CalibrationRon Maddalena

NRAO – Green BankJuly 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 TCal 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.

VHot_Off = g * THot

VCold_Off = g * TCold

VCold_On = g * (TCold + TCal)

g and TCal are unknown

Determining TCal 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 TCal may be off by 10% So… all good observers perform their own

astronomical calibration observation

Continuum - Point SourcesOn-Off Observing

N o ise D io de

D etec to r

SignalS ignal

•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 SourcesOn-Off Observing

Continuum - Point SourcesOn-Off Observing

Known: Equivalent

temperature of noise diode or calibrator (Tcal) = 3 K

Bandwidth (Δν) = 10 MHz

Gain = 2 K / Jy

Desired: Antenna temperature of

the source (TA)

Flux density (S) of the source.

System Temperature(Ts) when OFF the source

Accuracy of antenna temperature (σ TA)

Units of “intensity”

TA 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 observationsShape of the telescope beam Shape of

source.

Correcting for atmosphere and efficiencies

TR* -- secondary focus

TA* -- primary focus

Sometimes shortened to:

Telescope efficiencies – Part 1

GBT Gain Curve

Aperture efficiency

At low frequencies: ηSurf = 1

Almost always: ηr = 1

For GBT, ηfss and ηl > 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 TA.

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.

<103-104 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 observationsWeak wide lines with wide bandwdiths

High-Z CO lines 30 MHz line widths 14 GHz of bandwidth @ 30 GHz.

Raw Data

ReducedData – HighQuality

ReducedData – 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.