This chapter describes the various components of a radio telescope and
outlines the various detection mechanisms for the radiation.

**6.2 Antennas**

P=SnA Dn

where *Sn* is the flux density at the
earth from some astronomical source,* A* is the area of the antenna
and Dn is the frequency interval or bandwidth
of the measured radiation.

So, the larger antennas collect more power. The antenna also has the
capability of discriminating the signals coming from different directions
in space.

**6.2.2 Diffraction and reciprocity**

The operation of antennas, and telescopes in general, are governed by
electromagnetic theory and diffraction theory plays an important role.
In order to understand this, one first needs to know the reciprocity theorem.
This theorem states that the telescope operates the same way whether it
is receiving or transmitting radiation. So the response pattern of an antenna
that is receiving radiation is the same as the pattern produced when the
same antenna is transmitting. A schematic of a response pattern of an antenna
is given in Figure 6.1.

**Figure 6.1**

A telescope’s response pattern is then the same as the far-field diffraction
pattern produced by the aperture. In general, when radiation of wavelength l passes through an aperture of diameter *D, *the radiation diffracts
into a beam with angular size q *= l /D.* At large distances (or the far-field response), the pattern is
given by Fraunhofer diffraction theory and the pattern looks like that
in Figure 6.1, where the beamwidth is the full width at half power of the
main beam. The beamwidth q is also a measure
of the directivity of the antenna. A more precise statement that can be
made (and will not be derived here) is that the angular pattern of the
electric field in the far-field is the Fourier transform of the electric
field distribution across the aperture.

**6.2.3 Parabolic Antennas**

Parabolic antennas (or reflectors) are common to both radio and optical astronomy. The reflector focuses plane waves to a single point, or in other words, converts plane waves into converging spherical waves. In a radio telescope these spherical waves are then coupled to a transmission line using a feed horn, which is a horn antenna. The feed horn can be placed at the prime focus or at a secondary focus using a Cassegrain design (Figure 6.2).

**Figure 6.2**

Most radio telescopes have a Cassegrain design since placing the feed horn at the prime focus will block more of the surface. Small telescopes (such as the SRT) have a prime-focus arrangement in which the reflector is illuminated by the feed placed at the focal point on the axis of the parabola. The geometry of a parabola is given by

y=x^{2}/(4F)

where *y* is the distance from plane, *x* is the distance
from the vertex, and *F* is the focal length as shown in Figure 6.3.

**Figure 6.3**

The reflector surface must follow a parabola to within a small fraction
of a wavelength. An imperfect surface scatters some signal away from the
focus and produces a loss known as the *Ruze* loss after John Ruze,
who first derived the expression

L = exp(-(4p d/l )^{2})

where *L* is the loss factor, *d* is the root-mean-square
(rms) deviation from a parabola,and is *l *the
wavelength.

For most random distributions, the rms is about one quarter of the peak-to-valley variations. Figure 6.4 shows the Ruze loss in dB as a function of surface quality.

**Figure 6.4**

The angle subtended by the reflector, as seen by the feed, is determined
by the ratio of focal length to diameter or *F/D*. Most dishes have
a *F/D* ratio close to 0.4. A Radio Shack 9-foot satellite TV dish
has an *F/D* of 0.38. For this *F/D*, the edge of the dish is
about 64° out as seen by the feed. The feed should ideally be an antenna
with a uniform beam that illuminates only the reflector surface. The efficiency
in this case would be close to 100%. In practice, a good feed provides
about 60 to 70% efficiency, so that the gain of this 9-foot antenna is
39.6 dB at 4.1 GHz. A very popular feed design is a *scalar* feed,
which consists of a probe in a circular waveguide surrounded by choke rings
as illustrated in Figure 4. The beam of the feed, which usually tapers
down by about 10 dB at the edge of the dish, can be adjusted to some extent
by the choice of opening size and location of the choke rings. Figure 5
shows the effect on efficiency of varying this taper. The beamwidth of
a dish illuminated with such a scalar feed is approximately

q = 1.22 l/D

**6.2.4 Gain**

Radio and radar engineers normally speak about antennas in terms of
their gain in dB referred to a half-wave dipole (dBd) or referred to an
ideal isotropic antenna (dBi). A half-wave dipole has a gain of 2.15 dBi.
Radio astronomers prefer to talk of size and efficiency or effective collecting
area The gain, *G*, of an antenna relative to isotropic is related
to its effective collecting area, *A*, by

G = 4p A/l^{2}

where is the *l *wavelength

The gain is also related to the directivity of the antenna: An antenna with a smaller beam will have a higher gain. If we think of the antenna as a transmitter, as we can do owing to reciprocity, then if the transmitted energy is confined to a narrow angle, the power in this direction must be higher than average in order for the total power radiated in all directions to add up to the total power transmitted.

