What is the highest granularity focal-plane array on a dish radio telescope? Or is this the ONLY ONE?

What is the highest granularity focal-plane array on a dish radio telescope? Or is this the ONLY ONE?

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There is a short Wikipedia article Focal Plane Arrays that enumerates some projects, but my question is more along the lines of what is (at least) nearly complete or in "first light" phase, even if not commissioned yet.

I'd like to differentiate between focal plane arrays (an array of multiple feeds and amplifiers) used in single dish telescopes, and those integrated into multiple dish arrays, because I'm particularly curious about single dishes being used for spatial information, or even true imaging. Ideally, the answer will give some information for each case.

In the case of single dish instruments, are the elements - roughly speaking - used as pixels? Despite the longer wavelength, it's still optics and it is a telescope. If there are N individual, uncoupled feeds, does one build up an image roughly N times faster? Is the relative phase between the feeds ever used (for single dish instruments)?

For those like me who aren't already familiar with focal plane arrays, here is a random picture from one of the links I found in a quick internet search. It's from the Parkes 21cm Multibeam Receiver, has (had?) 13 receivers and sat at the focus of the 64m dish. The photo is dated 1997 - I have a hunch there's been some development in this technique in the intervening 20 years.

Is this actually the only one?

Edit: The Parkes array is still in use as shown below:

Above: Superposition of the half-power beam widths of the 13-element array of the Parkes 21-cm Mutlibeam Receiver, as used in a study of a Fast Radio Bursters.

It's likely the image is a screen shot from from The host galaxy of a fast radio burst Nature volume 530, pages 453-456 (25 February 2016), Keane et al. I can't find my archived copy now, but instead see's New fast radio burst discovery finds 'missing matter' in the universe

where the caption there reads:

This image shows the field of view of the Parkes radio telescope on the left. On the right are successive zoom-ins in on the area where the signal came from (cyan circular region). The image at the bottom right shows the Subaru image of the FRB galaxy, with the superimposed elliptical regions showing the location of the fading 6-day afterglow seen with ATCA. Image Credit: D. Kaplan (UWM), E. F. Keane (SKAO).

I am not a professional astronomer, so take this answer with a grain of salt, but just from visiting a few facilities, I know some.

For single dish applications, the 100m telescope in Effelsberg, Germany, uses a 7-beam receiver -- fewer than the Parkes array you mention, and I dont't know of any single dish setup with a larger number of beams.

Regarding arrays, the Westerbork Synthesis Array in the Netherlands uses the APERTIF arrays in most of its individual 25m dishes. With 121 elements per array, this seems to be on the higher-end side of granularity.


From for 31-01-2017 First image with Apertif: a new life for the Westerbork radio telescope

The first images made with the upgraded telescope that demonstrate this new 'wide-angle' capability is shown here. The first image shows the dwarf galaxy Leo T. The image is colour-coded and shows the gas (in blue) in this galaxy together with many distant radio galaxies in the background shown in orange. For comparison, the field of view of the previous Westerbork system and the size of the full moon are also indicated.

To make this new capability possible, ASTRON developed and built the hardware in-house. 121 small receivers are used in each telescope whose signals are combined electronically to produce the large field of view.

The upgraded telescope will also be used to search for and study new variable sources in the radio sky. With the new Apertif receivers, observations of large parts of the sky can be done much faster, and projects that used to be impossible as they would take tens of years can now be done in a much shorter time. Westerbork is therefore poised to make many new discoveries in the radio sky.

Characterization of dense focal plane array feeds for parabolic reflectors in achieving closely overlapping or widely separated multiple beams

[1] In the advent of modern mobile satellite communications requiring rapid and adaptive multiple beams, this work studies the ability of reflector antennas fed by dense focal plane arrays (FPA) in achieving arbitrarily shaped and sized footprints to meet the demands. In this paper, the efficiencies of single off-axis as well as multiple beams of FPA-fed paraboloids are investigated. The offset FPA considered here comprises hard rectangular waveguides. The focal plane field, which the FPA samples, is synthesized by integration of the physical optics induced electric currents over the reflector surface caused by the off-axis incident plane wave arriving at that incidence angle of interest. Full mutual coupling analysis has been performed in the FPA sampling, thereby taking into account mutual coupling losses in the arrays. The fields over the tilted elliptical aperture of off-axis beams needed for calculation of the aperture efficiency are obtained by projecting the usual focal plane fields to this tilted aperture using geometrical optics. Results show that the total efficiency of the offset FPA-fed reflector decreases with increasing beam angle and increases with larger number of FPA elements. It is also found that the maximum directive gain of the reflector radiation patterns falls noticeably with beam angle when the FPA population is low, but the directivity can be maintained well when an adequate number of FPA elements are used. Multiple beams that are either closely overlapping or widely separated are also successfully investigated.


