The radio band is too wide (five decades in wavelength) to be covered effectively by a single telescope design.  The surface brightnesses and angular sizes of radio sources span an even wider range, so a combination of single telescopes and aperture-synthesis interferometers are needed to detect and image them.  It is not practical to build a single radio telescope that is even close to optimum for all of radio astronomy.

The ideal radio telescope should have a large collecting area to detect faint sources.
The effective collecting area $A_{\rm e}(\theta, \phi)$ of any antenna averaged over all directions $(\theta, \phi)$ is
$$\langle A_{\rm e} \rangle= {\lambda^2 \over 4 \pi}~.$$ Large peak collecting areas imply extremely directive antennas. Only at long wavelengths ($\lambda > 1$ m) is it feasible to construct reasonably sensitive antennas from reasonable numbers of small, nearly isotropic elements such as dipoles.

The 20.5 MHz Bruce Array used by Karl Jansky. Image credit

Jansky's $\lambda \approx 15$ m "wire" antenna is an array of phased dipoles.  It produces a wide fan beam near the horizon but has a large collecting area because $\lambda^2$ is so large.  Directive aperture antennas are needed for adequate sensitivity at higher frequencies.

The simplest aperture antenna is a waveguide horn.  Radiation incident on the opening is guided by a tapered waveguide.  At the narrow end of the tapered horn is a waveguide with parallel walls, and inside this waveguide is a quarter-wave ground-plane vertical antenna that converts the electromagnetic wave into an electrical current that is sent to the receiver via a cable.

Horn antennas pick up very little ground radiation because, unlike most paraboloidal dishes, their apertures are not partially blocked by external feeds and feed-support structures, which scatter ground radiation into the receiver.   This freedom from ground pickup allowed Penzias & Wilson (1965, ApJ, 142, 419) to show that the zenith antenna temperature of the Bell Labs horn was 3.5 K higher at $\nu \approx 4$ GHz than expected—the first detection of the cosmic microwave background radiation.

The horn antenna at Bell Labs, Holmdel, NJ that Penzias and Wilson used to discover the 3 K cosmic microwave background radiation in 1965. Image credit

Because the aperture of a waveguide horn is not blocked by any feed-support structure, it is also easier to calculate the gain of a horn antenna from first principles than to calculate the gain of a partially blocked aperture.  Thus small horn antennas have been used by radio astronomers to measure the absolute flux densities of very strong sources such as Cas A.  Radio astronomers observing with large dishes typically do not measure the absolute flux densities of sources, only their relative flux densities by comparison with calibration sources whose absolute flux densities are known in advance.  The process of measuring the absolute flux densities of Cas A and comparing them with the flux densities of weaker point sources suitable for calibrating observations made with large radio telescopes was described in detail by Baars et al. (1977, A&A, 61, 99).

Small waveguide horns are frequently used as feed antennas for paraboloidal radio telescopes.

Most radio telescopes use circular paraboloidal reflectors to obtain large collecting areas and high angular resolution over a wide frequency range.
Because the feed is on the reflector axis, the feed and legs supporting it partially block the path of radiation falling onto the reflector.  This aperture blockage has a number of undesirable consequencies:
• The effective collecting area is reduced because some of the incoming radiation is blocked.
• The beam pattern is degraded by increased sidelobe levels.
• Radiation from the ground that is scattered off the feed and its support structure increases the system noise.

The first paraboloidal radio antenna, built in 1937 by Grote Reber. Notice how the cylindrical housing at the prime focus and the feed-support legs cast shadows on the reflector.  The tower in front of the telescope allows access to the receiver and feed located at the prime focus. Image credit

Radio telescopes are so large that paraboloids with high $f/D$ ratios are impractical; typically $f/D \approx 0.4$.  Thus radio "dishes" are relatively deep, as shown in the photo below.  Another consequence of a low $f/D$ ratio is a tiny field of view at the prime focus.  The instantaneous imaging capability of a large single dish is severely limited by the small number of feeds can fit into the tiny focal ellipsoid, the ellipsoidal region surrounding the prime focus in which a simple feed yields a beam with minimal gain loss and low sidelobes.

