Hands-On Calibration

Ron Maddalena

July 13, 2007

Preliminaries Change directory: cd /home/scratch/sdscal Start GBTIDL Access data

filein,’T_TCAL14MAR07.acs.raw.fits’ summary

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.

getps,6,ifnum=0 Try different windows to see what’s different

header Record elevation, UT date and time

getnod,42,ifnum=0 For the adventurous

.compile getscalquad.pro

Typical Position-Switched Calibration Equation

)()()(

)(

2/)()()(

2/)()()(

)(

)()()(

)(),(

2)( )()(

CalOffOn

RefSys

OffOn

OffOn

RefSysA

ElevAirMassA

pA

TRefRef

RefT

RefRefRef

SigSigSig

TRef

RefSigT

eTAElev

kS

dioden calibratio noise theof eTemperatur)(T

sbandswidth for wide vector a ,bandwidths

narrowfor scalar a -- eTemperatur System)(T

offor on diode noise h the taken witData Off On,

or volts) counts(in sky blank on taken Data )Ref(

or volts) counts(in source'on ' taken Data )Sig(

DensityFlux )S(

eTemperatur Antenna)(T

only) sourcespoint (for Efficiency Aperture ),(

telescope theof Area PhysicalA

Opacity Zenith cAtmospheri)τ(

15elevationsfor ion)Csc(Elevatev)AirMass(El

Cal

Sys

A

p

ElevA

Putting it all together

AirMassτ(ν)Cal

OffOnpA

eTRefRef

Ref

Ref

RefSig

AElevη

kνS

)(

)()(

)(

)(

)()(

),(

2

Remove AveragingSolve for Tcal

)(

2

,)(

S

RefSig

RefRef

ek

AElevT OffOn

AirMass

pACal

What Do We Need?

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) Table: pp 333-334 Functional fit: p. 335 Note that S will vary significantly

across wide bandwidths τ from weather models

At Linux prompt, type: cleo forecasts

What Do We Need?

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?

)(

2

,)(

S

RefSig

RefRef

ek

AElevT OffOn

AirMass

pACal

How to Calculate (RefOn-RefOff)/(Sig-Ref)

Use the commands ‘emptystack’, ‘select’ ‘avgstack’, ‘copy’, ‘subtract’, ‘divide’, and ‘scale’ Emptystack

Clears anything that peviously has been done with the stack Select,scan=6,cal=‘F’,ifnum=0,plnum=0,fdnum=0

Finds all data that meet this selection criteria Avgstack

Averages together the data found by ‘Select’ and places into Data Container (DC) zero

Copy,0,9 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)

Summary: DC 9 contains RefOff

DC 8 contains RefOn

DC 7 contains SigOff

DC 6 contains SigOn

Create Sig and place into DC 10: Add,7,6,10 Scale,0.5,10

Similarly create Ref and place into DC 11 Create Sig-Ref and place into DC 12

Subtract,10,11,12 Similarly create RefOn-RefOff and place into DC 13 Create (RefOn-RefOff)/(Sig-Ref) and place into DC 14

Divide,13,12,14 Show,14

What again are we calculating?

)(

2

,)(

S

RefSig

RefRef

ek

AElevT OffOn

AirMass

pACal

• 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 If system is linear, than

(SigOn-SigOff) – (RefOn-RefOff ) = 0 Model the response curve to 2nd order:

Pout = B * Pin + C * Pin2

Our observations provide: 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: 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…

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)