Spectral Line Calibration

Techniques with Single Dish Telescopes

K. O’NeilNRAO - GB

Determiningthe Source

Temperature

Determining Tsource

• Tmeas (,az,za) = Tsrc(,az,za)

Determining Tsource

• Tmeas (,az,za) = Tsrc(,az,za)

Or at least, that is what we want…

Determining Tsource

• Tmeas (,az,za) = Tsrc(,az,za)

+ Tsystem -> Rx, other hardware

The noise that is picked up as the signal is received and passed down through the

processing system

Determining Tsource

• Tmeas (,az,za) = Tsrc(,az,za)

+ TRX, other hardware + Tspillover (za,az)

Determining Tsource

• Tmeas (,az,za) = Tsrc(,az,za)

+ TRX, other hardware + Tspillover (za,az) + Tcelestial(t)

• Tmeas (,az,za) = Tsrc(,az,za)

+ TRX, other hardware + Tspillover (za,az) + Tcelestial(t) + TCMB

+ Tatm(za)

Determining Tsource

• Tmeas (,az,za) = Tsrc(,az,za) + TRX, other hardware + Tspillover (za,az) + Tcelestial(t) + TCMB

+ Tatm(za)

Tmeas = Tsource + Teverything else

Determining Tsource

• Tmeas (,az,za) = Tsrc(,az,za) + TRX, other hardware + Tspillover (za,az) + Tcelestial(t) + TCMB

+ Tatm(za)

Tmeas = Tsource + Teverything else

Determining Tsource

Determining Tsource

ON source OFF source Tsource + Teverything else Teverything else

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Determining Tsource

ON - OFF(Tsource + Teverything else) - (Teverything else)

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Determining Tsource

(ON – OFF)/OFF[(Tsource + Teverything else) - (Teverything else)]/ Teverything else

=(Source temperature)/(”System” temperature)

% T

sys

Determining Tsource

(ON – OFF)/OFF[(Tsource + Teverything else) - (Teverything else)]/ Teverything else

=(Source temperature)/(”System” temperature)

% T

sys

???

Choosing the

Best OFF

Off Source Observations

Two basic concepts

• Go off source in sky• Go off source in frequency/channels

Like most things in science:Easy to state, complicated in practice

Off Source Observations

Position SwitchingON Source OFF Source

Off Source ObservationsPosition Switching

• Little a priori information needed• Typically gives very good results• Can be done through:

– Moving the telescope (re-pointing onto blank sky)– Moving a secondary or tertiary dish– Beam switching (two receivers on the sky)

• Disadvantages: – System must be stable over time of pointings– Sky position must be carefully chosen– Source must not be extended beyond positions– May take significant time (not true for beam switching)

Off Source Observations

off source in frequency/channels

• Typically gives very good results

• Requires well understood line of interest

• Can be done through: – Baseline fitting– Frequency switching– Some combination of the two

Off Source ObservationsBaseline Fitting

• Simplest & most efficient method• Can be from average of multiple scans or single fit

• Not feasible if:Line of interest is large compared with bandpassStanding waves in data Cannot readily fit bandpassDo not know frequency/width of line of interest

• Errors are primarily from quality of fit

Off Source Observations

Frequency Switching

Off Source ObservationsFrequency Switching

• Allows for rapid switch between ON & OFF observations• Does not require motion of telescope• Can be very efficient• Disadvantages:

Frequency of line of interest should be known*System must be stable in channel spaceWill not work with changing baselines, wide lines

*But not always…

Mapping an Extended Source

Off Source ObservationsVariations

Possible alternative if frequency switching is not an option

System must be very stable

Off source must truly be off!

Off Source ObservationsVariations

There are many other variations to the main themes given:

• Position switching by moving subreflector• Using average offs from a variety of

observations• Frequency switching with many baseline scans • Etc, etc

The ideal off:• Is well understood• Has minimal systematic effects• Adds little noise to the results• Maximizes the on-source telescope time

Determining Tsource

(ON – OFF)/OFF[(Tsource + Teverything else) - (Teverything else)]/ Teverything else

Tsource

Tsystem

Result =

Units are % System Temperature

Need to determine system temperature to calibrate data

DeterminingSystem

Temperature

Determining Tsystem

Theory

Measure various components of Tsys:

TCMB ― Well known (2.7 K)

TRX, hardware ― Can be measured/monitored Tcel(t) ― Can be determined from other measurements Tatm(za) ― Can be determined from other measurements

Tgr(za,az) ― Can be calculated

Decreasing

Confidence

Determining Tsys

Noise Diodes

Tsrc/Tsys = (ON – OFF)/OFF

Tdiode/ Tsys = (ON – OFF)/OFF

Tsys = Tdiode * OFF/(ON – OFF)

Noise Diodes

Determining Tsys

Noise Diodes - Considerations

• Frequency dependence

Determining Tsys

Lab measurements of the GBT L-Band calibration diode, taken from work of M. Stennes & T. Dunbrack - February 14, 2002