The 250 foot Lovell Telescope in Jodrell Bank, England was the first truly large steerable dish, completed in 1957 and famous for detecting Sputnik. The  length of the central tower that supports the feed at the prime focus is only about 30% of the reflector diameter. Image credit

Nearly all radio telescopes have alt-az mounts consisting of a horizontal azimuth track on which the telescope turns in azimuth (the angle measured clockwise from north in the horizontal plane) and a horizontal elevation axle about which the telescope tips in elevation (the angle above the horizon) or zenith angle (the angle below the vertical). The 140-foot telescope in Green Bank is unique among large radio telescopes in having a polar mount.  The advantage of a polar mount is tracking simplicity—the declination axis is fixed and the hour-angle axis turns at a constant rate while tracking a distant celestial source.  In contrast, both the altitude and the azimuth of a celestial source change nonlinearly with time.  When the 140-foot telescope was being designed, the ability of computers to perform the real-time calculations needed for an alt-az telescope to track a source accurately was in doubt.  The disadvantage of a polar mount is mechanical—the sloped hour angle yoke and polar axis with its huge support bearing are very difficult to build and support.

The 140 foot telescope in Green Bank, WV is the largest telescope with a polar mount. Image credit

The photo above clearly shows the Cassegrain optical system of the 140 foot telescope.  Radiation reflected from the main dish is reflected a second time from the convex Cassegrain subreflector located just below the focal point down to feed horns and receivers near the vertex of the paraboloid.  Some advantages of a subreflector system over prime-focus system are:
• The magnifying subreflector can multiply the effective $f/D$ ratio; values of $f/D \sim 2$ are typical.  This greatly increases the size of the focal ellipsoid.  Multiple feeds can be located within the focal ellipsoid to produce multiple simultaneous beams for faster imaging.
• The subreflector is many wavelengths in diameter so it can be used to tailor the illumination taper to optimize the tradeoff between high aperture efficiency and low sidelobes.
• Receivers are located near the vertex, not the focal point, where they are easier to access.
• Feed spillover radiation is directed toward the cold sky instead of the warm ground, lowering overall system temperatures.
• The subreflector can by nutated rapidly to switch the beam between two adjacent positions on the sky.  Such differential observations can be used to remove receiver baseline drift and large-scale fluctuations in atmospheric noise.
• The subreflector can be tilted to select one of several feeds at the secondary focus, so that the observing frequency band can be changed rapidly.
Some disadvantages of a subreflector system are:
• Relatively large feeds are required to produce the narrow beams needed to illuminate the subreflector, which typically subtends only a small angle as viewed from the vertex.
• Standing waves in the leaky cavity formed by the reflector and subreflector cause sinusoidal ripples in the observed spectra of strong radio sources.
The geometry of a symmetrical radio telescope with a Cassegrain subreflector is shown below.  The paraboloidal shape of the primary reflector was determined by the requirement that all incoming rays parallel to the $z$ axis travel the same distance to reach the prime focus at $f_1$.  Likewise, the secondary reflector shape is determined by the requirement that these rays travel the same distance to reach the secondary focus at $f_2$.  For a subreflector located below the prime focus, the required shape is a hyperboloid whose major axis coincides with the major axis of the paraboloid.  The equation
$${z^2 \over a^2} - {r^2 \over b^2} = 1$$ with $a > b$ defines such a hyperboloid.  From any point on the hyperboloid, the difference between the distance to $f_2$ and the distance to $f_1$ is $2a$.  The distance between the foci is $2(a^2 + b^2)^{1/2}$.  The two free parameters $a$ and $b$ can be adjusted to set both (1) the diameter of the subreflector as needed to intercept rays from the edge of the primary and (2) the location of the secondary focus on the $z$ axis.  The magnification provided by the subreflector is $$M = {\tan (\theta_1 /2) \over \tan (\theta_2 / 2)}~,$$ where $\theta_1$ is the half angle subtended by the primary viewed from $f_1$ and $\theta _2$ is the half angle subtended by the secondary viewed from $f_2$.  A small subreflector is light, easy to tilt, and reduces standing waves, but it subtends a small angle $2\theta_2$ at $f_2$ so a feed horn several wavelengths in diameter is required to illuminate it properly.

