01

0.02

0.05

0.1

0.2 rms (rad)

0.5

1

2

5

0.001 0.01

0.02

0.05

0.1

0.2 rms (rad)

0.5

1

2

5

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

27 / 41


Results

Results without phase correction

Snapshot observation: sensitivity variance
Compact configuration
1

S

2

-S /S

0.1

2

0.01

0.001 0.01

0.02

0.05

0.1

0.2 rms (rad)

0.5

1

2

5

Standard deviation of relative point source sensitivity as function of phase rms on a 300 m baseline, for four thicknesses of the turbulent layer and no phase correction.
B. Nikolic, et al (University of Cambridge) Simulating Atmospheric Phase Errors September 2008 28 / 41


Results

Results without phase correction

Snapshot observation: sensitivity variance
Medium configuration
1

S

2

-S /S

0.1

2

0.01

0.001 0.01

0.02

0.05

0.1

0.2 rms (rad)

0.5

1

2

5

Standard deviation of relative point source sensitivity as function of phase rms on a 300 m baseline, for four thicknesses of the turbulent layer and no phase correction.
B. Nikolic, et al (University of Cambridge) Simulating Atmospheric Phase Errors September 2008 28 / 41


Results

Results without phase correction

Snapshot observation: sensitivity variance
Extended configuration
1

S

2

-S /S

0.1

2

0.01

0.001 0.01

0.02

0.05

0.1

0.2 rms (rad)

0.5

1

2

5

Standard deviation of relative point source sensitivity as function of phase rms on a 300 m baseline, for four thicknesses of the turbulent layer and no phase correction.
B. Nikolic, et al (University of Cambridge) Simulating Atmospheric Phase Errors September 2008 28 / 41


Results

Fast-switching phase calibration

Outline
1 2

Introduction Simulations method Framework Simulating a turbulent volume 2d projections and steepening of structure fn Results Results without phase correction Fast-switching phase calibration WVR + Fast-switching Summar y/Links

3

4

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

29 / 41


Results

Fast-switching phase calibration

Fast switching phase calibration
Medium configuration, 15 s cycle
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, et al (University of Cambridge)

antenna #

Simulating Atmospheric Phase Errors

September 2008

30 / 41


Results

Fast-switching phase calibration

Fast switching phase calibration
Compact configuration, 15 s cycle
50 1.5 1 40 0.5 antenna # 30 (rad) 20 10 -1.5 0 0 50 20 40 60 80 time (integration #) 1 100 120 140 0 1 40 30 (rad) 20 -0.5 10 -1 0 0 20 40 60 80 time (integration #) 100 120 140 0 1 0 0 -0.5 -1

0.5

B. Nikolic, et al (University of Cambridge)

antenna #

Simulating Atmospheric Phase Errors

September 2008

31 / 41


Results

Fast-switching phase calibration

Fast-switching calibration: point source sensitivity
Compact configuration
1

0.5

S 0.2 0.1 0.1

0.2

0.5

1 rms (rad)

2

5

10

Relative point source sensitivity, perfect fast-switching calibration with a 15 s duty cycle, 1.5 degree offset to calibrator, calibration transfer from lower frequency band.
B. Nikolic, et al (University of Cambridge) Simulating Atmospheric Phase Errors September 2008 32 / 41


Results

Fast-switching phase calibration

Fast-switching calibration: point source sensitivity
Medium configuration
1

0.5

S 0.2 0.1 0.1

0.2

0.5

1 rms (rad)

2

5

10

Relative point source sensitivity, perfect fast-switching calibration with a 15 s duty cycle, 1.5 degree offset to calibrator, calibration transfer from lower frequency band.
B. Nikolic, et al (University of Cambridge) Simulating Atmospheric Phase Errors September 2008 32 / 41


Results

Fast-switching phase calibration

Fast-switching calibration: point source sensitivity
Extended configuration
1

0.5

S 0.2 0.1 0.1

0.2

0.5

1 rms (rad)

2

5

10

Relative point source sensitivity, perfect fast-switching calibration with a 15 s duty cycle, 1.5 degree offset to calibrator, calibration transfer from lower frequency band.
B. Nikolic, et al (University of Cambridge) Simulating Atmospheric Phase Errors September 2008 32 / 41


