Transcript Fundamentals - Indiana University

National Radio Astronomy Observatory
Sept. 2005 – Indiana University
How do Radio Telescopes work?
K. Y. Lo
Electromagnetic Radiation
Wavelength
Radio Detection techniques developed from meter-wave to
submillimeter-wave:
= 1 meter   = 300 MHz
= 1 mm   = 300 GHz
National Radio Astronomy Observatory
September 2005 – Indiana Universe
General Antenna Types
Wavelength > 1 m (approx)
Wire Antennas
Dipole
Yagi
Helix
or arrays of these
Wavelength < 1 m (approx)
Reflector antennas
Feed
Wavelength = 1 m (approx) Hybrid antennas (wire reflectors
or feeds)
REFLECTOR TYPES
Prime focus
(GMRT)
Offset Cassegrain
(VLA)
Beam Waveguide
(NRO)
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Cassegrain focus
(AT)
Naysmith
(OVRO)
Dual Offset
(ATA)
REFLECTOR TYPES
Prime focus
(GMRT)
Offset Cassegrain
(VLA)
Beam Waveguide
(NRO)
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Sept 2005: Indiana University
Cassegrain focus
(AT)
Naysmith
(OVRO)
Dual Offset
(ATA)
What do Radio Astronomers measure?
• Luminosity of a source: L = dE/dt erg/s
• Flux of a source at distance R:
S = L/4R2
erg/s/cm2
• Flux measures how bright a star is. In optical
astronomy, this is measured in magnitudes, a
logarithmic measure of flux.
• Intensity: If a source is extended, its
surface brightness varies across its
extent. The surface brightness is the
intensity, the amount of flux that
originates from unit solid angle of the
source:
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Sept 2005: Indiana University
I = dS/d erg/s/cm2/steradian
Measures of Radiation
• The following should be clear:
L =  S d = 4R2  S for isotropic source
4
S =  I d
source
• Since astronomical sources emit a wide spectrum of radiation,
L, S and I are all functions of  or , and we need to be more
precise and define:
• Luminosity density: L() = dL/d
W/Hz
• Flux density:
S() = dS/d
W/m2/Hz
• Specific intensity: I() = dI/d
W/m2/str/Hz
• The specific intensity is the fundamental quantity
characterizing radiation. It is a function of frequency, direction,
s, and time.
• In general, the energy crossing a unit area oriented at an angle
to s, specified by the vector da, is given by
dE = I(, s, t) sda d d dt = I(, ) sda d d dt
Analogs in optical astronomy
• Luminosity is given by absolute magnitude
• Flux, or brightness, is given by magnitudes within
defined bands: U, B, V
• Intensity, or surface brightness, is given by
magnitude per square arc-second
• Optical measures are logarithmic because the eye is
roughly logarithmic in its perception of brightness
• Quantitatively, a picture is really an intensity
distribution map
National Radio Astronomy Observatory
Sept 2005: Indiana University
Rayleigh-Jeans Law and Brightness
Temperature
• The Specific Intensity of thermal radiation from a blackbody at temperature T is given by the Planck Distribution
I = (2h3/c2)/[exp(h/kT)  1]
= (2hc3/2)/[exp(hc/kT)  1]
= 2kT/2 if  >> hc/kT or h << kT, R-J Law
• Brightness Temperature
Tb  (2/2k)  I = T for thermal radiation
• Brightness temperature of the Earth at 100 MHz ~ 108 K
(due to TV stations)
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Sept 2005: Indiana University
Antenna = Radio Telescope
• The function of the antenna is to collect radio waves, and
each antenna presents a cross section, or Effective Area,
Ae(, ), which depends on direction (, )
• The power collected per unit frequency by the antenna
from within a solid angle d about the direction (, ) is
given by
dP = ½ I (, ) Ae (, ) d W/Hz
The ½ is because the typical radio receiver detects only
one polarization of the radiation which we assume to be
unpolarized.