Cross section of a radio telescope rotationally symmetric around the $z$ axis and having a Cassegrain subreflector.  Parallel rays from a distant radio source are reflected by a circular paraboloid whose prime focus is at the point marked $f_1$.  The convex Cassegrain subreflector is a circular hyperboloid located below the prime focus.  It reflects these rays to the feed located the secondary focus $f_2$ just above the vertex of the paraboloid. The angle $2\theta_1$ subtended by the main reflector viewed from the prime focus is much larger than the angle $2\theta_2$ subtended by the subreflector viewed from the secondary focus.

The Cassegrain subreflector on a VLA antenna is about 2.3 m across, much larger than the longest wavelength $\lambda \approx 30$ cm at which it is used.  Note the crossed half-wave dipoles extending about $\lambda/4$ below the center of the subreflector.  They are the $\lambda \approx 90$ cm primary feed, and the subreflector is just used as a reflecting "ground plane" at this wavelength.  Since Cassegrain subreflectors are located below the prime focus, the subreflector must be raised to place the dipoles near the prime focus.  The VLA subreflector cannot move up enough, so the $\lambda \approx 90$ cm feeds are never quite in focus.  Gregrorian subreflectors, which are located above the prime focus, are more suitable for use with prime-focus feeds.  The large, crude wire antenna is a pair of crossed dipoles used as a prime-focus feed at $\lambda \approx 4$ m. Photo by J. Condon.

This photo shows the ring of waveguide horn feeds at the secondary focus near the vertex of a VLA antenna.  The active feed is selected by repointing the Cassegrain subreflector.  Since the subreflector subtends a small solid angle at the vertex, the feed horns must have narrow beams and hence be many wavelengths across. The largest horn on the right is for L band, 1 to 2 GHz (15 cm $< \lambda <$ 30 cm).  Larger feeds are not practical, so only prime-focus feeds are used at lower frequencies.  Photo by J. Condon.

The Parkes 210-foot (since renamed to 64 m) telescope in Australia was built about the same time as the 140-foot telescope, but its alt-az mount and centrally concentrated reflector backup structure pointed the way to the design of modern radio telescopes.

The Parkes telescope was built about the same time as the Green Bank 140 foot telescope, but it has an excellent alt-az design and is still in active use, with multibeam receivers making HI and pulsar surveys of the southern sky. Image credit

When the 140-foot telescope in Green Bank suffered construction delays, a very simple and inexpensive 300-foot telescope was built nearby.  It was transit telescope that moved in elevation along the north-south line but not in azimuth.  It could observe sources over a wide range of declinations, but only when they were near the meridian.  The prime-focus feeds could be moved slightly in the east-west direction to track a source for a few minutes while they remained within the focal ellipsoid.

The surface of the 300-foot telescope was an open mesh with square holes about 6 mm on a side to reduce both weight and wind loading.  So long as the openings are much smaller than a wavelength, a mesh reflector appears nearly solid to radio waves and only a small amount of ground radiation leaks through the reflector to be picked up by the feed.

The 300-foot transit telescope in Green Bank, WV was built as a stopgap during the delayed construction of the 140-foot telescope.  Originally expected to have a scientific useful lifetime of only five years, it actually lasted 26 years. Image credit

At 9:43 p.m. EST on Tuesday the 15th of November 1988, the 300-foot telescope in Green Bank collapsed. The collapse was due to the sudden failure of a key structural element—a large gusset plate in the box girder assembly that formed the main support for the antenna. This is a photograph of the 300-foot telescope taken on November 16, 1988 after the collapse. The loss of the 300-foot telescope resulted in the Green Bank Telescope Project. Image credit

The real reason for the collapse of the 300-foot telescope!

