Hands-On Calibration
Ron Maddalena
July 13, 2007
Preliminaries
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Change directory: cd /home/scratch/sdscal
Start GBTIDL
Access data
 filein,’T_TCAL14MAR07.acs.raw.fits’
 summary
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getps,6,ifnum=0
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Record elevation, UT date and time
getnod,42,ifnum=0
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Try different windows to see what’s different
header
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Note: For 8 GHz receiver, used observing technique of ‘OffOn’ with,
for example, scan 6 an observation toward blank sky and scan 7
toward 3C286. Used 4 windows
Note: For 12 GHz, dual feed receiver, used observing technique of
NOD. Source in feed 1 for scan 31, in feed 2 for scan 32. Used 2
windows.
For the adventurous
.compile getscalquad.pro
Typical Position-Switched
Calibration Equation


2k

  TA ( )  e ( ) AirMass( Elev)
S ( ) 
  ( , Elev )  A 
p 
 A
 Sig ( )  Ref ( )  Ref
  TSys
TA ( )  
Ref ( )


Sig ( )  Sig On ( )  Sig Off ( )  / 2
Ref ( )  Ref On ( )  Ref Off ( )  / 2
Ref
Sys
T
Ref ( )

TCal ( )
Ref On ( )  Ref Off ( )
AirMass(El ev)  Csc(Elevat ion) for elevations  15
τ( )  Atmospheri c Zenith Opacity
A p  Physical Area of the telescope
 A ( , Elev )  Aperture Efficiency (for point sources only)
TA ( )  Antenna Temperatur e
S( )  Flux Density
Sig( )  Data taken ' on source' (in counts or volts)
Ref( )  Data taken on blank sky (in counts or volts)
On, Off  Data taken wit h the noise diode on or off
TSys ( )  System Temperatur e - - a scalar for narrow
bandwidths , a vector for wide bandswidth s
TCal ( )  Temperatur e of the noise calibratio n diode
Putting it all together

  Sig ( )  Ref ( ) 
2k
Ref ( )
τ(ν) AirMass


S ν   
T
(

)

e
 Ref ( )  Ref ( ) Cal
 η ( , Elev )  A  
Ref
(

)

A
p
On
Off


Remove Averaging
Solve for Tcal
TCal   
 A  , Elev   Ap  Ref On    Ref Off   

  S ( )
 ( ) AirMass 
2k  e
 Sig    Ref   
What Do We Need?
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η from graph, assume gain is
elevation independent
Ap from dish diameter
Calculate Air Mass from elevation
of observation
S from a catalog (e.g., Ott et al 1994,
A&A, 284, 331)
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Table: pp 333-334
Functional fit: p. 335
Note that S will vary significantly
across wide bandwidths
τ from weather models
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At Linux prompt, type:
cleo forecasts
What Do We Need?
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τ from weather models
 At Linux prompt, type:
cleo forecasts
 Select “Curves” tab
 Enter date and UT of the observations
 Enter frequency range for the receiver
(e.g., 7-11 GHz, 11-16 GHz)
 May want to select ‘Write Out Results’
to create an ASCII file of results
 Click on ‘Process’
 Read opacities off of graph
What again are we
calculating?
 A  , Elev   Ap  Ref On    Ref Off   

  S ( )
TCal   
 ( ) AirMass 
2k  e
 Sig    Ref   
How to Calculate (RefOn-RefOff)/(Sig-Ref)
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Use the commands ‘emptystack’, ‘select’ ‘avgstack’, ‘copy’,
‘subtract’, ‘divide’, and ‘scale’
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Emptystack
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Select,scan=6,cal=‘F’,ifnum=0,plnum=0,fdnum=0
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Averages together the data found by ‘Select’ and places into Data
Container (DC) zero
Copy,0,9
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Finds all data that meet this selection criteria
Avgstack
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Clears anything that peviously has been done with the stack
Moves the results to another DC for later use
DC 9 will now contain RefOff
Repeat for scan=6, cal=‘T’, place into DC 8 to create RefOn
Repeat for scan=7, cal=‘F’, place into DC 7 to create SigOff
Repeat for scan=7, cal=‘T’, place into DC 6 to create SigOn
How to Calculate (RefOn-RefOff)/(Sig-Ref)
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Summary:
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DC 9 contains RefOff
DC 8 contains RefOn
DC 7 contains SigOff
DC 6 contains SigOn
Create Sig and place into DC 10:
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Add,7,6,10
Scale,0.5,10
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Similarly create Ref and place into DC 11
Create Sig-Ref and place into DC 12
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Subtract,10,11,12
Similarly create RefOn-RefOff and place into DC 13
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Create (RefOn-RefOff)/(Sig-Ref) and place into DC 14
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Divide,13,12,14
Show,14
What again are we
calculating?
TCal   
 A  , Elev   Ap  Ref On    Ref Off   

  S ( )
 ( ) AirMass 
2k  e
 Sig    Ref   
• Finally, scale DC 14 by η, S, … to determine Tcal. For
example, using fictitious values:
• scale, 0.5*1234/2*22, 14
• scale, 1/1.38e-16*exp(-0.12/sin(33*180/!pi)), 14
• etc.
• show,14
Check for non-linearity
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If system is linear, than
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Model the response curve to 2nd order:
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Pout = Refoff when Pin=Tsys
Pout = Refon when Pin=Tsys+Tcal
Pout = Sigoff when Pin=Tsys+TA
Pout = Sigon when Pin=Tsys+TA+Tcal
It’s easy to show that:
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Pout = B * Pin + C * Pin2
Our observations provide:
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(SigOn-SigOff) – (RefOn-RefOff ) = 0
C = [(Sigon- Sigoff )-(Refon- Refoff)]/(2TATcal)
Try to estimate a value for C using ‘subtract’,
‘divide’ and ‘scale’
Things are really a bit more complicated since
we really measure Pout and want to determine
Pin . Must invert 4 simultaneous linear
equations.
Now for the real easy way…
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Getscal,7,6,ifnum=0,plnum=0,fdnum=0,tau=0.05,
ap_eff=0.55,smth=1
Show,13 (Tcal, assuming linearity)
Show,3 (Tcal, assuming non-linearity)
Show,15 (Tsys, assuming linearity)
Show,5 (Tsys, assuming non-linearity)
Show,11 (Source flux)