atmospheric phase correction atmospheric phase correction at the Plateau de Bure at the Plateau de Bure

interferometerinterferometer

IRAM interferometry school 2006IRAM interferometry school 2006

Aris KarastergiouAris Karastergiou

No atmosphereNo atmosphere

• Interferometers can image astronomical sources by measuring delays in arrival times of incoming wavefronts between pairs of antennas

Effects of the atmosphereEffects of the atmosphere

• Variations in the refractive index of the atmosphere above each antenna distort the wavefront and result in delays different to those predicted.

Water vapourWater vapour

• At radio frequencies, the variations of the refractive index are almost entirely due to parcels of water vapour, which are poorly mixed with the atmosphere.

• Luckily, water vapour not only causes delays in propagation, it also emits radiation. Both effects are proportional to the water vapour present along the line of sight.

therefore…

by monitoring the emission of water vapour in the line of sight of each antenna, we could compute the extra delay induced by the atmosphere, and correct the phase

But how do we do it?But how do we do it?

The atmosphereThe atmosphereAtmospheric transmission in the zenith direction from the Plateau de Bure site. The six curves correspond to different amounts of water vapour, starting from 0 (light blue) to 10 mm (black). Two blue arrows denote two water lines used for atmospheric phase correction, at 22 and 183 GHz.

IRAM against atmospheric phase IRAM against atmospheric phase noisenoise

• Until August 2004: The amount of water was derived from the total

power measurements of the astronomical receivers in the 1mm band. Good overall performance but some significant drawbacks. Clouds (high temperature, small path length effect) are not accounted for.

• After August 2004: Dedicated receivers placed in each of the six

antennas, monitor the 22 GHz emission line. New system is separate from the astronomical receivers.

The receiversThe receivers

Uncooled, broadband (~7 GHz).

Extremely stable

Gain fluctuations of order 10-4

• Filters extract three ~1 GHz bands from the total bandwidth.

Cloud contribution to Tsky has different frequency dependence (~ v2) to water vapour, so three channel system allows to remove this “baseline”, leaving only the water vapour emission.

• Effect of clouds can be removed :

Tsky,H2O = TvaporTcloud =

= TAtm (1 ev) + TCloud (1 ec) , C ~ 2

linearize cloud exponential term, measure at two frequencies, build weighted mean:

Tdouble = Tsky ,1 – Tsky,2 ()2 = Tvapor,1 – Tvapor,2 ()2

Same for the other frequency pair, and then a subtraction of one „double“ value

from the other, to form Ttriple

An unexpected advantage of the An unexpected advantage of the triple channel systemtriple channel system

• A geostationary satellite, HOTBIRD 6 is emitting inside the first 22 GHz channel. Channels 2 and 3 can still provide the information for correcting the phase.

The dataThe data

Channel 1

Channel 2

Channel 3

combination removes continuum baseline

The dataThe data

Antenna 1

Antenna 2

The dataThe data

Between 2 antennas, the difference in the measured water vapour emission is clearly correlated with the astronomical phase.

Converting water vapour emission Converting water vapour emission to phaseto phase

• Atmospheric model:– Based on the total amount of water in the line

of sight, parameters such as the ambient temperature and pressure, and a general description of the atmosphere at that moment.

• Empirical approach:– From observations of strong sources, where

the phase is well determined, a conversion coefficient can be calculated. Not constant with time.

22 GHz calibration22 GHz calibration

• Each channel of each radiometer needs to be calibrated separately, although triple combination is useful in removing various harmful effects.

• The process involves observing a “table” at ambient temperature, to estimate the conversion factor between counts and Kelvin.

• Ambient temperature 300 K is far from sky temperature 25 K, so conversion factor is assumed linear over this large range.

• For absolute phase correction, the calibration must be extremely precise.

Relative Vs AbsoluteRelative Vs Absolute

• When moving between sources, the radiometers are pointing through different parts of the atmosphere. The phase may change by many full cycles! To track it, calibration of the 22 GHz receivers needs to be excellent!

• Relative phase correction:– Aim is to remove phase fluctuations within each on-

source period.– Reduced phase rms means higher amplitude of the

visibilities.– Required for longer baselines / higher frequencies.– Phase is not tracked when the telescope is moving

from one source to another. Less sensitive to calibration problems.

• Phase noise is larger at longer baselines. Power law dependence on baseline length (see talks by R. Lucas and J. M. Winters from yesterday).

Corrected phase

does NOT depend

on baseline length.

Calibrator NRAO150, strong continuum point source

=> Factor 2.5 gain in amplitude

without phase correction with phase correction

• Absolute calibration:– Phase is constantly tracked, even when

changing source.– Calibration requirements much more

stringent.– Astronomical phase of point-like strong

sources should be used in the 22 GHz calibration process.

– Has not been achieved yet.

Points to rememberPoints to remember

• Water vapour in the atmosphere results in noisy phases. Effect is worst for longer baselines, higher frequencies.

• To attack the problem, the emission of a water line is monitored, in the line of sight of each antenna of the interferometer.

• 22 GHz line is better for conditions with high (>4mm) water vapour. 183 GHz is more useful for dryer sites.

Points to rememberPoints to remember

• The water vapour radiometers can be used for relative phase correction, which means the phase cannot be maintained after a source change.

• Calibration of the 22 GHz receivers is crucial, given the required precision.

• Conversion of calibrated signal into phase can be done either by atmospheric model, or empirically.

The relative phase correction works well in reducing the phase noise and increasing the visibility amplitudes.

No working absolute phase correction system exists today. Plans for arrays with extremely long baselines, observing at extremely high frequencies are well under way.