The 1000 foot (305 m) fixed spherical dish near Arecibo, PR.  Image credit

The Arecibo radio telescope was originally designed as a radar facility to study the ionosphere via Thomson scattering of 430 MHz ($\lambda = 70$ cm) radio waves by free electrons.  Thermal motions of truly free electrons would greatly Doppler broaden the radar echo and the received signal-to-noise ratio is inversely proportional to bandwidth, so a very large antenna was built for sensitivity.  However, ionospheric electrons are coupled to the much heavier ions on scales larger than the ionospheric Debye length, which is only a few mm.  This is much smaller than the 70 cm wavelength, so the actual bandwidth is determined by thermal motions of the much heavier ions and is lower by two orders of magnitude.  Thus a far smaller dish would have sufficed!  Astronomers have benefited from this oversight and use Arecibo's huge collecting area at frequencies up to about 10 GHz for solar-system radar (planets, moons, asteroids), pulsar studies, HI 21 cm line observations of galaxies, and other observations that need high sensitivity.

The Arecibo feed-support platform can steer the beam anywhere up to 20 degrees from the zenith even though the spherical reflector is fixed. The curved azimuth arm rotates about the vertical under a circular ring at the base of the fixed triangular structure. The carriage house under the left side of the azimuth arm carries a waveguide line feed that corrects for spherical aberration. The dome under the carriage house on the right side contains the Gregorian correcting mirrors and waveguide point feeds.  The carriage houses can move along tracks at the bottom of the azimuth arm to change the zenith angle of the beam. Photo by J. Condon

The spherical reflector can be very large because it is does not move.  A sphere is symmetric about any axis passing through its center, so the Arecibo beam can be steered by moving the feed instead of the reflector.  The curved feed-support arm visible in the photo above is 300 feet long and rotates in azimuth below the fixed triangular structure.  The feeds are mounted under two carriage houses that move along tracks on the bottom of the feed arm. This permits tracking at zenith angles up to 20 degrees.  The feed illumination spills over the edge of the fixed reflector at high zenith angles, so a large ground screen surrounds the spherical reflector to reflect the spillover onto the cold sky instead of the warm and noisy ground.

The fixed spherical reflector is suspended over a huge limestone sinkhole near Arecibo, PR.  Tiny holes in the reflector transmit enough sunlight that erosion-controlling plants can grow underneath.  The reflector surface accuracy is 2 mm rms, permitting observations at wavelengths as short as 3 cm. Photo by J. Condon.

A spherical reflector focuses a distant point source onto a line segment, so a line feed is needed to illuminate the entire aperture efficiently from the prime focus.  Slotted-waveguide line feeds are inherently narrow band, and ohmic losses increase the system temperature significantly at short wavelengths.  The large "golf ball" under the feed arm at Arecibo house an enormous Gregorian subreflector and a tertiary reflector that allow low-noise wide-band point feeds to illuminate an ellipse about 200 m by 225 m.

This 96-foot-long slotted waveguide can illuminate the entire 1000 foot reflector at 430 MHz.  The ground screen surrounding the reflector reduces noise pickup from ground radiation.  Photo by J. Condon.

Gravitational deformations degrade the short-wavelength performance of tilting reflectors.   The deformations can be controlled by clever design of the backup structure so that the deformed surface remains nearly paraboloidal at all elevations.  Such homologous deformations cause the focal point to shift slightly in elevation, but this can be corrected by moving the feed slightly to track the focal shift.  The first large homology telescope deliberately designed to deform in this way is the 100 m telescope of the Max Planck Institut für Radioastronomie (MPIfR) near Effelsberg, Germany.  Despite its huge size, the surface is accurate enough to work at wavelengths as short as $\lambda = 7$ mm.

The 100 m telescope near Effelsberg, Germany.  The first homologous telescope, it works to $\lambda \sim 7$ mm.  Note the large Gregorian subreflector above the prime focus. Image credit

The 100 m telescope has a concave Gregorian subreflector above the prime focus.  The geometry of a symmetric Gregorian system is shown below.
As with the Cassegrain subreflector, the Gregorian reflector shape is determined by the requirement that all parallel axial rays travel the same distance to reach the secondary focus at $f_2$.  For a subreflector located above the prime focus, the required shape is an ellipsoid whose major axis coincides with the major axis of the paraboloid.  The equation
$${z^2 \over a^2} + {r^2 \over b^2} = 1$$ with $a > b$ defines such an ellipsoid.  From any point on the ellipsoid, the sum of the distance to $f_2$ and the distance to $f_1$ is $2a$.  The distance between the foci is $2(a^2 - b^2)^{1/2}$.

