Calibration and Data reduction Strategies

Cormac Purcell & Ned Ladd

Mopra Training Weekend

May 2005

I Calibration

Measuring Source Intensity

Source

Atmosphere … Opacity)

Background Emission (CMB)

Electronic Noise

Measuring Source Intensity

Pon-src = C [ Isrc e- + J(Tatm)(1-e-) + Ibg e- + IRx ]

Poff-src = C [ J(Tatm)(1-e-) + Ibg e- + IRx ]

Source Atmosphere MicrowaveBackground

ElectronicNoise

Isrc = (Pon-source – Poff-source) (e/C)

TA* (Pon-source – Poff-source)

Poff-source

Poff-source e

C Tsys

Measuring Source Intensity

= C [ J(Tatm)(1-e) + Ibge + Irx ] eC

Tsys = Poff-source e/CIsrc

Tsys = J(Tatm)e– J(Tatm) + Ibg + Irxe

Tsys is a measure of noise in the whole system.

Measuring Tsys with a Hot Load

Compare blank sky to a known temperature standard:

Psky Pload

Measuring Tsys with a Hot Load

Pload = C[Iload + Irx]

Poff-src J(Tatm)(1-e) + Ibge + IRx

Pload – Poff-src Iload + IRx - J(Tatm)(1-e) - Ibge - IRx

=

Compare power from blank sky and known load:

Power measered from blackbody paddle:

Measuring Tsys with a Hot Load

Psky J(Tatm)(1-e) + Ibge + IRx

Pload – Psky Iload - J(Tatm)(1-e) - Ibge =

Assume: Tload = Tatm i.e. Iload = J(Tatm)

Psky J(Tatm)(1-e) + Ibge + IRx

Pload – Psky J(Tatm) e - Ibge =

Measuring Tsys with a Hot Load

Psky J(Tatm)(1-e) + Ibge + IRx

Pload – Psky J(Tatm) e - Ibge =

J(Tatm)e – J(Tatm) + Ibg + IRxe

J(Tatm) - Ibg

=

Tsys

J(Tatm) - Ibg

= Psky

Pload – Psky

Measured Assumed : 300 K & < 1K

Tsys

What if Tload = Tatm?

Psky J(Tatm)(1-e) + Ibge + IRx

Pload – Psky Iload - J(Tatm)(1-e) - Ibge=

Cannot merge terms.

What if Tload = Tatm?

Psky J(Tatm)(1-e) + Ibge + IRx

Pload – Psky (Iload – J(Tatm)) + J(Tatm)e - Ibge=

J(Tatm)e – J(Tatm) + Ibg + IRxe

(Iload – J(Tatm))e + J(Tatm) - Ibg

=

Tsys

(Iload – J(Tatm))e + J(Tatm) - Ibg

=

Tsys no longer depends on Measurable Quantities

Calibration to TA* scale

(Pon-source – Poff-source)

Poff-source

TsysTA* =

Tsys = Psky

Pload - Psky(J(Tload) – Ibg)

Assumed 300 K (Ambient temperature)

<1 K From CMB

TA* is Not Enough:Calibrating to a Telescope-Independent

Scale

•TA* scale assumes source emission fills the forward hemisphere

•TA* = Tsource only if this is true

•In practice, one needs to consider the coupling between the source intensity distribution and the telescope response as a function of angle

Antenna Temperature from an Extended Source

TA* = sourcePb

Pb2

2

need to know something about the beam…

Tsource()Pb()

2003 Beam

Greyscale: 10% - 100%

Contours: 1% - 10%

Greyscale: 10% - 100%

Contours: 1% - 10%

2004 Beam

Pb()

Main Beam

+/- 40’’

Extended beam

+/- 80’’

Main Beam Efficiency, mb

TA* =

2

2sourcePmb

Pmb2

2Pmb

Pb

TA* = mb

sourcePmb

Pmb2

2

Tmb = TA*/ mb

Main Beam brightness temperature

Main Beam Brightness Temperature Scale

• Tmb = Tsource for a source which fills only the main beam

• @Mopra, this means sources with size ~80”– For smaller sources, need to consider beam dilution– i.e., Tmb = <TR> over the main beam

• mb = 0.4 @86 GHz in 2004

Extended Beam Efficiency, xb

TA* =

2

2sourcePxb

Pxb2

2Pxb

Pb

TA* = xb

sourcePxb

Pxb2

2

Txb = TA*/ xb

Extended Beam brightness temperature

Extended Beam Brightness Temperature Scale

• Txb = Tsource for a source which fills both the main and extended beams

• @Mopra, this means sources with size >150”

• mb ~ 0.6 @86 GHz in 2003

Calibration of Mopra Data

• Frequent Tsys measurements – Every 20 minutes in good weather– Always after changing target source– TA* scale

• Knowledge of source size– Choose efficiency based on coupling between

source intensity distribution and beam pattern Tmb, Txb, or Tsource

II Data Reduction

Reduction Steps

• Remove band-pass (off position)

• Fit a polynomial to the baseline

• Average individual spectra

• Scale to required temperature scale

• Measure line profiles - e.g. fit with Gaussian

ATNF Single-dish Analysis Package

ATNF Single-dish Analysis Package

ATNF Single-dish Analysis Package

Exporting your data

• Export from ASAP– Export as an ASCII text file (e.g. TA* vs V)

• Export from SPC– Export as FITS & use perl script to fix headers

• Import to CLASS– Read ASCII file & manualy fill headers– Use CFITS to convert from SPC-FITS

Exporting your data

Direct export from ASAP to FITS coming soon!

Questions?