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Fourth IRAM Millimeter Interferometry School 2004: Atmospheric phase correction 3 Effect of phase noise An 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) V1V1 → V3V3 → V2V2 → V= V i →→ Without phase noise With phase noise V1V1 → V3V3 → V2V2 → V= V i →→ Degradation of amplitude + smearing out of structure information |V|= V i | →→ |V|< V i | →→
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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|→ →
Fourth IRAM Millimeter Interferometry School 2004: Atmospheric phase correction 4
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
Fourth IRAM Millimeter Interferometry School 2004: Atmospheric phase correction 5
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
Fourth IRAM Millimeter Interferometry School 2004: Atmospheric phase correction 6
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)
Fourth IRAM Millimeter Interferometry School 2004: Atmospheric phase correction 7
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
Fourth IRAM Millimeter Interferometry School 2004: Atmospheric phase correction 8
22GHz monitor
Sampling rate: 1s
Fourth IRAM Millimeter Interferometry School 2004: Atmospheric phase correction 9
• 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
Fourth IRAM Millimeter Interferometry School 2004: Atmospheric phase correction 10
Fourth IRAM Millimeter Interferometry School 2004: Atmospheric phase correction 11
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
Fourth IRAM Millimeter Interferometry School 2004: Atmospheric phase correction 12
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
Fourth IRAM Millimeter Interferometry School 2004: Atmospheric phase correction 13
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)
Fourth IRAM Millimeter Interferometry School 2004: Atmospheric phase correction 14
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
Fourth IRAM Millimeter Interferometry School 2004: Atmospheric phase correction 15
Results 22GHz correction (IV)
@ 3mm