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Technical Fundamentals of Radio Astronomy. Chris Salter NAIC/Arecibo Observatory. The Atmospheric Windows. The Full Electromagnetic Spectrum. Cm-wavelength Radio Spectrum. If you can measure it with a ruler, then it's a RADIO WAVE!. τ (Transparency = e –τ ) ‏. Wavelength Ranges:

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Technical Fundamentals


Radio Astronomy

Chris Salter

NAIC/Arecibo Observatory


The Atmospheric Windows

The Full Electromagnetic Spectrum

Cm-wavelength Radio Spectrum

If you can measure it with a ruler, then it's a RADIO WAVE!

τ(Transparency = e–τ)‏

Wavelength Ranges:

Radio: 30 meter →1 millimeter = 3 × 104:1

Optical: 0.3 → 0.75 = 2.5:1

Frequency (GHz)‏


Observational Astronomy

Q: In what way does Observational (Passive) Astronomy differ from Other Sciences?

A:It is NOT experimental!

E.g. Zoology: Rats in mazes: Planetary Radar:

Particle Physics: The Larger Hadron Collider:

In Observational Astronomy, “What you see in what you get!”



Arecibo 305-m telescope (Puerto Rico)‏

GBT 100-m telescope (WV, USA)‏

Single-Dish Radio Telescopes

Effelsberg 100-m telescope (FRG)‏

IRAM 30-m mm-wave telescope (Spain)‏

Ooty Radio Telescope 530  30 m (India)‏



(1 arcmin = a Quarter

at 100 yds)‏


Telescope Beam Pattern

The response of the telescope to signal power arriving from a direction (θ, Φ) is known as the BEAM PATTERN, or the POWER POLAR DIAGRAM, P(θ, φ).

We normalize the response such that, P(0,0) = 1.0

The pattern has a MAIN BEAM and SIDELOBES. The sidelobes in the rear 2π steradians are called the BACK LOBES.

A design requirement is to minimize the sidelobes as they represent unwanted responses accepting power where you would like it rejected. The lower the sidelobes, the better the telescope can detect weak objects near a strong source, giving a higher DYNAMIC RANGE.

Main-Beam Resolving Power:

This is defined as the angular width of the main beam between directions where the response has fallen to one half of the maximum, called the HALF-POWER BEAMWIDTH (HPBW)‏


For a single-dish telescope of diameter, D;

HPBW = 1.2 × λ/D radians, where λ is the wavelength.

NOTE: D/λ = Number of wavelengths across the telescope.


HPBW of the Arecibo 305-m Telescope

Wavelength Frequency HPBW

2.3 meter 130 MHz 37 arcmin

70 cm 430 MHz 11 arcmin

21 cm 1400 MHz 3.4 arcmin

13 cm 2300 MHz 2.0 arcmin

6 cm 5000 MHz 1.0 arcmin

3 cm 10000 MHz 0.5 arcmin


Specific Intensity or Surface Brightness

Intensity/Surface Brightness is the fundamental observable in radio astronomy representing the intensity of radio waves arriving at the Earth.

(x, y)‏

Considering the energy in a frequency band of width, dυ, about a central value, υ, arriving per sec from the direction (x,y) in solid angle, dΩ. Then the Intensity, I(x, y) is given by;

I(x,y,υ,t) = lt dE(x,y,υ,t)

dA,dΩ,dυ,dt → 0 cosθ dA dΩ dυ dt

NOTE: dE/dt is the power received from dΩ on area dA in bandwidth dυ. So, I is the power per unit area, per Hz from unit solid angle in the direction (x, y).

The units of I are W m-2 Hz-1 ster-1.

Solid angle dΩ

Area = dA

Brightness Temperature: Often Intensity is expressed as a brightness temperature TB,i.e. if the sky at dΩ were replaced by a black body of temperature TB K, then at our observing frequency we would measure the same intensity. Luckily, most radio frequencies are sufficiently low, and TB sufficiently high that the Rayleigh-Jeans approximation holds, and;

I = 2 k TB υ2 = 2 k TB (where c = speed of light

c2 λ2 and k = Boltzmann's Constant)‏


Flux Density

We can scan our radio telescope over a radio source such as to measure its intensity distribution, and in the process produce a “radio photograph” (i.e. an image) of the source.

To define a global parameter that characterizes the strength of the emission from our source at observing frequency υ, we use the power received from the whole source on unit area, per Hz of bandwidth. This we call theFLUX DENSITY, S(υ, t).

Integrating over solid angle;

S(υ, t) = ∫ I(x, y, υ, t) dΩ


Note that for our tiny piece of sky, dΩ, S = I dΩ = dE , so the units are W m-2 Hz-1

dA dυ dt

However, the flux densities of radio sources are so small that a more practical unit has been adopted. This is the Jansky, where;

1 Jansky (Jy) = 10-26 W m-2 Hz-1

This looks pretty small, but in the 38 years since the Jansky was adopted things have moved along sufficiently that we can now detect sources whose flux densities are ~10-5 Jy!