Noise Diodes - Considerations

• Frequency dependence

• Time stability

Determining Tsys

Lab measurements of the GBT L-Band calibration diode, taken from work of M. Stennes & T. Dunbrack - February 14, 2002

Determining Tsys

Noise Diodes - ConsiderationsNoise Diodes - Considerations• Frequency dependence

• Time stability

• Accuracy of measurementsTypically measured against another diode or other calibrator

Errors inherent in instruments used to measure both diodes

Measurements often done in lab -> numerous losses through path from diode injection to back ends

2 measured value = 2

standard cal + 2 instrumental error + 2

loss uncertainties

Determining Tsys

Noise Diodes - Considerations• Frequency dependence

2total = 2

freq. dependence

+ 2stability

+ 2measured value

+ 2conversion error

• Time stability• Accuracy of measurements

Determining Tsys

Hot & Cold Loads

• Takes antenna into account

• True temperature measurement

Hot LoadThot

Cooling SystemTcold

Determining Tsys

Hot & Cold Loads

• Takes antenna into account• True temperature measurement

Requires:• Reliable loads able to encompass the receiver• Response fast enough for on-the-fly measurements

Determining Tsys

Theory:Needs detailed understanding of telescope & structureAtmosphere & ground scatter must be stable and understood

Noise Diodes:Can be fired rapidly to monitor temperatureRequires no ‘lost’ timeDepends on accurate measurements of diodes

Hot/Cold Loads:Can be very accurateObservations not possible when load onMust be in mm range for on-the-fly measurements

In reality, all three methods

could

be combined for best accuracy

Determining Tsource

Tsource = (ON – OFF)

Tsystem

OFF

From diodes, Hot/Cold loads, etc.

Blank Sky or other

Telescope response has not been accounted for!

DeterminingTelescope Response

Telescope Response

Ideal Telescope:

– Accurate gain, telescope response can be modeled

– Can be used to determine the flux density of ‘standard’ continuum sources

– Not practical in cases where telescope is non-ideal

(blocked aperture, cabling/electronics losses, ground reflection, etc)

Telescope Response

• Ideal Telescope:

Telescope Response

• ‘Bootstrapping’:

Observe source with pre-determined fluxesDetermine telescope gain

Tsource = (ON – OFF) Tsystem 1

OFF GAIN

GAIN = (ON – OFF) Tsystem OFF Tsource

Telescope Response

• ‘Bootstrapping’:

Useful when gain is not readily modeledOffers ready means for determining telescope

gain

Requires calibrator flux to be well known in advance

Not practical if gain changes rapidly with position

Telescope Response

Pre-determined Gain curves:

Allows for accurate gain at all positionsSaves observing timeCan be only practical solution (complex

telescopes)

Caveat:Observers should always check the predicted

gain during observations against a number of calibrators!

Tsource = (ON – OFF)

Tsystem 1

OFF GAIN

From diodes, Hot/Cold loads, etc.

Blank Sky or other

Theoretical, or Observational

Determining Tsource

Great, you’re done!Great, you’re done?

A FewOther Issues

Other Issues:Pointing

Results in reduction of telescope gainAlways check telescope pointing!

Other Issues:Focus

Results in reduction of telescope gainCorrected mechanicallyAlways check focus!!!

Other Issues:Side Lobes*

• Allows in extraneous or unexpected radiation

• Can result in false detections, over-estimates of flux, incorrect gain determination

• Solution is to fully understand side lobes

*Covered more fully in talk by Lockman

Beam

Other Issues:Coma & Astigmatism

Comatic Error: – sub-reflector shifted perpendicular from main beam– results in an offset between the beam and sky

pointing

Image from ATOM 99-02, Heiles

Other Issues:Coma & Astigmatism

Astigmatism: deformities in the reflectors

Can result in false detections, over-estimates of flux, incorrect gain determination

Solution is to fully understand beam shape

Image from ATOM 99-02, Heiles

Other Issues:The Atmosphere

This is a huge issue.

Can result in false detections, over-estimates of flux, incorrect gain determination

Solution is to fully understand beam shape

Image from ATOM 99-02, Heiles

Other Issues:The Atmosphere

This is a huge issue.

So huge it deserves its own talk.

Can result in false detections, over-estimates of flux, incorrect gain determinationSolution is to fully understand beam shape

Image from ATOM 99-02, Heiles

Other Issues:The Atmosphere

This is a huge issue.

So huge it deserves its own talk.

Which is next.

Can result in false detections, over-estimates of flux, incorrect gain determinationSolution is to fully understand beam shape

Image from ATOM 99-02, Heiles

Conclusion:(applies to all science research)

• Astronomy instrumentation and calibration is complicated

• Learn the system you are using well

• Talk with the instrument staff frequency, and visit often

• To produce good science you must understand the instrument and techniques you are using

You are ultimately responsible for the quality of your data!

The End