Results

Fast-switching phase calibration

Fast-switching: beamsize
15 s calibration cycle, 1.5 degree offset to calibrator

Point-source sensitivity
1
1

Gaussian beam size

0.5
D (arcsecs)

0.5

S 0.2

0.2

0.1

0.1

0.2

0.5

1 rms (rad)

2

5

10

0.1

0.1

0.2

0.5

1 rms (rad)

2

5

10

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

33 / 41


Results

WVR + Fast-switching

Outline
1 2

Introduction Simulations method Framework Simulating a turbulent volume 2d projections and steepening of structure fn Results Results without phase correction Fast-switching phase calibration WVR + Fast-switching Summar y/Links

3

4

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

34 / 41


Results

WVR + Fast-switching

Radiometric phase correction
Expected to work in combination with switching on a 3 minute time scale Want to correct:
Phase fluctuation in between phase calibration scans Phase error due to transfer of the phase solution from the quasar

The specification is very ambitious:
corrected uncorrected prms = (1 + c )10 µm + 0.02 в prms

(1)

The additive (left-hand) term is expected to be due to thermal noise in the radiometer, so Gaussian-distributed, uncorrelated between antennas, independent of baseline length Some encouraging test results, but:
Dr y fluctuations? Need to get the models almost perfect to meet the propor tional par t of error budget
B. Nikolic, et al (University of Cambridge) Simulating Atmospheric Phase Errors September 2008 35 / 41


Results

WVR + Fast-switching

183 GHz WVR Testing at SMA results
Total fluctuations (no running mean removed): reduced from 271 to 75 µm
1000

500

p (µm)

0

-500

-1000

4

4.5

5 t (hours UT)

5.5

6

6.5

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

36 / 41


Results

WVR + Fast-switching

183 GHz WVR Testing at SMA results
Fluctuations from five minute average: reduced from 164 to 56 µm
600

400

200

p (µm)

0

-200

-400

-600

4

4.5

5 t (hours UT)

5.5

6

6.5

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

36 / 41


Results

WVR + Fast-switching

WVR phase correction: point source sensitivity
Assuming wet path fluctuations only and to-spec performance

If to-spec:
1

0.5 S 0.2 0.1 0.1

0.2

0.5

1

2 rms (rad)

5

10

20

50

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

37 / 41


Summary/Links

Outline
1 2

Introduction Simulations method Framework Simulating a turbulent volume 2d projections and steepening of structure fn Results Results without phase correction Fast-switching phase calibration WVR + Fast-switching Summar y/Links

3

4

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

38 / 41


Summary/Links

Summary
If phase correction techniques work as well as we hope, the user will only ever need to include thermal-like phase errors in simulations Simulations useful for algorithms development, especially as a fully 2D array at the high site is at least a couple of years away In this case, the simulations steps are separable, linked by a standard file format
Can easily use a range of available tools Easy to integrate own tools Components can be easily re-used in other projects

Full writeup, results, code available at: http://www.mrao.cam.ac.uk/~bn204/alma/memo- turb

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

39 / 41


Summary/Links

References/Links I

Workshop on Simulations for ALMA, Grenoble 2008 http://www.mrao.cam.ac.uk/~bn204/almasim08/ B. Nikolic, et al. Simulating Atmospheric Phase Errors, Phase Correction and the Impact on ALMA Science ALMA Memo to be published http://www.mrao.cam.ac.uk/~bn204/alma/ W. Cotton Astronomy Software for Algorithm Development http://www.cv.nrao.edu/~bcotton/Obit.html

B. Nikolic, et al (University of Cambridge)

Simulating Atmospheric Phase Errors

September 2008

40 / 41


Summary/Links

References/Links II
B. Nikolic, et al Phase Correction for ALMA: Adaptive Optics in the Submillimetre http://www.eso.org/sci/publications/messenger/ archive/no.131- mar08/ Lane R. G., Glindemann A., Dainty J. C., 1992, Waves in Random Media, 2, 209 Carilli C. L., Holdaway M. A., 1999, Tropospheric phase calibration in millimeter interferometry. ALMA Memo Series 262, NRAO --, 2004, Does the aca need phase compensation? ALMA Memo Series 491, The ALMA Project Holdaway M. A., Owen F. N., 1995, A test of fast switching phase calibration with the vla at 22 ghz. ALMA Memo Series 126, The ALMA Project
B. Nikolic, et al (University of Cambridge) Simulating Atmospheric Phase Errors September 2008 41 / 41