Calibration Ron Maddalena NRAO – Green Bank July 2009

Receiver calibration sources allow us to convert the backend’s detected voltages to the intensity the signal had at the point in the system where the calibration signal is injected.

Determining T Cal from hot-cold load measurements in the lab Place black bodies (absorbers) of two known temperatures in front of the feed and record detected voltages. V Hot_Off = g * T Hot V Cold_Off = g * T Cold V Cold_On = g * (T Cold + T Cal ) g and T Cal are unknown

Determining T Cal from hot-cold load measurements in the lab Course frequency resolution Uncertainties in load temperatures Are the absorbers black bodies? Detector linearities (300 & 75 K) Lab T Cal may be off by 10% So… all good observers perform their own astronomical calibration observation

Continuum - Point Sources On-Off Observing Observe blank sky for 10 sec Move telescope to object & observe for 10 sec Move to blank sky & observe for 10 sec Fire noise diode & observe for 10 sec Observe blank sky for 10 sec

Continuum - Point Sources On-Off Observing

Known:  Equivalent temperature of noise diode or calibrator (T cal ) = 3 K  Bandwidth (Δν) = 10 MHz  Gain = 2 K / Jy Desired:  Antenna temperature of the source (T A )  Flux density (S) of the source.  System Temperature(T s ) when OFF the source  Accuracy of antenna temperature (σ TA )

Units of “intensity” T A is usually not a unit with much scientific interest. Need to correct for:  Lost power due to… Earth’s atmosphere at the observing elevation. Telescope efficiencies Rayleigh-Jeans approximation may not be appropriate for your high-frequency observations  Shape of the telescope beam  Shape of source.

Correcting for atmosphere and efficiencies T R * -- secondary focus T A * -- primary focus Sometimes shortened to:

Telescope efficiencies – Part 1

GBT Gain Curve

Aperture efficiency At low frequencies: η Surf = 1 Almost always: η r = 1 For GBT, η fss and η l > 0.98 All may be dependent upon frequency and observing elevation (Gain or Efficiency curve) Telescope efficiencies – Part 2

Shape of the telescope beam  Shape of source. Ta, Tr, etc. will be different for different telescopes for the same sky position.

To wink or not to wink? Reminder – diode used to measure the gain and, thus, to calibrate from V to T A. GBT – traditionally winks diode when on source  Tracks fast gain changes  Slightly easier to reduce  Adds to Tsys during all your observations More time to achieve the desired sensitivity Always observing the source Arecibo – traditionally performs separate calibration observation off the source  Adds extra time to your observation  tracks gain changes less often

Should wink if 1/f gain changes will add baseline structure >10 sec for z=2.5 CO(J=1-0) at Ka-band The shorter the scan, the more likely winking will require less telescope time. < sec for galactic & extragalactic HI. Assumes 1% calibration, Tsys/Tcal = 10 To wink or not to wink? – Spectral Line

Spectral Line Calibration Today’s line observations should be treated like yesterday’s continuum observations  Weak wide lines with wide bandwdiths High-Z CO lines 30 MHz line widths 14 GHz of 30 GHz.

Raw Data Reduced Data – High Quality Reduced Data – Problematic

Spectral Line Calibration Difference experiments  Position switching  Frequency witching  Nutating secondaries  Dual-beam systems: Nodding telescope’s position Nodding optics  Multi-feed systems Atmosphere is common to all receivers (atmosphere is in the near field)

Traditional calibration algorithms Good for narrow-band observations or strong lines when baseline structures aren’t important. Not good for wide band work  Tsys and Tcal have frequency structure  Any difference in power between Sig and Ref will produce baseline structueres that are mirrors of the frequency structures inn Tsys and Tcal

Wide-bandwidth calibration Same equations but with different averaging  Vector Tcal calibration Identical to the equation used in the exercise for continuum observation Not yet incorporated into the official GBTIDL release.