Resolving power is the ability of an imaging device to separate (i.e., to see as distinct) points of an object that are located at a small angular distance or it is the power of an optical instrument to separate far away objects, that are close together, into individual images. The term resolution or minimum resolvable distance is the minimum distance between distinguishable objects in an image, although the term is loosely used by many users of microscopes and telescopes to describe resolving power. As explained below, diffraction-limited resolution is defined by the Rayleigh criterion as the angular separation of two point sources when the maximum of each source lies in the first minimum of the diffraction pattern (Airy disk) of the other. In scientific analysis, in general, the term "resolution" is used to describe the precision with which any instrument measures and records (in an image or spectrum) any variable in the specimen or sample under study.

The imaging system's resolution can be limited either by aberration or by diffraction causing blurring of the image. These two phenomena have different origins and are unrelated. Aberrations can be explained by geometrical optics and can in principle be solved by increasing the optical quality of the system. On the other hand, diffraction comes from the wave nature of light and is determined by the finite aperture of the optical elements. The lens' circular aperture is analogous to a two-dimensional version of the single-slit experiment. Light passing through the lens interferes with itself creating a ring-shape diffraction pattern, known as the Airy pattern, if the wavefront of the transmitted light is taken to be spherical or plane over the exit aperture.

The interplay between diffraction and aberration can be characterised by the point spread function (PSF). The narrower the aperture of a lens the more likely the PSF is dominated by diffraction. In that case, the angular resolution of an optical system can be estimated (from the diameter of the aperture and the wavelength of the light) by the Rayleigh criterion defined by Lord Rayleigh: two point sources are regarded as just resolved when the principal diffraction maximum of the Airy disk of one image coincides with the first minimum of the Airy disk of the other, [1] [2] as shown in the accompanying photos. If the distance is greater, the two points are well resolved and if it is smaller, they are regarded as not resolved. Rayleigh defended this criterion on sources of equal strength. [2]

Considering diffraction through a circular aperture, this translates into:

where θ is the angular resolution (radians), λ is the wavelength of light, and D is the diameter of the lens' aperture. The factor 1.22 is derived from a calculation of the position of the first dark circular ring surrounding the central Airy disc of the diffraction pattern. This number is more precisely 1.21966989. ( OEIS: A245461 ), the first zero of the order-one Bessel function of the first kind J 1 ( x ) (x)> divided by π.

The formal Rayleigh criterion is close to the empirical resolution limit found earlier by the English astronomer W. R. Dawes, who tested human observers on close binary stars of equal brightness. The result, θ = 4.56/D, with D in inches and θ in arcseconds, is slightly narrower than calculated with the Rayleigh criterion. A calculation using Airy discs as point spread function shows that at Dawes' limit there is a 5% dip between the two maxima, whereas at Rayleigh's criterion there is a 26.3% dip. [3] Modern image processing techniques including deconvolution of the point spread function allow resolution of binaries with even less angular separation.

Using a small-angle approximation, the angular resolution may be converted into a spatial resolution, Δ, by multiplication of the angle (in radians) with the distance to the object. For a microscope, that distance is close to the focal length f of the objective. For this case, the Rayleigh criterion reads:

This is the radius, in the imaging plane, of the smallest spot to which a collimated beam of light can be focused, which also corresponds to the size of smallest object that the lens can resolve. [4] The size is proportional to wavelength, λ, and thus, for example, blue light can be focused to a smaller spot than red light. If the lens is focusing a beam of light with a finite extent (e.g., a laser beam), the value of D corresponds to the diameter of the light beam, not the lens. [Note 1] Since the spatial resolution is inversely proportional to D, this leads to the slightly surprising result that a wide beam of light may be focused to a smaller spot than a narrow one. This result is related to the Fourier properties of a lens.

