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Continuum - Point Sources Data Reduction and Analysis Techniques
Ronald J. Maddalena
N oise D iode

On-Off Observing

Sign Signall a

www. nra o.edu/~ rmaddale/Education

·Observe b lank sky for 10 sec ·Mo ve telescope to object & observe for 10 sec ·Mo ve to blank sky & obser ve for 10 sec ·Fire noise diode & observe for 10 sec ·Observe b lank sky for 10 sec

Detec tor

Continuum - Point Sources
On-Off Observing

Continuum - Point Sources
On-Off Observing · Know n:
· Equivalent temperature of noise diode or calibrator (Tcal) = 3 K · Bandwidth () = 10 MHz · Gain = 2 K / Jy

· Desired:
· Antenna temperature of the source (TA ) · Flux density (S) of the source. · System Temperature(Ts) when OFF the source · Accuracy of antenna temperature ( TA )

Continuum - Point Sources
On-Off Observ ing

Continuum - Point Sources
On-Off Observ ing ­noise est imate

TSreference = TSsig
nal

P

reference cal cal _ off reference reference cal _ on cal _ off

T P

-P

20 K

1. Write down data analysis e quation:
TA = Pcrael
fe re n ce _ on

=

P

cal reference cal _ on

n T Pcsilg_ a

-P

al off reference cal _ off

26 K

Tcal - Pcrael

fe re n ce _ o ff

sa Pcailg_noflf - Pcrael

(

fe re n ce _ o ff

)

TA = TSsig

nal

- TSreference = Tcal n Pcsailg_ ce ee - Pcraelf_rofnce f

2. Use " propa gation of errors":

e en Pcraelf_ron

(

al off

-P

reference cal _ off

)

6K



2 TA

=



TA P i

2

2 Pi

3. Use the followi ng substitutions :

T = Ts
A

t

0 .0 0 2 K SNR = 3000

T = T

t t

P = G k T 1 P = T = t P T
2 2

P = P

1


Continuum - Point Sources
On-Off Observ ing ­ noise estimate
Tcal - Pcrael

Continuum - Point Sources
Assumptions:

TS =
T Pi
2

Pcrael

fe re n ce _ on
2

fe re n ce _ o ff

sa Pcailg_noflf - Pcrael

(

fe re n ce _ o ff

)
A _ on



2 TA

=



A

2 TA Pi = P sign
2

al



2 Psig n a l

TA + P re f e re

n ce



2

2 P r e f re n c e

T + P ca l
2



2

2 Pca l _ o n



2 TA

T = reference Cal referen Pcal_ on - Pcal_ off

ce



(

2 Psignal

+

2 P ref rence

)

+ re f e Pcal_

re n c e on

TA r - Pcraelf_eoefn f

ce



(

2 Pcal _ on

+

2 P r e f re n c e

)

2 2 2 2 n e ref erence 2 e Pcsailg_ alffl + Pcraelf_ roefnce + Pcraelf_roefnce 1 TA Pcal _ on o f f = + = signal ref erence 2 e e SNR TA Pcraelf_ roennce - Pcraelf_roefnce 2 Pcal _ off - Pcal _ off f 1 S NR = (10 4 ) ~ 900 ( Not 3000! 103 + 30

(

(

)(

)

)(

(

)(

)

)

2

1 t

"Classical" Radiometer equation assum es: · Narrow bandwidths, · Linear power detector, · TA << Ts, · Noise diode temperature << Ts, · treference = tsignal · tcal_on = tcal_off · Blank ing time << tsignal · No data reduction!

)

Phases of an Observation
Total Power

Phases of an Observation
Total Power

N oise D iode

Sw itc hing Signals

Detec tor Cal On

Detec tor Cal Of f

· Tc a l = 4 K · Ts = 1 0 0 K ------------· theor =0.1 K · meas =1 K ------------·Sha pe s ve ry si milar ·Exce ss noi se from at mospheric fluctuation


Phases of a Observation
Beam Switched Power

Phases of a Observation
Beam Switched Power

Reference Signal

N oise Dio de

N oise Dio de

Sw it ch in g Sign als D et ec to r Sig Cal O n

Sw it ch in g Sign als D et ec to r Sig Cal O n

D et ec to r S ig Cal Of f

D et ec to r S ig Cal Of f

Det ec to r Ref Cal On

Det ec to r Ref Cal On

Detect o r Ref Cal Off

Detect o r Ref Cal Off

2


Phases of a Observation
Double Beam Switched Power

Continuum - Point Sources
Beam-Switched Observation

TSreference (i ) =
Referenc e Signal
No ise D iode

Tcal e e Pcraelf_roennce (i ) - Pcraelf_roefnce (i f Tcal (i ) - Pcsailg_noaflf (i

