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ATCA ­ Calibration at mm wavelengths
Rick Forster University of California, Berkeley Hat Creek Radio Observatory Berkeley-Illinois-Maryland Association

Topics:

Basics of interferometry The atmosphere Amplitude & phase calibration Atmospheric & instrumental effects Antenna effects
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ATCA synthesis workshop - May 2003


ATCA Bands
Band
L S C X K W

cm
20 13 6 3 1.2 0.35

GHz
1.5 2.3 5.6 8.6 20.5 87.5

mJy/b
0.19 0.24 0.22 0.21 0.53 2.70

beam
33 22 10 5 2 0.6

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A few definitions
Brightness B = 2k TB/2 W/Hz m2 Flux density S = B d W/Hz m-2 Effective area Aeff = D2 m2 Received power VA2 = Aeff S Watts Janskys/K S/TA = 3510/D2 Jy/K V2 or the total output power is TSYS = TR + TSKY + TA K (100+200+.04 K) V (volts)
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Tsys ­ `Paddle' or Chopper Wheel method
RF

~

LO

G

PB

Sampler

Amb Sky

IF

s

Delay

Digitized IF (V)



V2

Tsys =

(

Tamb - Tsky V2amb ­ V2sky

)

V2sky -Tsky
Tsys Tsky Tamb

T

Tsys sets the flux scale and the noise level! sn
)

n= = sin-1(n/s)

2 k Tsys

bw·t

Jy

k=1380 Jy m2/K Tsys=300 K A=380 m2 =0.3 bw=128 MHz t=10 sec

= sin-1(0.2) ~ 12o
ATCA synthesis workshop - May 2003

n=0.2 Jy
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Basic Interferometry
g = B x ^ s

_

g = geometrical delay
Tsys = system temperature Tant = antenna temperature

^ s

_
B

= Ny­Nn correlation coefficient N

Digitized IF from two antennas

Correlator

Ant 1 Ant 2

1x2



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Correlation Coeffieient

~ 5 10

-4

Tsys ~ 200 K Jy/K ~ 150

Correlation Function

64 lag channels (+/- 32)

Fourier Transform
32 freq channels (amp & pha) S = Tsys Jy/K ~ 15 Jy

Ampl (Jy) & Phase

Visibility

V = Aei



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delay
Lay, 1997

Atmosphere

absorption
TA = Tsou ( e- ) Tsky = Tatm (1-e- ) Tsys = TR+Tsky+TA

Tsys = TR+Tatm(1-e-)+Tsou(e-) T'
sys

= TRe +Tatm(e -1)+Tsou

T'

sys

= Tsyse

for = 1, e = 2.7
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Opacity of the Atmosphere ­ O2 & H2O
50-70 GHz

O2

84.9-87.3 H42 SO SiO

118 GHz
88.5-91.3 HCN HCO+ CH3OH HC3N

O2

180-190 GHz

H2O

H2O
22 GHz

H2O O2

50

100

150

Frequency (GHz)
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Butler & Desai, 1999 D Log

Structure Function ( vs D)
= 1.0 (Gaussian) = 5/6 (Kolmogorov) = 1/2 (Lorentzian)

D saturation ~0

Log Distance (D) Lay, 1997
10 min

Power density

"Frozen Turbulence" Model ( power vs t)
= 5/6, 1km layer, 5km/s wind, 500m D
3 hrs

30 sec

Longer baselines shifts peak right Stronger winds shifts peak left

Log time
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M87 data calibrated with 3C273
Amplitude Phase
80m

45m

15m

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Baseline Solution ­ C-array, March 2003
Phases BEFORE Correction Phases AFTER Correction

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Absolute flux calibration

Test source

1310+323 (QSO)

0909+013 (QSO)

cal

test
source

MWC 349 (HII)

Use a primary flux calibrator (planet or HII region) to check the value of Jy/K. Use your phase calibrator to monitor temporal gain changes.
ATCA synthesis workshop - May 2003

Use a test source to help quantify the effects of atmospheric decorrelation in the image plane.
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Passband ­ 32 visibility
channels over 100 MHz Channel BW = 3.125 MHz (~11 km/s)
4 MHz = 14 km/s 64ch = 0.2 km/s

n = 2.6 Jy (each 11 km/s channel) s/n = 12/2.6 ~ 4.6 phase noise ~ 11 deg
(ave 100 MHz ~ 6 times better)

At 0.2 km/s channel n = 8x2.6 ~ 21 Jy
k = 1380 Jy m2/K Tsys = 560 K A = 28 m2 = ac = .70x.88 = .61 bw = 100/32 = 3.125 MHz t = 6m = 360 s
ATCA synthesis workshop - May 2003

2 k Tsys n= Jy bw t ·
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Az El
30 min

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A few final suggestions
! ! ! ! ! ! ! ! ! ! ! ! Calibrate Tsys often Check Jy/K on a flux cal Mosaic sources larger than Ѕ fwhm Use offset pointing for extended sources In a pinch total power correction might help Choose nearby calibrator if baseline is uncertain Choose integration time so S/N > 5 on calibrator Use a guest calibrator to gauge atmospheric effects Don't push your observations beyond the seeing limit Avoid unnecessary PB calibration, & check sensitivity Monitor the atmosphere ­ abort 3mm in severe conditions Fast-switching might be worth a try in reasonable conditions

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