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Sept 2005: Indiana University
• The power density collected by the antenna from all
directions is
P = ½  I (, ) Ae (, ) d
W/Hz
• Antenna Temperature TA is defined by
TA = P/k
in K (Nyquist Theorem)
• Therefore
TA = (1/2k)  I (, ) Ae (, ) d
K
• For a point source, I = S (, )
kTA = ½ Ae,max S
W/Hz
if Ae (, ) has a maximum value Ae,max at (, ) = (0, 0)
• (Maximum) Effective Area of an antenna:
Ae,max = ap Ag
m2
where Ag is the geometric area and ap is the aperture efficiency.
But, for a dipole antenna, Ag is zero but Ae is not.
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Sept 2005: Indiana University
• Antenna pattern:
Pn(,) = Ae(,)/Ae,max
Pn(0,0) = 1
if the pattern is maximum in the forward direction
• If the antenna is pointed at direction (o,o)
TA (o,o) = (1/2k)  I (, ) Ae (o, o) d
In terms of Tb and Pn ,
TA (o,o) = (Ae,max/2)  Tb (, ) Pn (o, o) d
= (1/A)  Tb (, ) Pn (o, o) d
where 2/Ae,max= A. Note the antenna temperature, which
measures the power density P (W/Hz) collected by the
antenna is the convolution of the antenna pattern Pn with
the source brightness distribution Tb
National Radio Astronomy Observatory
Sept 2005: Indiana University
Antenna Properties
Effective area: Ae(,,) m2
On-axis response
Ae,max = Ag
 = aperture efficiency
Normalized power pattern
(primary beam)
Pn(,,) = Ae(,,)/Ae,max
Beam solid angle A=  Pn(,,) d   4,  =
frequency
all sky
=
wavelength
Mapping by an Antenna
TA (o,o) = (Ae,max/2)  Tb (, ) Pn (o, o) d
• Point source: Tb(, ) = (2/2k)S (, )
TA (o,o) = (Ae,max/2) (2/2k)S  (, ) Pn (o, o) d
= (Ae,max/2k) S Pn (o, o)
 Antenna pattern can be determined by scanning a point source
 If pointing at the point source, then kTA = ½ Ae,maxS
 If S is known, then Ae,max can be determined by measuring TA
• Unresolved source: s < m ~ A  2/Ae,max
TA (0, 0) = (Ae,max/2)  Tb (, ) Pn (, ) d
= (s/ A)  Tb  = (m/ A) (s/ m)  Tb 
TA = m(s/ m)  Tb 
Beam dilution
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Sept 2005: Indiana University
Milky Way
Maxwell Equations?
• Radio telescopes operate in the physical optics regime,  ~
D, instead of the geometric optics regime,  << D, of optical
telescope  diffraction of radiation important
• Easier to think of a radio telescope in terms of transmitting
radiation
• A point source of radiation (transmitter) at the focus of a paraboloid is
designed to illuminate the aperture with a uniform electric field
• The diffraction of the electric field across the aperture according to
Huygens’ Principle determines the propagation of the electric field
outward from the aperture or primary telescope surface
• The transmitted electric field at a distant (far-field) point P in
the direction (,) is given by the Fourier Transform of the
electric field distribution across the aperture u(, ):
u(,)   u(, ) exp[2(  +  )/] dd
National Radio Astronomy Observatory
Sept 2005: Indiana University
Antenna Pattern: Directional Response
• Field Pattern of an antenna is defined by the Fourier
Transform of the illumination of the aperture:
u(,)  u(, )
• Antenna Pattern is defined in terms of power or the square
of the E field,|u|2.

