how do radio telescopes work?

National Radio Astronomy ObservatorySept. 2005 – Indiana University

How do Radio Telescopes work?

K. Y. Lo

National Radio Astronomy Observatory

September 2005 – Indiana Universe

Electromagnetic Radiation

Wavelength

Radio Detection techniques developed from meter-wave to submillimeter-wave: = 1 meter = 300 MHz

= 1 mm = 300 GHz

General Antenna TypesWavelength > 1 m (approx) Wire Antennas

Dipole

Yagi

Helix

or arrays of these

Wavelength < 1 m (approx) Reflector antennas

Wavelength = 1 m (approx) Hybrid antennas (wire reflectors or feeds)

Feed


Sept 2005: Indiana University

REFLECTOR TYPES

Prime focus Cassegrain focus

(GMRT) (AT)

Offset Cassegrain Naysmith

(VLA) (OVRO)

Beam Waveguide Dual Offset

(NRO) (ATA)



What do Radio Astronomers measure?

• Luminosity of a source: L = dE/dt erg/s• Flux of a source at distance R:

S = L/4R2 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:

I = dS/d erg/s/cm2/steradian

Measures of Radiation• The following should be clear: L = S d = 4R2 S for isotropic

source 4

S = I dsource

• 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) sda d d dt = I(, ) sda 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



Rayleigh-Jeans Law and Brightness Temperature

• The Specific Intensity of thermal radiation from a black-body at temperature T is given by the Planck Distribution:

I = (2h3/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)



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.



• 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.



• 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

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

Ae,max A = 2



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 dilutionBeam dilution

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( + )/] dd



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(, )

Aperture-Beam Fourier Transform Relationship

u (, ) = aperture illumination

= Electric field distribution

across the aperture

(, ) = aperture coordinates ;

u(,) = far-field electric field

( , ) = direction relative to

“optical axis” of telescope

: :

|u ()|2

|u ()|2



Antenna Key Features

Types of Antenna Mount

+ Beam does not rotate + Lower cost

+ Better tracking accuracy + Better gravity performance

- Higher cost - Beam rotates on the sky

- Poorer gravity performance

- Non-intersecting axis



Antenna pointing designSubreflector mount

Quadrupod

El encoder

Reflector structure

Alidade structure

Rail flatness

Az encoder

Foundation

What happens to the signal collected by the antenna?

• 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.

Pre-amplifier

LO at fLO

Amplification and filtering

Voltage |E|2

RF at fsky

IF at fsky fLO

Heterodyne Detection

VLA and EVLA Feed System Design

VLA

EVLA



Wideband LBand OMT and Feed Horn

Receivers in the telescope

Gregorian Receiver Room

PF 1-1: 0.29 - 0.40 GHzPF 1-2: 0.38 - 0.52PF 1-3: 0.51 - 0.69PF 1-4: 0.68 - 0.92PF 2 : 0.91 - 1.23

L : 1.15 - 1.73 GHzS : 1.73 - 2.60C : 3.95 - 5.85X : 8.00 - 10.0Ku : 12.0 - 15.4K1 : 18.0 - 22.0K2 : 22.0 - 26.5Q : 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.



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)

D



VLA = Very Large Array (1980) Plain of San Augustine, New Mexico

27-antenna array: Extremely versatileMost 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

how do radio telescopes work?

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