1. Calibration You never know – it might be important.

2. Flux density : 1 Jansky = 10 -26 W/m 2 /Hz P r = ½ A eff S d  (A eff := collecting area, S:=flux density) P c = kT ref d kT A = ½ A eff.S T sys = T A + T spill + T sky + T rx Equivalent noise temperature PrPr PcPc

3. What are we measuring? Typical receiver systems have large gain which varies with time. Abandon detected power for calibration: use only equivalent noise temperatures. ~100dB ( ) 2 Sampler

4. The noise equation T sys = T A + T spill + T sky + T rx + T 2.7K Atmospheric “seeing” Time, temp etc kT A = ½ A eff.S Elevation Position on sky

5. NAR – noise- adding radiometer Jargon: “noise tube” =“noise diode” =“noise source” =“cal”

6. A real receiver …

7. Antenna gain kT A = ½ A eff.S T A /S =1/2k. A eff

8. Bandpass calibration Calibrate bandpass by observing “off source”

9. Interferometers…. at last Single dish : amplitude (vs frequency) Interferometer –Amplitude (but no large DC term) –Phase –Delay (phase vs frequency)

10. ATCA calibration practice Fiducial calibrator (delays, amplitude) once per ~12 hour observation Secondary calibrators (phase, amplitude) once per 10 minutes ~ 2 hours linear interpolation of amp, phase

11. Atmosphere  Ionosphere dominant < ~3 GHz,  ~    eutral atmosphere,  ~  ”Outer-scale” ~ 30km  nstrumental effects Phase errors

12. Measured visibility vs true visibility: Assume errors small: Interferometer calibration Real = amplitude Perfect response Imaginary=phase

13. Image distortion Amplitude errors (symmetric) Phase errors (antisymmetric )

14. Self-calibration Standard calibration : image quality ~100:1 Self-calibration: G i : N complex gains N*(N-1)/2 visibilities (complex constraints)  Can solve for the G i  Image quality >> 1000:1

15. More to think about Self-calibration Polarization calibration: online XY phases Spectral-line (bandpass) calibration Data flagging/editing Absolute flux calibration Pointing calibration RFI Astrometry (milli-arcsecond positions)