1. Radio Telescopes and Radiometers
2015 Single Dish School
Jim Condon
The PowerPoint material is available online and in book (4 copies here), so students can just look at the slides and listen, instead of furiously scribing notes.
NRAO, Charlottesville

2. Radio Telescopes and Antennas
An antenna is any device that converts electromagnetic radiation traveling through space to electrical currents flowing in a wire (receiving antenna) or vice-versa (transmitting antenna).
Radio telescopes, and only radio telescopes, contain antennas.
Most of a typical radio telescope is not an antenna − the big dish just redirects electromagnetic radiation to the antenna part.
The antenna output waveform matches the EM input waveform; e.g., a 1 GHz EM sine wave becomes a 1 GHz sine wave in the wire output of an antenna. All information in the EM wave is preserved, so the signal can be processed electronically (e.g., spectroscopy), unlike optical telescopes which must perform signal processing on the input EM wave (e.g., a prism to disperse colors for spectroscopy) because the optical detector (e.g., a CCD camera) destroys the input waveform and measures only power. The antennas can’t even be seen in this photo of the GBT.
Single Dish School July 6

3. Electromagnetic radiation is produced by accelerating charged particles
How can a transmiftting antenna create radio waves? The transverse component of field line moves outward with speed c, decays as 1/r (not 1/r**2), is EM radiation. Note amplitude E of the radiated electric field is proporiional to sin theta, the acceleration perpendicular to the line of sight. Power radiated is proportional to E**2
Single Dish School July 6

4. Dipole antenna Power pattern
Note that the radiated E field is parallel to the dipole; that is, the dipole is a linearly polarized antenna.
Single Dish School July 6

5. Reciprocity theorem
Time symmetry t = -t of Maxwell’s equations for a lossless antenna. Likewise for polarization. Thus it takes two orthogonal dipoles to receive all of the power in an arbitrarily polarized electromagnetic wave. (The prime-focus feeds of the GBT are two orthogonal dipoles in front of small reflectors.) It is usually easier to calculate the properties of a transmitting antenna and measure the properties of a receiving antenna. The reciprocity theorem allows such calculations and measurements to be compared.
 The receiving and transmitting patterns of an antenna are identical.
Single Dish School July 6

6. Ground-plane Waveguide horn vertical = ½ of a half-wave dipole
AM broadcast transmitting antennas are usually ¼ wavelength ground-plane verticals; e.g., 1 MHz corresponds to 300 m wavelength, so the antenna is a 75 m tall tower. At radio astronomy frequencies, the antenna is only cm or mm in size.
Single Dish School July 6

7. The waveguide horn used to discover λ = 21 cm HI emission from our Galaxy
Now in front of the Jansky Lab. Look inside, note coaxial cable connector on the rear waveguide. Waveguide width at back is slightly over ½ wavelength and height is < ½ wavelength to allow only a single mode to propagate.
Single Dish School July 6

8. Parabolic reflector: directivity and collecting area
Prime focus
“Feed” antenna (note the transmitting term used even for receiving) is at the prime focus, the focal point of the primary mirror. See the Reber dish rebuilt in front ot the Science Center.
Single Dish School July 6

9. Aperture
The electric field beam pattern f of an aperture antenna is the sum of the vector fields from each small part of the aperture. Thus it is the Fourier transform of the electric field g illuminating the aperture. The x coordinate in wavelengths is called u, and l = sin(theta) ~ theta is the angle in radians from the normal to the aperture plane.
Single Dish School July 6

10. Illumination, field, and power patterns
Similarity theorem of Fourier transforms implies beamwidth is inversely proportional to aperture size in wavelengths.
Note: single feed produces only one beam, making a single-pixel radio telescope. To image an extended region, must scan the beam across that region.
Sidelobes are bad. They pick up unwanted radiation from strong radio sources away from the beam (e.g., the sun or HI emission from the plane of our galaxy), “spillover” noise from ground radiation, and RFI.
Single Dish School July 6

11. Cassegrain subreflector
Cassegrain multiplies the low f/D ~ 0.4 of radio telescope dishes (increases size of focal ellipsoid (field of view) for more pixels), puts spillover onto cold sky instead of warm ground, and moves the feed/receiver box to a more accessible location. However, the feed beamwidth needed to illuminate the subreflector from the vertex is much smaller than the feed beamwidth needed to illuminate the primary mirror from the prime focus, so Cassegrain feeds get very large at long wavelengths (frequencies < 1 GHz or so). Note the Cassegrain subreflector is below the prime focus, so it blocks the prime focus.
Single Dish School July 6

