Atmospheric phase correctionfor ALMA

Alison Stirling

John Richer

Richard Hills

University of Cambridge

Mark Holdaway

NRAO Tucson

ALMA GoalTo achieve:• Diffraction-limited operation at sub-mm

wavelengths on baselines up to 14 km

Atmospheric phase correction essential

• 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: on 300m baselines at 25-75% level• Corresponds to fluctuations of ~300- at 14km

Atmospheric phase dependence

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

Phase correction strategyTo 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

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?

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 siteDay time: 390-1000 m (on 300 m baselines)Night: 90-290Need separate analysis for day and night time conditions

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

Daytime profiles

.H

eig

ht

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Horizontal distance / km0

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Y /

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X /km

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Location of dry, wet and total refractive index fluctuations

Significant anticorrelation between dry and wetFluctuations at the temperature inversion.

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

Daytime structure function

• Solid = dry • Dot dashed = wet• Dotted = cross-

correlation term• Consistent with

Kolmogorov spectrum on small scales

Nocturnal mean profiles

Gradient of temperature profile opposite sign fromwater vapour profile

Evolution of night time fluctuations

Hei

gh

t / k

m

0

0.6

-0.3 0.3Horizontal distance / km

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Location of dry, wet and total refractive index fluctuations

Negative correlation between wet and dry fluctuations near ground

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)

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)

Correction process: WVR

WVR: rms error

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