Cross section of a radio telescope rotationally symmetric around the $z$ axis and having a Gregorian subreflector.  Parallel rays from a distant radio source are reflected by a circular paraboloid whose prime focus is at the point marked $f_1$.  The Gregorian subreflector is a circular ellipsoid located above the prime focus.  It reflects these rays to the feed located the secondary focus $f_2$ just above the vertex of the paraboloid.

The 100 m Robert C. Byrd Green Bank Telescope (GBT) is the successor to the 300 foot telescope, and it incorporates a number of new design features to optimize its performance.

The actual reflector is a 110 m $\times$ 100 m off-axis section of an imaginary symmetric paraboloid 208 m in diameter.  Projected onto a plane normal to the beam, it is a 100 m diameter circle. Because the projected edge of the actual reflector is 4 m away from the axis of the 208 m paraboloid, the focal point does not block the aperture.  The GBT enjoys the same clear-aperture benefits of waveguide horns—a very clean beam and low spillover noise—but is much larger than any practical horn antenna.  The clean beam is especially valuable for suppressing radio-frequency interference (RFI) and stray radiation from very extended sources, such as HI emission from the Galaxy.

Plan view showing the GBT reflector as an off-axis section of a larger symmetric parent paraboloid.

The vertical cross section of the GBT plotted below shows how the offset Gregorian subreflector does not block any radiation falling onto the primary reflector.  Since the Gregorian secondary is above the prime focus at $f_1$, prime-focus operation is possible by raising a swinging boom carrying the prime-focus feeds into position, although this temporarily blocks the Gregorian secondary.

Vertical cross section showing the symmetry plane of the GBT.  The actual dish shown by the continuous curve is an asymmetric section of the symmetric parent paraboloid whose diameter is 208 m. The inner edge of the GBT is 4 m to the right of the $z$ axis of symmetry so the foci and feed-support structure to the left of the $z$ axis never block the incoming radiation.  The primary focal length is $f_1 = 60$ m, and the distance from $f_1$ to the secondary focus $f_2$ is 11 m.  The secondary focus is offset by 1.068 m from the symmetry axis to minimize instrumental polarization. The diameter of the Gregorian subreflector is 8 m.  The secondary focus is far above the vertex of the parent paraboloid, but the off-axis feed support arm of the GBT is strong enough to support a large feed/receiver cabin at this height.

The huge feed-support arm is over 60 m long, the focal length of the 208 m paraboloid.  The feed-support arm has a much larger cross section than the feed-support structures of symmetrical telescopes, which must be kept as thin as possible to minimize blockage.  This GBT arm is very strong and can support heavy subreflectors, feeds, and equipment rooms.  At the top of the arm and above the prime focus is the concave Gregorian subreflector.  This subreflector illuminates feeds emerging through the roof of a large receiver cabin attached to the feed arm a short distance below.  Since these feeds are relatively close to the subreflector, even a moderately small subreflector subtends a large angle as viewed from the feeds, which can then be moderately small themselves.  Most of the receivers and feeds needed to cover the frequency range $1 < \nu{\rm (GHz)} < 100$ can fit into the receiver cabin simultaneously and are available for use on short notice.

Aerial view of the 100 m Robert C. Byrd Green Bank Telescope (GBT). Image credit

### A Photo Tour of the GBT

This side view shows the major components of the GBT: the azimuth ring on which the telescope rotates about a vertical axis, the pyramidal alidade that supports the tipping structure, the elevation bull gear and axle, the reflector backup structure, the offset feed arm with the receiver cabin and feeds, the prime focus boom, and the Gregorian subreflector near the top. Photos by J. Condon.

Each corner of the alidade is supported by a two layers of whiffletrees (pivoted horizontal arms) that divide the corner weight evenly among the four wheels.  The GBT is the largest moving structure on land.  The total moving weight is 16 million pounds, so each wheel must support about one million pounds.

