noise diodes, calibration, baselines & nonlinearities
DESCRIPTION
Noise Diodes, Calibration, Baselines & Nonlinearities. Ron Maddalena NRAO, Green Bank, WV Shelly Hynes Louisiana School for Math, Science and the Arts, Natchitoches, LA Charles Figura Wartburg College, Waverly, IA July 27, 2006. Calibration Data. June 18, 2006 - PowerPoint PPT PresentationTRANSCRIPT
Noise Diodes, Calibration, Baselines & Nonlinearities
Ron MaddalenaNRAO, Green Bank, WV
Shelly HynesLouisiana School for Math, Science and the Arts, Natchitoches, LA
Charles FiguraWartburg College, Waverly, IA
July 27, 2006
Calibration Data
June 18, 2006 C-Band – Off-On Observations Multiple calibration sources, same hardware, same
attenuator/filter settings Tcal calibration data – Various combinations of
polarization, high/low noise diodes Data consists of:
Sigon = On source, noise diode on Sigoff = On source, noise diode off Refon = Off source, noise diode on Refoff = Off source, noise diode off
Sig and Ref Definitions
offonoffon
atmsrcoffonoffon
calrcvratmspillCMBon
rcvratmspillCMBoff
calsrcrcvratmspillCMBon
srcrcvratmspillCMBoff
srcsysoff
RefRefSigSigResids
ΔTνTRefRefSigSig
νTνTTTTRef
νTTTTRef
νTνTνTTTTSig
νTνTTTTSig
TT Sig
Sig and Ref Definitions
2
νTνTTTTT
2
SigSigSig
2
νTνTTTT
2
RefRefRef
calrcvrsrcatmspillCMB
offon
calrcvratmspillCMB
offon
Current Calibration Method
caloffon
A
caloffon
calsys
TνRefνRef
νRefνRef
νRefνSigνT
TνRefνRef
νRef2
TT
So Tsys loses all frequency information…
Astronomical Tcal
= Efficiency
Ap = Area
k = Boltzman’s Constant
=
ElevationOpacity
νS2k
ηAνT
e
S
RefSig
RefRefνS
calp
cal
sinθτ
offoff
offoncal
ηSA
2kTastrocalp
engcal If is unknown…
Source: Johnson et.al., 2002
Linear Vector Tcal Expressions
AνSigBνTνTνT
AνSigBνTνT
AνRefBνTνT
AνRefBνT
onoAcalsys
offoAsys
onocalsys
offosys
Now Tsys retains the frequency structure
νT
νRefνRef
νRefνSig
νTνRefνRef
νRef
νRef
νRefνSigνT
νTνRefνRef
νRef
2
νTνT
caloffon
caloffon
A
caloffon
calsys
Power Characterization
Power In0 5 10 15 20 25 30 35 40
Pow
er O
ut
0
20
40
60
80
100
Expected Linear/Nonlinear Power Response
‘Resids’ for Spectral Processor
0.0 5.0 10.0 15.0 20.0 25.0 30.0
Res
ids_
R
-4000
-3000
-2000
-1000
0
1000Epoch 3
1420
49
67
85
95
121172
178
1006 10121075
P_Out
0.0 5.0 10.0 15.0 20.0 25.0 30.0
Res
ids_
L
-4000
-3000
-2000
-1000
0
1000
14
20
49
67
85
95
121
172
178
1006
10121075
Nonlinear Theory
Include a second-order correction for gain –
So the temperature equations become
2outout
'out P
B
CPP
2ononsourcecalsys
2offoffsourcesys
2ononcalsys
2offoffsys
SigB
CSigTTT
SigB
CSigTT
RefB
CRefTT
RefB
CRefT
Non-Linear SolutionsFor Calibration
src
onoffonoffononoffoff
2ononoffonoff
2off
2onoffcal
sys
srconoffonoffononoffoff
onoffonoff
srconoffonoffononoffoff
2on
2off
2on
2offcal
srconoffonoffononoffoff
onoffonoffonoffonoffcal
TSigSigRefRefSigRefSigRefSigSigSigRefRefSigRefRef
T
TSigSigRefRefSigRefSigRef
SigSigRefRef C
TSigSigRefRefSigRefSigRef
SigSigRefRef-B
TSigSigRefRefSigRefSigRefSigSigSigSigRefRefRefRef
T
Nonlinear Application
Evaluate C, B, Tcal, using a known calibration source.
Because nonlinearity is encapsulated within P’out, we can use the previous expressions from the linear case:
νT
νRefνRef
νRefνSigνT
νTνRefνRef
νRef
2
νTνT
caloffon
A
caloffon
calsys
calsysT
Calibration Data
June 18, 2006 C-Band – Off-On Observations Multiple calibration sources, same hardware,
same attenuator/filter settings Tcal calibration data – Various combinations of
polarization, high/low noise diodes July 15, 2006
3C147 C-Band, low-diode, linear polarization
Various attenuator settings at various places S-band Scal calibration data – Various
combinations of polarization, high/low noise diodes
Source of ‘Baselines’ – Traditional
Assuming Linear
2
νTνTTTTT
2
SigSigSig
2
νTνTTTT
2
RefRefRef
calrcvrsrc
SigatmspillCMB
offon
calrcvr
RefatmspillCMB
offon
ScalarsysTνRef
νRefνSigνTA
2
νTνTTTT
TTTν
calrcvr
RefatmspillCMB
Refatm
Sigatmsrc
ScalarsysT
Baselines
Source of ‘Baselines’ – Traditional Non-Linear
2
νT))(T)TTT(21(νT
))(T)(T2(TTT[Smooth]ν
cal2rcvr
RefAtmSpillCMBrcvr
calrcvrRefatm
Sigatmsrc
fccSmooth
ffc
T
BaselinesScalarsys
Noise Estimates – Vector Tcal
sigref
sigT tChanWidthtNchan
t
11
T
T2T)TT(
νTνRefνRef
νRefνSigνT
2
cal
src2sys
2srcsys
2
caloffon
A
Assume Tsys = 10*Tcal, NChan = 1, tref = tsig
Tsrc = 0 --- σ2=2*Tsys/(ChanWidth * tsig)
Tsrc = Tcal --- σ2=4.2*Tsys/(ChanWidth * tsig)
Tsrc = 2Tcal --- σ2=10.4*Tsys/(ChanWidth * tsig)
Tsrc = Tsys --- σ2=205*Tsys/(ChanWidth * tsig)
Assuming Tcal << Tsys
Summary
Using a vector form of Tcal for baselines is better than traditional, regardless of linear or non-linear assumptions.
Baselines are slightly improved by the quadratic approximation,
Cannot achieve good noise, good baselines, and good calibration simultaneously – Compromise!!
System rebalancing restores original nonlinearity. Data taken with major ‘distortions’ to power levels
can be recovered. ‘C’ remains fairly constant with time.
Conclusions
Extended sources should not be used to determine linearities, Scals, etc.
Polarized sources must be corrected for.
Very bright sources cannot be handled by the 2nd order nonlinear approximation.
Recommendations
At a minimum, use the vector form of Tcal. Use compact sources for calibrations. For many observations, the linear
approximation is sufficient. Balancing often isn’t necessary and actually
may be detrimental since C will change. Don’t skimp on channels – more channels,
less compromises between noise and baseline