To achieve an effective area or aperture of many square wavelengths (gains of more than, say, 26 dBd), a parabolic reflector is the simplest and best approach. For long wavelengths, for which an antenna with more than 26 dBd would have enormous dimensions, other approaches are more appropriate. As radio amateurs doing Moon-bounce know, it is hard to beat an array of Yagi antennas for simplicity and minimum wind loading. A single 20-wavelength-long Yagi can give a gain of 20 dBd. Stacking 2 Yagis adds 3 dB and another 3 dB for every doubling. The effective aperture of a 20 dBd Yagi, however, is only 13 square wavelengths, so that stacking 50 Yagis to get 37 dBd of gain at, say, 4 GHz doesn’t make much sense when you can do as well with a 9-foot-diameter dish of 60% efficiency. At UHF frequencies around 400 MHz, the choice between Yagis and a dish is not so clear.

With the availability of excellent LNAs, optimizing the antenna efficiency
is less important than optimizing the ratio of efficiency to system noise
temperature or gain over system temperature, *G/T _{s}*. This
means that using a feed with low sidelobes and slightly under-illuminating
the dish may reduce

**6.2.5 Spillover**

With advent of superb Low Noise Amplifiers (LNAs), the antenna noise
is also a very important performance parameter along with the gain or equivalent
effective aperture. Antenna noise originates from the sky background, ohmic
losses, and ground pickup or *spillover* from sidelobes. While the
sky noise is fundamental, the losses and sidelobes can be made small by
a good design. Sky noise is frequency dependent but never gets any lower
than the cosmic 3-K background. The minimum is near 1.4 GHz, where Galactic
noise has declined and atmospheric attenuation, due primarily to the water
line at 22 GHz, is still low. The lowest system noise achievable is about
18 K. At the NASA deep space network (DSN), where every fraction of a dB
of performance is worth $millions, the S-band (2.3 GHz) system budget is
approximately 3 K from cosmic background plus 7 K spillover plus 3 K atmospheric
plus 5 K LNA. At 408 MHz, galactic noise will dominate, and system noise
will be at least 50 K increasing to over 100 K toward the Galactic center.
Figure 6.5 shows the relative system-noise contributions as a function
of frequency.

**Figure 6.5**

Figure 6.6 is a schematic of a minimalist receiver for continuum radio astronomy.

The usual root-mean-square (rms) noise calculations in radio astronomy are based on

where *T _{sys}* is the system temperature in Kelvins, b is the noise bandwidth,

which is only approximately equal to the resolution in spectroscopy
or the total usable bandwidth in continuum, and *t* is the total integration
time (on plus off) for normal switched observing. Set a to 2 for ordinary single switching where 2 is the product of two Ö 2, one for spending half the time on source, another for differencing two
equally noisy measurements. The correlation quantization correction g is approximately 1.16 for Haystack’s spectrometer with its modified 3×3
multiplication table. Set g to 1 for continuum.
Then D*T* is the rms fluctuation in the
corresponding measurement. The b*t *in
the denominator of this equation is, in effect, the number of samples averaged
to make the measurement.

**B. Why heterodyne?**

Most receivers used in radio astronomy (all receivers used for spectroscopy) employ so-called superheterodyne schemes. The goal is to transform the frequency of the signal (SF) down to a lower frequency, called the intermediate frequency (IF) that is easier to process but without losing any of the information to be measured. This is accomplished by mixing the SF from the LNA with a local oscillator (LO) and filtering out any unwanted sidebands in the IF. A bonus is that the SF can be shifted around in the IF, or alternatively, the IF for a given SF can be shifted around by shifting the LO.

**C. Why square-law detectors?**

Inside radio-astronomy receivers, a signal is usually represented by
a voltage proportional to the electric field (as collected by the antenna).
But we normally want to measure power or power density. So, at least for
continuum measurements and for calibration, we need a device that produces
an output proportional to the square of the voltage, a so-called square-law
detector, and also averages over at least a few cycles of the waveform.

**6.3.2 Extracting weak signals from noise**

As mentioned above, radio-astronomy systems usually operate close to the theoretical noise limits. With a few exceptions, signals are usually extremely weak. One such exception is the Sun. Depending on frequency, Solar cycle, antenna size, and system noise temperature, pointing an antenna at the Sun normally increases the received power several fold. Toward other sources, it is not unusual to detect and measure signals that are less than 0.1% of the system noise. The increase in power, measured in K, due to the presence of a radio source in the beam is given by

T_{a }= AF/(2k)

where *A* is the effective aperture (m^{2}) or aperture
efficiency times physical aperture, *F* is the radio flux density
in watts/m^{2}/Hz, and *k* is Boltzmann’s constant, 1.38 x
10^{-23} w/Hz/K.

