Calibration Ron Maddalena NRAO – Green Bank November 2012.
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Transcript of Calibration Ron Maddalena NRAO – Green Bank November 2012.
![Page 1: Calibration Ron Maddalena NRAO – Green Bank November 2012.](https://reader030.fdocuments.net/reader030/viewer/2022032702/56649ccb5503460f94993d31/html5/thumbnails/1.jpg)
CalibrationRon Maddalena
NRAO – Green BankNovember 2012
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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.
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Reference observations
Difference a signal observation with a reference observation
Types of reference observations Frequency Switching
In or Out-of-band Position Switching Beam Switching
Move Subreflector Receiver beam-switch
Dual-Beam Nodding Move telescope Move Subreflector
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Position-Switched (On-Off) Observing
N o ise D io de
D etec to r
SignalS ignal
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Typical Position-Switched Calibration Equation for a Point Source
BW
CalOffOn
RefSys
RefSysA
tElevAtA
pA
TRefRef
RefT
TRef
RefSigT
eTAreaElev
kS
)()()(
)(
)(
)()()(
)(),(
2)( ),(),(
A(Elev,t) = Air Massτ(ν,t) = Atmospheric Zenith OpacityTcal = Noise Diode TemperatureArea = Physical area of the telescopeηA (ν,Elev) =Aperture efficiency (point sources)TA (ν) = Source Antenna Temperature
S(ν) = Source Flux DensitySig(ν), Ref (ν) = Data taken on source and on blank sky (in units backend counts) On,Off = Data taken with the noise diode on and offTsys = System Temperature averaged over bandwidth
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Position-Switched Calibration Equation
)()()()(
)(
)(
)()(
),(
2 ElevAτ(ν)Cal
OffOnpA
eTRefRef
Ref
Ref
RefSig
AreaElevη
kνS
22
222
)(
η
η
T
TAA
S
S
Cal
cal
Sources of uncertainties
• 10-15% accuracy have been the ‘standard’• Usually, errors in Tcal dominate• Goal: To achieve 5% calibration accuracy without
a significant observing overhead.
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Air Mass Estimates
Depends upon density and index of refraction as a function of height
But, how can one get this information?
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Air Mass Estimate
Air Mass traditionally modeled as 1/sin(Elev) For 1% calibration accuracy, must use a better
model below 15 deg.
35.3
18.5sin
014.10234.0
ElevElev
A
• Good to 1 deg• Use 1/sin(Elev) above 60 deg• Coefficients are site specific, at
some low level
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Typical Position-Switched Calibration Equation
BW
CalOffOn
RefSys
RefSysA
tElevAtA
pA
TRefRef
RefT
TRef
RefSigT
eTAreaElev
kS
)()()(
)(
)(
)()()(
)(),(
2)( ),(),(
A(Elev,t) = Air Massτ(ν,t) = Atmospheric Zenith OpacityTcal = Noise Diode TemperatureArea = Physical area of the telescopeηA (ν,Elev) =Aperture efficiency (point sources)TA (ν) = Source Antenna Temperature
S(ν) = Source Flux DensitySig(ν), Ref (ν) = Data taken on source and on blank sky (in units backend counts) On,Off = Data taken with the noise diode on and offTsys = System Temperature averaged over bandwidth
![Page 10: Calibration Ron Maddalena NRAO – Green Bank November 2012.](https://reader030.fdocuments.net/reader030/viewer/2022032702/56649ccb5503460f94993d31/html5/thumbnails/10.jpg)
Opacities from the various components
Dry Air Continuum
Water Continuum
Oxygen Line
Water Line
Hydrosols
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Opacities from the various components
Total Opacity
gfs3_c27_1190268000.buf
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Determining Opacities
)1( AATM
ACMBSpilloverRcvrSYS eTeTTTT
Slope ~ TATM
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Typical Position-Switched Calibration Equation
BW
CalOffOn
RefSys
RefSysA
tElevAtA
pA
TRefRef
RefT
TRef
RefSigT
eTAreaElev
kS
)()()(
)(
)(
)()()(
)(),(
2)( ),(),(
A(Elev,t) = Air Massτ(ν,t) = Atmospheric Zenith OpacityTcal = Noise Diode TemperatureArea = Physical area of the telescopeηA (ν,Elev) =Aperture efficiency (point sources)TA (ν) = Source Antenna Temperature
S(ν) = Source Flux DensitySig(ν), Ref (ν) = Data taken on source and on blank sky (in units backend counts) On,Off = Data taken with the noise diode on and offTsys = System Temperature averaged over bandwidth
![Page 14: Calibration Ron Maddalena NRAO – Green Bank November 2012.](https://reader030.fdocuments.net/reader030/viewer/2022032702/56649ccb5503460f94993d31/html5/thumbnails/14.jpg)
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
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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
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Noise Diode Estimates Instead, we recommend an On-Off observation
Use a point source with known flux -- polarization should be low or understood
Use the same exact hardware, exact setup as your observation. (i.e., don’t use your continuum pointing data to calibrate your line observations.)
Observations take ~5 minutes per observing run Staff take about 2 hrs to measure the complete band of a
high-frequency, multi-beam receiver. Resolution sufficient: 1 MHz, sometimes better Accuracy of ~ 1%, mostly systematics.
