Fourth IRAM Millimeter Interferometry School 2004: Atmospheric phase correction 1

Atmospheric phase correction

Jan Martin Winters

IRAM, Grenoble

Fourth IRAM Millimeter Interferometry School 2004: Atmospheric phase correction 2

The problem

Atmosphere introduces (complex) refractive index => path delay + absorption/emission

Water vapor poorly mixes with dry air => „eddies“ Atmosphere is turbulent => fluctuating path delay Time varying deformation of wavefront => Phase

fluctuation=>

Degradation of source amplitudeDegradation of spatial resolution

Fourth IRAM Millimeter Interferometry School 2004: Atmospheric phase correction 3

Effect of phase noiseAn interferometer measures amplitude and phase of the incoming wave (complex visibility). Integration of the signal can be concieved as the summation of vectors, characterized by their length (amplitude) and orientation (phase)

V1→

V3→

V2→

V=Vi→ →

Without phase noise With phase noise

V1→

V3→

V2→

V=Vi→ →

Degradation of amplitude + smearing out of structure information

)2

exp(VV2

sourcemeas

|V|=Vi|→ → |V|<Vi|→ →

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The idea

Determine the amount of water vapor in front of each telescope by measuring its emission

Deduce the path delay caused by this water column

Apply a corresponding phase correction

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The methodAtmospheric emission

Tsky = TAtm (1 e)

Withdwdpwv

Excess path

L = Ld + LV = Ld + 6.52 pwv [cm]

Phase delay

L = L/ Tsky) Tsky

=> Measure Tsky (fluctuating) in front of each telescope Use atmospheric model to derive (, TAtm,) pwv, L/ Tsky

Compute phase correction and apply it to data

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In practice (I): Total power radiometry, e.g., in the 1mm band (a factor ~6

more sensitive to pwv than 3mm band) using the astronomical receivers

This was the standard method used at the PdBI until August 2004

Problems: Clouds: large , low n => large variations in Tsky, but only small

effect on the path excess L Measurement at only one frequency(band): effect of clouds

cannot be removed Long-term stability of the astronomical receivers (which are

designed for sensitivity) (important for absolute phase correction)

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In practice (II):B) Multi channel radiometry in a water line (here: at 22GHz)

using dedicated instruments (Rem.: ALMA will use the 183GHz line)

This is the standard method used at the PdBI since August 2004

Advantages: 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

Instruments designed for stability => absolute phase correction

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22GHz monitor

Sampling rate: 1s

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• unstable atmospheric conditions• 4.4mm pwv• phases @ 110 GHz• A-configuration: E23-W27-N29-E16-W23-N13• 8 min on NRAO150

Results 22GHz correction (I)

Temporal phase variation

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Results 22GHz correction (II)Turbulent conditions, 4.4mm pwv, A-configuration

Calibrator NRAO150, strong continuum point source

=> Factor 2.5 gain in amplitude

without phase correction with phase correction

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Kolmogorov turbulenceTurbulence is fed by energy input on large scales L (= outer scale of the turbulent field) This energy is cascaded down to smaller scales (in a stationary process) until it is dissipated into heat on the smallest scales 0 (inner scale) by viscosityThe velocity fluctuation associated with linear scale is v, the typical time scale of the fluctuation is = / v

Per unit mass, the rate at which energy is fed into eddies of size is then

~ v2 / = v

3 / = vL3 / Lor v

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Phase structure functionCharacterization of fluctuations by the structure function

Dv(d) = < [vx+dvx)]2 > ≈ vd2 ~ d(velocity)

Phase fluctuations are induced by fluctuations of the refractive index due to water vapor eddies in the turbulent atmosphere

Dn(d) ~

d(refractive index)

On large scales (d ≫ height of turbulent layer, “thin screen”, 2D) D(d) ~

d(phase, 2D)

On smaller scales: 3D description, “thick screen” D(d) ~

d(phase, 3D)

For the rms phase noise = (D(d))1/2 power law spectra are expected with exponents between 1/3 and 5/6

(On scales d > L: uncorrelated, D(d) ≈ const)

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Results 22GHz correction (III)Turbulent conditions, 4.4mm pwv, A-configuration

exp(- 2/2)

15 0.97

30 0.87

50 0.68

70 0.47

100 0.22

200 0.002

Decorrelation factors

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Results 22GHz correction (IV)

@ 3mm