A similar result holds for a small sensor imaging a subject at infinity: The angular resolution can be converted to a spatial resolution on the sensor by using f as the distance to the image sensor this relates the spatial resolution of the image to the f-number, f /#:

Since this is the radius of the Airy disk, the resolution is better estimated by the diameter, 2.44 λ ⋅ ( f / # )

Single telescope Edit

Point-like sources separated by an angle smaller than the angular resolution cannot be resolved. A single optical telescope may have an angular resolution less than one arcsecond, but astronomical seeing and other atmospheric effects make attaining this very hard.

The angular resolution R of a telescope can usually be approximated by

where λ is the wavelength of the observed radiation, and D is the diameter of the telescope's objective. The resulting R is in radians. For example, in the case of yellow light with a wavelength of 580 nm, for a resolution of 0.1 arc second, we need D=1.2 m. Sources larger than the angular resolution are called extended sources or diffuse sources, and smaller sources are called point sources.

This formula, for light with a wavelength of about 562 nm, is also called the Dawes' limit.

Telescope array Edit

The highest angular resolutions can be achieved by arrays of telescopes called astronomical interferometers: These instruments can achieve angular resolutions of 0.001 arcsecond at optical wavelengths, and much higher resolutions at x-ray wavelengths. In order to perform aperture synthesis imaging, a large number of telescopes are required laid out in a 2-dimensional arrangement with a dimensional precision better than a fraction (0.25x) of the required image resolution.

The angular resolution R of an interferometer array can usually be approximated by

where λ is the wavelength of the observed radiation, and B is the length of the maximum physical separation of the telescopes in the array, called the baseline. The resulting R is in radians. Sources larger than the angular resolution are called extended sources or diffuse sources, and smaller sources are called point sources.

For example, in order to form an image in yellow light with a wavelength of 580 nm, for a resolution of 1 milli-arcsecond, we need telescopes laid out in an array that is 120 m × 120 m with a dimensional precision better than 145 nm.

Microscope Edit

The resolution R (here measured as a distance, not to be confused with the angular resolution of a previous subsection) depends on the angular aperture α : [5]

It follows that the NAs of both the objective and the condenser should be as high as possible for maximum resolution. In the case that both NAs are the same, the equation may be reduced to:

The practical limit for θ is about 70°. In a dry objective or condenser, this gives a maximum NA of 0.95. In a high-resolution oil immersion lens, the maximum NA is typically 1.45, when using immersion oil with a refractive index of 1.52. Due to these limitations, the resolution limit of a light microscope using visible light is about 200 nm. Given that the shortest wavelength of visible light is violet ( λ ≈ 400 nm),

Oil immersion objectives can have practical difficulties due to their shallow depth of field and extremely short working distance, which calls for the use of very thin (0.17 mm) cover slips, or, in an inverted microscope, thin glass-bottomed Petri dishes.

However, resolution below this theoretical limit can be achieved using super-resolution microscopy. These include optical near-fields (Near-field scanning optical microscope) or a diffraction technique called 4Pi STED microscopy. Objects as small as 30 nm have been resolved with both techniques. [6] [7] In addition to this Photoactivated localization microscopy can resolve structures of that size, but is also able to give information in z-direction (3D).

Aperture array antennas

Aperture Arrays have been progressively developed to become a strong candidate technology for radio telescopes capable of a large collecting area. The cost of an element is critical for SKA implementation since the total number of elements is on the order of millions. The antenna element needs to operate between two and three octaves in frequency bandwidth. To allow the Stokes Parameters of the received field to be measured two orthogonal polarization components are needed over the entire bandwidth. Additionally a wide scan angle must be provided to achieve a wide FoV. Low noise is another parameter critical for providing the high sensitivity required in radio astronomy applications, as a result, the low-loss antenna elements and low noise receivers have been desired. Multiple broadband antenna element designs for aperture array application are examined in the following sections. In particular, Crossed Octagonal Ring Antenna (C-ORA) is covered more intensively as it represents a novel approach compared to other antennas and less known in the community. However, other antennas mentioned below have being continuously improved and actively used for radio astronomy, it is beneficial to report their progress and performance as a benchmark. An artistic view of a MFAA station based on C-ORA and a section of C-ORA array is shown in Fig. 1.