Pn(,) = |u(,)|2/|u(0,0)|2
• Alternately, the antenna pattern is proportional to the Fourier
Transform of the auto-correlation function of the aperture
illumination, u(, )
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Sept 2005: Indiana University
Aperture-Beam Fourier Transform Relationship
u (, ) = aperture illumination
|u ()|2
= Electric field distribution
across the aperture
(, ) = aperture coordinates ;
u(,) = far-field electric field
( , ) = direction relative to
|u ()|2
“optical axis” of telescope
:
:
Antenna Key Features
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Sept 2005: Indiana University
Types of Antenna Mount
+ Beam does not rotate
+ Lower cost
+ Better tracking accuracy
- Higher cost
+ Better gravity
performance
- Beam rotates on the sky
- Poorer gravity performance
- Non-intersecting axis
Antenna pointing design
Subreflector mount
Reflector structure
Quadrupod
El encoder
Alidade structure
Rail flatness
Foundation
Az encoder
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Sept 2005: Indiana University
What happens to the signal collected by the antenna?
Heterodyne Detection
• At the focus, the radiation is collected by
the receiver through a “feed” into a receiver
that “pre-amplifies” the signal.
• Then, the signal is mixed with a local
oscillator signal close in frequency to the
observing frequency in a nonlinear device
(mixer).
• The beat signal (IF or intermediate
frequency signal) is usually amplified again
before going through a bandwidth defining
filter. (Frequency translation)
•Then the IF signal is detected by a
square-law detector.
RF at fsky
Pre-amplifier
LO at fLO
IF at fsky fLO
Amplification and
filtering
Voltage  |E|2
VLA and EVLA Feed System Design
VLA
EVLA
Wideband LBand OMT
and Feed Horn
National Radio Astronomy Observatory
Sept 2005: Indiana University
Receivers in the telescope
PF 1-1:
PF 1-2:
PF 1-3:
PF 1-4:
PF 2 :
Gregorian Receiver Room
L
S
C
X
Ku
K1
K2
Q
0.29 - 0.40 GHz
0.38 - 0.52
0.51 - 0.69
0.68 - 0.92
0.91 - 1.23
: 1.15 - 1.73 GHz
: 1.73 - 2.60
: 3.95 - 5.85
: 8.00 - 10.0
: 12.0 - 15.4
: 18.0 - 22.0
: 22.0 - 26.5
: 40.0 - 52.0
Radiometer Equation
• For an unresolved source, the detection sensitivity of a radio
telescope is determined by the effective area of the telescope
and the “noisiness” of the receiver
• For an unresolved source of a given flux, S, the expected
antenna temperature is given by
kTA = ½ Ae,maxS
• The minimum detectable TA is given by
TA = Ts/(B)
where Ts is the system temperature of the receiver, B is the
bandwidth and  is the integration time, and  is of order unity
depending on the details of the system. The system
temperature measures the noise power of the receiver (Ps =
BkTs). In Radio Astronomy, detection is typically receiver noise
dominated.
National Radio Astronomy Observatory
Sept 2005: Indiana University
High Resolution: Interferometry
• Resolution  /D
– 5 cm/100m = 2 arc-minute
• Uses smaller telescopes to
make much larger 'virtual'
telescope
• Maximum distance between
antennas determines
resolution
• VLA = 22-mile diameter
radio telescope
– 5 cm/22 miles = 0.3 arc-second
• Aperture Synthesis: Nobel
Prize 1974 (Ryle)
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Sept 2005: Indiana University
D
VLA = Very Large Array (1980)
Plain of San Augustine, New Mexico
National Radio Astronomy Observatory
Sept 2005: Indiana University
27-antenna array: Extremely versatile
Most productive telescope on ground
Interacting Galaxies
• Optical image (left) shows nothing of the Hydrogen gas
revealed by radio image by VLA (right).
Very Long Baseline Array
• 10  25m antennas
• Continent-wide:
5400-mile diameter
radio telescope
• 6 cm/5400 miles
= 0.001 arc-second
• Highest resolution
imaging telescope in
astronomy:
1 milli-arc-second = reading a
news-paper at a distance of
2000 km
National Radio Astronomy Observatory
Sept 2005: Indiana University