```Introduction to Radio Telescopes
Frank Ghigo, NRAO-Green Bank
The Fourth NAIC-NRAO
July 2007
Terms and Concepts
Parabolic reflector
Blocked/unblocked
Subreflector
Frontend/backend
Feed horn
Local oscillator
Mixer
Noise Cal
Flux density
Jansky
Bandwidth
Resolution
Antenna power pattern
Half-power beamwidth
Side lobes
Beam solid angle
Main beam efficiency
Effective aperture
Aperture efficiency
Antenna Temperature
Aperture illumination function
Spillover
Gain
System temperature
convolution
Karl Jansky
1932
Grote Reber
1938
Unblocked Aperture
• 100 x 110 m section of a parent parabola 208 m in diameter
• Cantilevered feed arm is at focus of the parent parabola
Subreflector and
Verschuur, 1985. Slide set produced by the Astronomical Society of the Pacific, slide #1.
Signal paths
Intrinsic Power P (Watts)
Distance R (meters)
Aperture A (sq.m.)
Flux = Power/Area
Flux Density (S) = Power/Area/bandwidth
Bandwidth ()
A “Jansky” is a unit of flux density
10 26Watts / m 2 / Hz
P  10264R 2 S
Antenna Beam Pattern (power pattern)
Beam solid angle
 HPBW 

Main Beam
Solid angle
 A   Pn ( ,  )d
4
M 
 P ( , )d
n
main
lobe
D
Pn = normalized power pattern
Kraus, 1966. Fig.6-1, p. 153.
Some definitions and relations
Main beam efficiency, M
M
Antenna theorem
M

A
Aperture efficiency, ap
Effective aperture, Ae
Geometric aperture, Ag
A 
 ap
2
Ae

Ag
1

Ag (GBT )    (100m)  7854m 2
2


2
Ae
 ap   pat surf  block ohmic 
Detected power (W, watts) from a resistor R
at temperature T (kelvin) over bandwidth (Hz)
W  kT
Power WA detected in a radio telescope
Due to a source of flux density S
power as equivalent temperature.
Antenna Temperature TA
Effective Aperture Ae
WA  12 AS
2kTA
S
Ae
Kraus, 1966. Fig.1-6, p. 14.
Aperture Illumination Function

Beam Pattern
A gaussian aperture illumination
gives a gaussian beam:
 pat  0.7
Kraus, 1966. Fig.6-9, p. 168.
Gain(K/Jy) for the GBT
2kTA
S
Ae
TA ap Ag
G

S
2k
G ( K / Jy )  2.84   ap

Including atmospheric absorption:
S
2kTA a
e
Ae
Effect of surface efficiency
 ap   pat surf   
System Temperature
= total noise power detected, a result of many contributions
a
Tsys  Tant  Trcvr  Tatm (1  e )  Tspill  TCMB     
Thermal noise T
= minimum detectable signal
For GBT spectroscopy
T  k1
Tsys
  tint
Convolution relation
for observed brightness distribution
S ( ) 
 A( ' ) I ( ' )d '
source
Thompson, Moran, Swenson, 2001. Fig 2.5, p. 58.
Smoothing by the beam
Kraus, 1966. Fig. 3-6. p. 70; Fig. 3-5, p. 69.
Physical temperature vs antenna temperature
For an extended object with source solid angle s,
And physical temperature Ts, then
for
for
In general :
s   A
s   A
1
TA 
A
TA 
s
Ts
A
TA  Ts
 P ( , )T ( , )d
n
source
s
Calibration: Scan of Cass A with the 40-Foot.
peak
baseline
Tant = Tcal * (peak-baseline)/(cal – baseline)
(Tcal is known)
More Calibration : GBT
Convert counts to T
Tcal
G
Ccal on  Ccal off
Tsys  G  Csys
1
1
 G  (Coffsource,calon  Coffsource,caloff )  Tcal
2
2
Tant  G  Csource
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