The factor of 2 in the denominator is because radio astronomers usually
define the flux density as that present in both wave polarizations, but
a receiver is sensitive to only one polarization. Radio telescopes use
linear or circular polarization depending on the type of observations being
made, and with two LNAs and two receivers, one can detect two orthogonal
polarizations simultaneously. In order to detect and measure signals that
are a very small fraction of the power passing through the receiver, signal
averaging or *integration* is used. If the receiver gain were perfectly
stable, our ability to measure small changes in signal is given by the
noise equation in the previous section. There D*T* is the one-sigma measurement noise.

If the receiver bandwidth is 1 MHz and *T _{sys}* = 100
K, for example, then we can measure down to 0.013 K in one minute. For
a sure detection, we need to see a change of 10 sigma or about 0.1 K change.
The receiver gain in practice is seldom exactly constant, and the additional
spillover noise and atmospheric noise may also be changing, so it will
be difficult at this level to distinguish a real signal from a change in
gain or atmospheric noise. There are several solutions to this problem,
depending on the type of observing, all of which rely on some way of forming
a reference. If we are making spectral-line measurements, the reference
is often just adjacent frequencies. If we scan the frequency or simultaneously
divide the spectrum into many frequency channels, then the gain or atmospheric
noise changes will be largely common to all frequencies and will cancel
with baseline subtraction in the final spectrum. In making measurements
of broadband or

Another powerful technique for extracting weak signals from noise is
correlation. The radio telescope in this case has two or more receivers
either connected to the same antenna, or, more often, two or more separate
antennas. The signal voltages are multiplied together before averaging
instead of multiplying the signal voltage by itself to obtain the power.
With separated antennas, the correlation output combines the antenna patterns
as an interferometer, which generates lobes on the sky that are separated
in angle by the wavelength divided by the projected baseline between the
antennas. Correlation techniques are common in radio astronomy, and they
are becoming popular also in communications. Correlation is used, for example,
to detect and demodulate spread-spectrum signals as in code-division multiple-access
(CDMA) digital cellular telephones.

**6.3.3 An analog-to-digital converter (ADC)**

Since all the final processing of a radiometer output is done with a
computer, we need to convert analog voltages from the detector to numbers
that can be processed in software. A very accurate and effective ADC is
a voltage-to-frequency converter followed by a counter. This ADC provides
integrated power with as many bits as are needed to represent the count
over the integration interval. If reading the output of the counter at
perfectly regular intervals is difficult, then another counter can be used
simultaneously to count the constant-frequency output of a crystal oscillator.
The integrated power is then proportional to the ratio of the counts from
the voltage-to-frequency converter to the counts from the crystal oscillator.

**6.3.4 Interference**

Radio astronomy is often limited by interference especially at low frequencies.
The spectrum is overcrowded with transmitters: Earth-based TV, satellite
TV, FM, cellular phones, radars, and many others. Radio astronomy has some
protected frequency bands, but these bands are often contaminated by harmonics
accidentally radiated by TV transmitters, intermodulation from poorly designed
transmitters, and noise from leaky high-voltage insulators and automobile
ignition noise. Some of the worst offenders are poorly designed satellite
transmitters, whose signals come from the sky so that they effect even
radio telescopes that are well shielded by the local terrain. Radio telescopes
and their receivers can be made more immune to interference by:

- Including a bandpass filter following the LNA to prevent interference from being generated inside the receiver by intermodulation.
- Placing the telescope in a location with as much shielding as possible from the local terrain. Low spots (e.g., valleys) are good for low-frequency radio telescopes because they reduce the level of interference from ground-based transmitters. (Prefer a dry mountain-top to reduce atmospheric attenuation at millimeter and shorter wavelengths.)
- Tracking down interference and trying to reduce it at the source.
- Designing and using an antenna with very low sidelobes.
- Using an interferometer and correlation processing, which is far more immune to interference.
- Using data editing to remove data corrupted by interference.

**6.4 Spectrometers and Spectroscopy**

**6.4.2 Comb of filters-filter bank**

**6.4.3 Autocorrelations and Fourier transforms**

**6.4.4 Switching schemes and baselines-Why switch?**

Switching schemes are needed for either continuum or spectral measurements.
A price to be paid for switching is increased noise. There are two contributions
to the added noise: The receiver spends only half the time looking at the
signal, and the result is the difference between two equally noisy measurements.
The result is twice the noise compared with not switching for the same
integration time (this is ain the noise equation
above), or four times the integration time to achieve the same noise.

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