)



(P

reference cal _ on

(i )

e + Pcraelf_roefnce (i f

))

2

Sw itc hin g S ig nals Detec to r Sig Cal On

TSsi

gnal

(i )

=

P

si gnal cal _ on

)

(P

si gnal cal _ on

(i )

+ Pcsailg_nalff (i o 2

))

D etec to r S ig Cal Of f

TA = TSsi
Detec to r Ref Cal On Detector Ref Cal Off

gnal

(i) - TSreference (i )

Continuum - Point Sources
On-The-F ly Observation

Continuum - Point Sources
On-The-F ly Observation

If total power:

TS (i ) =

Pcal

_ on

(i )

Tcal - Pcal

_ off

(i )



(P

cal _ on

(i )

+ Pcal 2

_ off

(i))

Beamw idth

TA

If bea m-switc hing (switc hed power): TSreference (i ) = P
reference cal _ on

Tcal (i ) - Pcraelf_eroefnf ce (i

P osit ion

TSsi

gnal

(i)

=

Ts
TA (i ) = TSsi

P
gnal

si gnal cal _ on

Tcal (i ) - Pcsailg_noaflf (i

)



(P

)



(P

reference cal _ on

(i )

e + Pcraelf_roefnce (i f

))

2

si gnal cal _ on

(i )

a + Pcsailg_noflf (i

))

2

(i ) - TSreference (i )

Baseline Fitting
Polynom ials
· Set order of pol ynomial · Define areas dev oid of emission. --------------------------· Creates fals e features · Introduc es a random error to an observation

Continuum - Point Sources
Gaussian Fitting



2 Pe a k

2 = TA +

2 Polynomial

Why Polynomial s?

· Define initi al guess es · Set flags to fit or hold c onstant eac h parameter · Set number of iter ations · Set c onvergenc e criteria ---------------------------· Fitted parameters · Chi-square of the fit · Parameter standard deviati ons. ---------------------------· Restrict data to between the half pow er points for fitti ng to a telesc ope's beam · Multi-component fits should be done simultaneousl y

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Continuum - Point Sources
Gaussian Fitting

Template Fitting
· Create a template:
· Sufficient kno wle dge of the te lescope bea m, or · Avera ge of a lar ge number of obser vatio ns .

Whe re is noi se the highe st?

Whe re is noi se the lowe st ?

· change s ac ross t he obse rvation. · Weight s (1 / 2) for least-squa re-fit cha nge s across the observation. · For st rong source s, should worry a bout using proper weight s in data analysi s.


· --------------· Conv olve the template with the data => x-offset. · Shift b y the x-offs et. · Perform a linear least-squares fit of the template to the data:

Al wa ys try t o fit physicallymea ningful functions

Averaging Data / Atmosphere
· ·

Gain Correction

Ts changes due to atmosphere emission.
Use weighted average with weights = 1/2


T
A

TA

1

=


1
2 j

2 j





av rg

=
j

1





1



2 j

· ·

TA changes due to atmosphere opacity.
Opacity from the literature or theory, from a tipping radiometer, from atmospheric vertical water vapor profiles, or by "tipping" the antenna

TA' = TA e
'
TA TA

tau / sin( el ) tau / sin( el )

= e

* TA = TA' /
TA TA

A A

or

' TB* = TA /

M M

* = ' /



*
TB

' = TA /

Continuum - Extended Sources
On-The-F ly Mapping
· Telesc ope slews from row to row. Row spaci ng: ~0.9 /2D · A few samples /s ec. · Highly oversampled in direction of slew <0.3 /2D · Could be beam switc hing ---------------------· Conv ert Power into TS. · Fit baseline to each row? · Grid into a m atrix


Continuum - Extended Sources
On-The-F ly Mapping - Co mmon Problems · Striping (Em erson 1995; Klei n and Mack 1995). · If beam -switched, Em erson, Kl ei n, and Hasl am (1979) t o rec onstruct the im age. · Make m ultipl e m aps with the sl ew in di fferent directi on.