Distance Dependencies

Suppose we observe a galaxy of radius, r, at distance, D,

Then we see the galaxy as subtending a solid angle of πr2/ D2.

So, dΩ α D-2

Now, the energy, dE received from the galaxy α D-2 (inverse square law)‏

And as I = dE / (dA dΩ dυ dt) ,I is Distance Independent.

(i.e. while a distant source looks smaller than a similar nearby one, it has the same intensity/surface brightness.

In contrast, the flux density, S = dE / (dA dυ dt) so, S falls as the inverse-square of the distance.


2 × r


Effective Area of a Telescope

A Point Source is one that has an angular size, θs << HPBW of the antenna.

Its flux density is S(υ) = dE/(dA dυ dt), so the power collectedby our telescope can be written as S(υ) Aeff(υ) Δυ, where Δυ is the receiver bandwidth, and Aeff(υ) is called theEffective Areaof the telescope.

Note that a single radio receiver can only collect the power from one of the two polarizations of the incoming signal. Hence it can only collect ½ S(υ) Aeff(υ) Δυ.

Suppose that after observing a point source, we replace the receiving dipole by a resistor whose temperature is adjusted to a value TA, where the noise power from the resistor equals the power previously received from the point source. Now the power received from a resistor at a temperature T = k T Δυ. Hence;

k TA Δυ = ½ S(υ) Aeff(υ) Δυ

and, Aeff (υ) = 2 k TA,where TA is called the Antenna Temperature.


Hence, if we measure a source of known flux density, we can calculate Aeff.

If AP is the physical area of the antenna, we define its Aperture Efficiency to be; ηA = Aeff/AP < 1.0


A Simple Radio Receiver

The celestial source provides a “noise-power” giving Antenna Temperature = TA.

The preamplifier is very important as it provides most of the noise against which we are trying to detect a radio source!


The mixer changes the frequency of the received signal to a (usually) lower frequency. Most amplification occurs at the IF Stage, and a “Standard IF” can be used for received signals of all frequencies.


A Square-Law Detector is used so:

Output voltage α(Input Voltage)2

α Input Power


The integrator sums up the detector output, “beating down” the noise level in the process.

The data are recorded for subsequent analysis.


Receiver Noise




Q: “How weak a source can we detect with our receiver?”

A: The answer is provided by the RADIOMETER EQUATION: Trms = Tsys ,

(Δυ τ)0.5

where Δυ is the receiver bandwidth (Hz), and τ is the integration time (sec).

A good rule-of-thumb is that a source will be detected if it provides TA > 5 × Trms



If the biggest telescope in the World (Arecibo) has a resolution of ~1 arcmin, can we ever discover what the radio sky looks like at arsecond resolution, or finer?

Yes — Thanks to radio interferometery! Despite dealing with the longest wavelength electromagnetic waves, radio astronomy has provided our most detailed images of the Universe, achieving not only arcsecresolution, but even sub-milliarcsec resolution!

Combining the voltages from 2 telescopes separated by a distance,b, there is a phase difference between them of;

φ = (2π b cos θ) / λ , where λ is the wavelength.

This produces a fringe pattern, with maxima at cos θ = n λ / b

If b = 30 km and λ = 3 cm, fringe maxima are separated by

~0.2 arcsec. If b = 6000 km, then the fringe separation is

~1 milliarcsec!

While two antennas will give you a fringe pattern, combining the signals from many (N) telescopes separated by large distances, and allowing the Earth's rotation to move a radio source through their mutual N(N – 1)/2 fringe patterns, allows us to make images of the sky with the angular resolution obtainable by a “virtual” single telescope whose diameter is that of the widest separation of any pair of telescopes present.


GMRT (India)‏

Angular Resolution = ( / Separation) radians





(1 arcsec = a Quarter

at 3.5 miles)‏

(1 milliarcsec = a Quarter

at 3500 miles)‏


(NM, USA)‏

Telescope Arrays


Very Long Baseline Interferometry

When the telescopes in an interferometer array are separated by large distances, it was for many years impossible to directly combine their signals. The voltages from each telescope were recorded on magnetic tapes, and later disc packs, which are Fed-Exed to a central location where the signals from each antenna pair are cross- multiplied in a special Very Long Baseline Interferometry (VLBI) correlator.

In recent years, real-time correlation has become possible by transmitting the signals directly to the correlation center via the internet — eVLBI.

A number of major VLBI arrays have come into being;

VLBI Space Observatory Project (VSOP; Japan)‏

Very Long Baseline Array (VLBA; USA)

European VLBI Network (EVN; EEC)‏