This closeup shows one wheel and a short section of the azimuth track.  The original track was overstressed and was replaced by a stronger track during the summer of 2007.

The pintle bearing under the center of the alidade supports the GBT against horizontal loads.  This concrete supporting the azimuth track and pintle bearing extend to bedrock about 16 feet below ground.

This stairway and an elevator extend up one side of the alidade from the bottom, past the elevation drive, to the level of the elevation axle and the horizontal part of the feed arm.

This walkway goes to the bottom of the elevation bull gear, where it is driven by two pairs of motors.

These motors drive the telescope in elevation via the bull gear.  The wide structure just overhead carries the concrete counterweights needed to balance the tipping structure.

The bearing at one end of the elevation axle.

This side view shows additional counterweight plates attached to the side of the original counterweight structure.

This walkway on the horizontal part of the feed arm extends from the elevation axle to the elevator at the base of the vertical feed arm.  Two workmen are just visible on the walkway.  The complex backup structure for the reflector consists of many small beams designed to deform homologously; that is, it keeps a paraboloidal shape under gravitational loading as the telescope is tipped in elevation.  This requires that the backup structure be equally soft and not contain any hard points supported by the strongest structural members.

The main reflector is supported by a backup structure that deforms homologously to ensure good efficiency at wavelengths as short as $\lambda = 2$ cm.  The reflecting surface consists of approximately two thousand panels, each about two meters on a side.  The corners of individual panels are mounted on computer-controlled actuators that can move the panels up or down as needed to make active corrections to the overall shape of the surface.  Photogrammetry was used to measure the surface at the "rigging elevation," and the panels were initially adjusted to correct the measured surface at that elevation.  The gravitational deformations at other elevation angles predicted by the finite-element computer model of the GBT are continuously removed by the actuators as the telescope moves.  As a result, the GBT has a high surface efficiency at wavelengths as short as $\lambda = 6$ mm.  Efforts are underway to make the GBT a $\lambda = 3$ mm telescope.

The GBT has an "active" surface of panels whose corner heights are continuously adjustable by motor-driven screws at their corners. Image credit

The concave Gregorian subreflector just above the prime focus images sources onto conical horn feeds extending through the top of the receiver cabin. The prime-focus feed arm is shown stowed out of the way of the subreflector.  None of these offset structures block radiation reflected from the main aperture. Image credit

The Gregorian feed horns are mounted on a rotating turret in a hole at the top of the receiver cabin so that the desired feed can be placed at the secondary focus of the Gregorian subreflector.  The largest is the L-band (approximately 1–2 GHz) feed horn.

Inside the receiver cabin, the large L-band feed and receiver extend almost to the floor.

This photograph shows the prime-focus boom and feed extended in front of the Gregorian subreflector.

The GBT is about 480 feet tall.  Antennas always seem taller when you look down from the top.  The small white rectangle in the upper right of this photo is the top of a large tour bus.

The pioneering millimeter-wave telescope was the 36-foot telescope on Kitt Peak, since upgraded and enlarged slightly to become the 12 m telescope.  Millimeter-wave telescopes must be located on high dry sites to minimize atmospheric emission and absorption.

The 12 m telescope at Kitt Peak, AZ pioneered millimeter-wave astronomy and discovered many new interstellar molecules. Image credit

SCUBA (the Submillimetere Common-User Bolometer Array) is the bolometer array "camera" for $\lambda = 850 \mu$m and $\lambda = 450 \mu$m (Holland et al. 1999, MNRAS,  303, 659) used on the 15 m JCMT (James Clerk Maxwell Telescope) to make sensitive continuum images and detect dust emission from ultraluminous starburst galaxies at cosmological distances.

The 15 m James Clerk Maxwell Telescope (JCMT) on Mauna Kea, HI. Image credit

The 30 m IRAM (Institut de RAdioastronomie Millimétrique) telescope is the largest telescope operating at 3, 2, 1, and 0.8 mm.  Its rms surface error is only $55~\mu{\rm m}$, and its pointing accuracy is about 1 arcsec.

The 30 m IRAM telescope on Pico Veleta in Spain. Image credit