4


GBT Continuum Images ­ Rosette

GBT Continuum Images ­ M17

GBT Continuum Images ­ W3

GBT Continuum Images - Orion

Spectral-line - Point Sources
On-Off Observing

Spectral-Line - Point Sources
Position -Switched Observ ing

N oise D iode

Sign Signall a

·Observe blank sky for treference sec ·Fire noise diode to determine Ts ·Move telescope to object & observe for tsignal sec ·Can observe an extended source using this technique -`signa l' obser vations arranged in a "grid" map.

Detec to r

5


Spectral-Line - Point Sources
Position -Switched Observ ing

Phases of a Observation
Switched Po wer ­ Frequency Switching
Signal Freq uenc y Reference Frequency

Psignal- Preference e TA( f ) =Tsreferenc( f ) reference P
Smoothed/ Ave raged Ts of Denominator Signal (line expe cted) Reference (No line expecte d)

Loc al Osciflator

Noise D io de

Tsref

erence

(f)=
2

ref erence ref erence Tcal Pcal _ on ( f ) + Pcal _ off ( f ) 2 P reference ( f ) - P reference ( f ) cal _ on cal _ of f

Sw it ch ing Sig nals Det ec to r Sig Cal On

M _ Channels

TA 1 K 1 reference + signal + T T ~ / N t TS A channels t

s



2

D et ec to r S ig Cal Of f

· But onl y for weak line s and no strong continuum! · Constant depe nd s upon details of t he detecting backend

Det ec to r Ref Cal On

Detect or Ref Cal O ff

Spectral-Line - Point Sources
Frequency-Switched Observ ing - In band

Spectral-Line - Point Sources
Frequency-Switched ­ "Fold ing" In Band
TA ( f ) = TSref P ( f )
signal erence

(f )-P P
ref erence

ref erence

(f )

( f ) + ( f + f )

"Signa l"

TA = Ts (REF)*[(SIG-REF)/REF]

TSsi

gnal

P ( f )

ref erence

( f + f ) - P P
signal

signal

( f + f )

"Reference "

Tant( f ) = T

referen ce S

l Psigna( f ) - Preferenc(e f ) - Preferenc(e f ) ( f ) signal referen ce ( f + f ) P ( f + f ) - P referen ce ( f + f ) P

Line appea rs t wice ­ should be able to `fold' the spectra to increa se SNR

Spectral-Line
Baseline F itting

Spectral-Line
Other Algorithms

· Polynomial: same as before · Sinusoid

1.00

· Velocity C alibration · Velocity/Frequency Shifting & Regriding
· Doppler tracking limitations

DATA

0.50

0.00

· Smoothing ­ Ha nning, Boxcar, Gaussia n
0 100 200 300 400

-0.50

-1.00 0.4 0.3

· Decimating vs . non-decim ating ro utines · For "Optim al Filtering", match smoothing to expected line w idth

0.2 0.1 0.0 -0.1 -0.2 -0.3 -0.4 0 100 200 300 400

· Filtering ­ low pa ss, high pass, med ian, ... · Moments for Integ rated Intensities; Velocity centroid s, ....

RESIDUALS

6


Spectral-Line
RFI Excision

Spectral-Line Mapping
Grid or On-the -Fly

RA

Spectral-Line Mapping
Grid and On-the-F ly
W ( , ) =
Vmax

Spectral-Line Mapping
Grid and On-the-F ly

Vi =Vmin

T (

, , Vi ) Vi
V el oc it y

(If V1=V2 => Channel Map)

V el oc it y

DEC

(Position-velocity map)

V el oc it y

DEC

For {v= vmin} {v <= vmax} {v++} { if T( , ,v) > Tmin then W( , )=W( , )+ T( , ,v) endif endfor
RA


T ( , V ) =
RA



DEC

=

T (
max min

, ,V

)

Spectral-Line Mapping
The Future of Sing le-Dish Data Analys is · · · · · · · · · Increase in the use of RDB MS. Support the anal ysi s of arc hived dat a. Sophi stic at ed visuali zati on t ool s. Sophi stic at ed, robust algorithm s (m apping). Dat a pi peli ning for the general user. Autom atic dat a c alibrati on using m odels of the t el esc ope. Algorithm s that deal with dat a sets. Analysi s syst em s support ed by cross-observat ory groups More will be done with com m erci al softw are pac kages

7