12. 140-foot (43 m) Cassegrain
The beam of a parabolic dish is steered by moving the dish and keeping the feed on-axis. Gravitational loading depends on how far over it is tilted and deforms the reflector surface. Arecibo avoids this problem by having a fixed spherical reflector, which has no axis, so the beamican be moved by moving the feed. This allows a really big reflector (1000 feet = 305 m) but requires large feeds to correct the phase errors caused by not having a parabolic reflector.
Single Dish School July 6

13. Reflector surface errors
The maximum tolerable rms surface deviation from a perfect paraboloid is usually considered to be ~ 1/16 = wavelength (aperture efficiency ~ 0.54).
Single Dish School July 6

14. 100 m homology telescope in Effelsberg
The dish backup structure of the 100 m was designed to deform “homologously” – it remains a good paraboloid at 7 mm wavelength whose focus shifts and can be tracked by moving the feed. Large radio telescopes don’t scale well: small subreflector for nutating far from feeds at vertex require impractically large feeds at long wavelengths.
Note also feed/subreflector shadows on dish, reducing effecting collecting area, increasing far-out sidelobes picking up “stray radiation” from the Sun, HI from the galactic plane, etc., and increasing pickup of ground noise and RFI.
Single Dish School July 6

15. GBT: homology plus active surface
The GBT has 0.2 mm (thickness of two sheets of paper over 100 m dish) rms surface error, good for observing down to 3 mm wavelength.
Computer-driven screws continuously adjust the surface as the dish tilts.
Single Dish School July 6

16. GBT Offset Gregorian + Prime Focus for unblocked aperture
The GBT is a 100 m offset section of a symmetric 208 “parent” paraboloid so the focal points and feed arm do not block the beam. That means a very large feed arm can be built and the secondary focus can be raised from the vertex closer to the prime focus, where the angle subtended by a small subreflector is larger, so the secondary feeds can be smaller. The Gregorian focus is above the prime focus, so both foci can be used. The GBT’s unblocked aperture yields lower noise from ground pickup, better attenuation of RFI, less stray radiation from Sun and Galactic HI.
Single Dish School July 6

17. Note that the GBT beam is lower than perpendicular to the plane of the dish rim. For next slide, point out locations of the Gregorian subreflector above the prime focus, feed/rx cabin the secondary focus below the prime focus, and the retracted boom holding the prime-focus feeds used below ~ 1 GHz.
Single Dish School July 6

18. GBT feeds and radiometers
Point out Gregorian subreflector above the prime focus, feed/rx cabin at the secondary focus below the prime focus, and the retracted boom holding the prime-focus feeds used below ~ 1 GHz. Snakes dry feed covers. Rotating turret moves selected feed to secondary focus. Biggest feed, longest lambda (L band 1-2 GHz). Note pair of smaller feeds for two beams. The horns protrude through the top of the receiver cabin. The antennas are hidden inside the small ends of the circular waveguide horns. The RF amplifiers are located near the antennas and hang from the bottom ends of the feed horns.
Single Dish School July 6

19. Antenna output noise: voltage and power
TA = “antenna temperature”
Ae = effective area
S = flux density
Pν = power per unit frequency
k = Boltzmann’s constant
≈ 1.38 × 10−23 Joules per Kelvin
The noise voltage fluctuates on time scales ~ inverse bandwidth ~ nanoseconds. It has zero mean and a Gaussian amplitude distribution. The radiometer selects frequency ranges from the broadband noise and measures the average noise power, which is proportional to the square of the noise voltage. The desired signal is usually much smaller than the total noise power.
Single Dish School July 6

20. The simplest radiometer
The bandpass filter box usually also contains an amplifier to increase the tiny input voltage. The “square law” detector (circle with X = multiplication sign) multiplies the noise voltage by itself, so its output voltage is proportional to its input power.
Single Dish School July 6

21. Square-law detector: output noise voltage is proportional to input power
The ouput voltage has nonzero mean.
Single Dish School July 6

22. Integrator output noise for: N = 50 samples N = 200 samples
Sampling theorem: two independent samples per bandwidth * time product; e.g., if bandwidth = 1 MHz, there are two independent samples per microsecond.
Single Dish School July 6

23. Differential radiometer
This beam-switching differential radiometer reduces the effects of atmospheric and gain fluctuations.
Single Dish School July 6

24. Superheterodyne receiver
The superheterodyne receiver has a fairly broadband RF= radio frequency amplifier and is tuned by changing the LO = local oscillator frequency only (as in an FM radio covering 88 to 108 MHz with station selectivity ~ 200 kHz in the IF, for example).
Single Dish School July 6

25. Spectrometers and software-defined digital back ends
Analog filter bank shown. Normally a digital back end samples IF data stream and calculates the spectrum (“software-defined radio”).
Single Dish School July 6

26. To learn more about radio astronomy, Google Essential Radio Astronomy
or see the printed book
(4 copies are on reserve)
The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.
Single Dish School July 6