1. Atmospheric phase correction for ALMA
Alison Stirling
John Richer
Richard Hills
University of Cambridge
Mark Holdaway
NRAO Tucson

2. ALMA Goal Atmospheric phase correction essential To achieve:
Diffraction-limited operation at sub-mm wavelengths on baselines up to 14 km
Corresponds to 0.01 arcsec resolution requirement
To achieve at ALMA’s highest frequencies (~950 GHz), require phase errors < 50 microns on baselines of 14 km
Typical atmospheric phase fluctuations at Chajnantor:
90-400m on 300m baselines at 25-75% level
Corresponds to fluctuations of ~ m at 14km
3% 14 degrees
5% 18 degrees
Atmospheric phase correction essential

3. Atmospheric phase dependence
Atmospheric phase fluctuations in sub-mm caused by variations in water vapour and air density

4. Phase correction strategy
To use a combination of:
Fast switching
Measure phase from a nearby point source calibrator
Measures total atmospheric phase
Intermittent (every ~10s of seconds)
Gives phase along a different line of sight
Water vapour radiometry
183 GHz radiometers four channels
Only sensitive to wet component
Continuous, on source
Two prototype WVRs built by Cambridge and Onsala now ready for testing

5. Correction Strategy Issues
How often to switch to a calibrator?
Time spent on calibrator?
Angular distance to calibrator?
Smoothing time for WVR brightness temperatures?
Calculation of conversion factor for WVR?

6. Correction Strategy
Answers depend in detail on atmospheric structure, e.g.
Ratio of wet to dry phase fluctuations
Phase structure function
Also depends on
Instrumental noise (antenna and WVR)
Distribution and brightness of point source calibrators
Aim of work: to simulate realistic atmospheric
phase fluctuations for the Chajnantor site
Day time: m (on 300 m baselines)
Night: m
Need separate analysis for day and night time conditions

7. Met Office Large Eddy Model
Solves Navier-Stokes equation on a grid
Assumes a Kolmogorov energy cascade on sub-grid scales
Models water vapour, temperature, pressure
Two scenarios:
daytime -- convection from surface heating
night time -- wind shear induced turbulence

8. Daytime profiles

9. .
1.2
Height / km
-2.5
Horizontal distance / km
2.5

10. 2.5
Y / km
-2.5
-2.5
X /km
2.5

11. Location of dry, wet and total refractive index fluctuations
Significant anticorrelation between dry and wet
Fluctuations at the temperature inversion.

12. Estimation of fluctuations from radiosonde profiles
Solid = total, Dotted wet, Dashed = dry
* = Interferometric measurements of total daytime rms phase (Evans et al, 2003)
At 50% level:
Dry: 200 microns
Wet: 400 microns
Total: 400 microns
Independent confirmation of phase fluctuation amplitude
Initial estimates of dry fluctuation component

13. Daytime structure function
Solid = dry
Dot dashed = wet
Dotted = cross-correlation term
Consistent with Kolmogorov spectrum on small scales

14. Nocturnal mean profiles
Gradient of temperature profile opposite sign from
water vapour profile

15. Evolution of night time fluctuations
0.6
Height / km
-0.3
Horizontal distance / km
0.3

16. Location of dry, wet and total refractive index fluctuations
Negative correlation between wet and dry fluctuations
near ground

17. Nocturnal structure function
Blue dashed = wet; black solid = dry
r.m.s. wet fluctuations ~ 2 x r.m.s dry
Exponent of wet: 1.0, dry: 0.8
Turn over around 800m (~ depth of layer)

18. Simulations of phase correction
AIPS++ code written by Mark Holdaway
Combines Mark’s fast switching simulator with our 3-D simulations of atmosphere
WVR simulated using `am’ radiative transfer code to calculate brightness temperatures (Scott Paine)

19. Correction process: WVR

20. WVR: rms error

21. Conclusions
Now have realisations of the atmosphere at Chajnantor for day and night conditions
Dry and wet fluctuations have different distributions depending on time of day
Have developed simulations of FS+WVR phase correction
Future plans:
Investigate different phase correction strategies
Validation of the two ALMA prototype WVRs on SMA