Interferometric Gain Calibration for ALMA

Jim Gibson and Jack Welch

UC Berkeley RAL

Major Features

• Accuracy comes from (a) a well understood standard horn gain calculation: e<1% (Schelkunoff and Frijs), and (b) accurate two load ALMA Tsys calibration

• Use simple ambient temperature cal receiver• Use wideband natural source, flux need not be known• Decorrelation delay path with 1GHz band > 40cm• Use the system correlator as the power meter• Use the two load cal system for the gain transfer

antenna

Single Antenna

ki

Interferometer Pair

jiij kkk with

form the fraction

Gain Determination

Jovian Spectrumnear λ 1 cm

Tk R

10 1.42

15 2.00

20 2.38

25 2.63

30 2.83

35 2.99

40 3.09

45 3.18

50 3.25

CO Line Ratio vs. Kinetic Temperature

Derived Tk from different Brightness ratio accuracies

• A. 20% : R=2.5: range: 1.75 – 3.25• 13K ≤ Tk ≤ 51K

• B. 10% : R=2.5: range :2.15 – 2.85• 17K ≤ Tk ≤ 32K

• C. 5%: R=2.5: range: 2.3 – 2.7• 20K ≤ Tk ≤ 27K

Saturn as a transfer standard at 2.8 mm

• Assumptions:• ALMA rcvr Tsys = 50k• Cal rcvr Tsys = 1000k• Receiver bandwidth = 1 GHz• Cal antenna: 20x2.7x2.0 cm ~30db gain (exactly known)• Horn loss: 2% +/- .2%• Saturn flux ~ 220 Jy• Saturn diameter: ~16”• Geom mean Tsys = 220k• Geom mean effective area: (68 x 5.4 x10 -4)1/2 =0.2m2

• S/N = 150 in 1000 seconds with four antenna pairs

Proposed Calibration Receiver

LO1 ref

LO2 ref

IF

Mixer and IF amplifiers

Issues/Alternatives

• Mount cal receiver on an ACA antenna• Use an STI 65K cooler on cal receiver for

better Tsys. 5000$, 106 hours life.• Horn gain: Shelkunoff and Frijs: Advanced

Antenna Theory; Wrixon and Welch, IEEE Trans AP, AP20, 1972; Chiu and Semplak, BSTJ, 44,,527, 1965; Gibson et al, 2005, Icarus, 173, 439.

• Transfer of Tsys to cal horn