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Noise Diode Estimates
Aτ(ν)Cal
OffOnpA
eTRefRef
Ref
Ref
RefSig
AElevη
kνS
)(
)()(
)(
)(
)()(
),(
2
Remove Averaging, Solve for Tcal
)(
2
,)(
S
RefSig
RefRef
ek
AreaElevT OffOn
A
pACal
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Noise Diode Estimates
Frequency (MHz)
7000 8000 9000 10000 11000 12000 13000
TC
AL
(K)
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
X-band Low CalsRight-Circular Polarization
Created with PSI-Plot, Tue May 10 14:36:23 2005 X_LC_Rc s.pgw
LegendAstEng
Frequency (MHz)
1600 1800 2000 2200 2400 2600 2800
TC
AL
(K)
1.00
1.50
2.00
2.50
3.00
3.50
4.00
S-band Low CalsY-Linear Polarization
Created with PSI-Plot, Tue May 10 16:59:49 2005S_LL_Ycs.pgw
Legend
Eng (21 Oct 2004)Eng (22 Oct 2004)Ast
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Typical Position-Switched Calibration Equation
BW
CalOffOn
RefSys
RefSysA
tElevAtA
pA
TRefRef
RefT
TRef
RefSigT
eTAreaElev
kS
)()()(
)(
)(
)()()(
)(),(
2)( ),(),(
A(Elev,t) = Air Massτ(ν,t) = Atmospheric Zenith OpacityTcal = Noise Diode TemperatureArea = Physical area of the telescopeηA (ν,Elev) =Aperture efficiency (point sources)TA (ν) = Source Antenna Temperature
S(ν) = Source Flux DensitySig(ν), Ref (ν) = Data taken on source and on blank sky (in units backend counts) On,Off = Data taken with the noise diode on and offTsys = System Temperature averaged over bandwidth
![Page 20: Calibration Ron Maddalena NRAO – Green Bank November 2012.](https://reader030.fdocuments.net/reader030/viewer/2022032702/56649ccb5503460f94993d31/html5/thumbnails/20.jpg)
Telescope efficiencies – Part 1
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GBT Gain CurveRuze Equation – Surface errors
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GBT Gain Curve
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Non-linearity If system is linear, Pout = B * Pin (SigOn-SigOff) – (RefOn-RefOff ) = 0
Model the response curve to 2nd order: Pout = B * Pin + C * Pin
2
Our ‘On-Off’ observations of a calibrator provide: Four measured quantities: Refoff, Refon, Sigoff, Sigon TA From catalog Four desired quantities: B, C, Tcal, Tsys
It’s easy to show that: C = [(Sigon- Sigoff )-(Refon- Refoff)]/(2TATcal)
Thus: Can determine if system is sufficiently linear Can correct to 2nd order if it is not
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Non-linearity(S
igO
n-S
igO
ff) –
(R
efO
n-R
efO
ff )
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Reference observations
Difference a signal observation with a reference observation
Types of reference observations Frequency Switching
In or Out-of-band Position Switching Beam Switching
Move Subreflector Receiver beam-switch
Dual-Beam Nodding Move telescope Move Subreflector
![Page 26: Calibration Ron Maddalena NRAO – Green Bank November 2012.](https://reader030.fdocuments.net/reader030/viewer/2022032702/56649ccb5503460f94993d31/html5/thumbnails/26.jpg)
Position switching
Move the telescope between a signal and reference positionOverhead½ time spent off source
Difference the two spectra Assumes shape of gain/bandpass doesn’t
change between the two observations. For strong sources, must contend with
dynamic range and linearity restrictions.
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Frequency switching
Eliminates bandpass shape from components after the mixer
Leaves the derivative of the bandpass shape from components before the mixer.
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In-Band Frequency Switching
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Out-Of-Band Frequency Switching
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Beam switching – Internal switch
Difference spectra eliminates any contributions to the bandpass from after the switch
Residual will be the difference in bandpass shapes from all hardware in front of the switch.
Low overhead but ½ time spent off source
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Atmosphere is in the near field
Common to all feeds in a multi-feed receiver
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Beam Switching – Subreflector or tertiary mirror
Optical aberrations Difference in spillover/ground pickup Removes any ‘fast’ gain/bandpass changes Low overhead. ½ time spent off source
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Nodding with dual-beam receivers - Telescope motion
• Optical aberrations• Difference in spillover/ground pickup• Removes any ‘fast’ gain/bandpass changes• Overhead from moving the telescope. All the time is spent on source
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Nodding with dual-beam receivers - Subreflector or tertiary mirror
Optical aberrations Difference in spillover/ground pickup Removes any ‘fast’ gain/bandpass changes Low overhead. All the time is spent on source
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References
Rohlfs & Wilson, “Tools of Radio Astronomy” Stanimrovis et al, “Single-Dish Radio Astronomy:
Techniques and Practices” Baars, 1973, IEEE Trans Antennas Propagat, Vol AP-21,
no. 4, pp 461-474 Kutner & Ulich, 1981, Astronomica Journal, Vol 250,pp
341-348 Winkel, Kraus, & Bach, 2012, Astronomy & Astrophysics,
vol. 540.