Mid-frequency aperture array based on crossed octagonal ring antenna

Tapered slot antenna

Tapered Slot Antenna (TSA) was proposed by Lewis in 1974 [28].TSA Antennas are widely utilized in mobile telecommunications and radars. One type of TSA whose slot is opened exponentially and it was called Vivaldi antenna [29]. Vivaldi Notch antennas can provide bandwidths up to several octaves in phased arrays that scan over wide angles. A parameter study of Vivaldi Notch-Antenna for phased array is investigated in [30]. Within ASTRON multiple demonstrators and phased array instruments have been built. The THousand Element Array (THEA) is the first out-door phased-array system used to detect (strong) radio sources using adaptive digital multi-beam beamforming techniques employing Vivaldi antenna [20]. The total number of Vivaldi antenna elements in THEA is 1024. EMBRACE is a dual station single polarization aperture array telescope, which covered an area of 162 m 2 in Westerbork, The Netherlands and 70.8 m 2 in Nançay, France. EMBRACE in Westerbork has 10368 active elements and 4608 active Vivaldi antenna elements are used in Nançay. The performance of the Vivaldi antenna designed for EMBRACE is described in [22]. Two EMBRACE stations have been tested in different phases of their construction [31,32,33].

EMBRACE at Nançay has been fully operational since 2011. Characterization of the 70.8 m 2 dense array at Nançay is reported in [34, 35]. APERTIF, a focal plane array instrument, currently being commissioned, uses 12 dishes of the Westerbork Synthesis Radio Telescope [36]. Each focal plane array holds 121 Vivaldi elements. Most recently the Low Noise Tile prototypes have been built to further decrease the receiver noise figure of the antenna and LNA combination to 35 K levels [37] and below at room temperature. Environmental prototypes are installed at the SKA Karoo site to gain experience in material degradation, tile designs and local rodents. The new mechanical connections have been made for Vivaldi antennas for SKA MFAA [38] to ensure resistance to damage from local rodents. A prototype tile of Vivaldi antenna array is shown in Fig. 2.

The Vivaldi antenna array tile for SKA MFAA, developed in ASTRON, The Netherlands

Crossed octagonal ring antenna

The initial Octagonal Ring Antenna (ORA) is a novel dual-polarized array antenna with broad bandwidth. The detailed ORA design has been described in [39]. Very different to Vivaldi antenna design, the ORA is designed to be a planar, easily fabricated, and potentially low cost structure. The ORA operates at wide scan angles with a smooth polarimetric performance over the entire FoV. The fundamental electromagnetics has been confirmed through previous studies with field measurements [39]. In order to feed elements of dual polarization at the same position, hence a Low Noise Amplifier (LNA) board for two polarizations can be shared, Crossed Octagonal Ring Antenna (C-ORA) is proposed based on the same principle as ORA. The layered antenna array structure and the artistic view of the corresponding MFAA station is shown in Fig. 1.

The array based on C-ORA elements is a three-layered structure. The embedded active radiators or receptors are mutual coupled rings with a meta-material superstrate layer above the element rings. The embedded receptors and the active layer they formed are above the groundplane with a defined distance. The unit cell design of C-ORA element is illustrated in Fig. 3. The dual polarized elements are fed at the crossing point and share the same phase center. To achieve the required bandwidth this antenna includes capacitive coupling loads between the elements. The C-ORA structure itself presents a high radiation efficiency leading to a low noise temperature due to its unique configuration. In addition, a customized balanced LNA using a Monolithic Microwave Integrated Circuit (MMIC) has been produced and integrated locally with the antenna element to minimize feeding loss [40]. This work is ongoing. With the current LNA design, the view of the LNA box and its respective location to the antenna elements is shown in Fig. 1b.

The C-ORA array element design models

To reduce the number of active elements needed in the aperture, the C-ORA design is also being explored with non-Cartesian distribution of the elements. This new geometry is not viable from the conventional Vivaldi-type antennas. A triangular grid based C-ORA array is designed and the prototype has been produced and compared to a more conventional square grid C-ORA. Unit cells of the C-ORA designs for the square and triangular grid arrays and the respective section of arrays showing the arrangements of elements is given in Fig. 3. The value of parameters for an optimized C-ORA design is summarized in Table 2. The capacitor value between the square grid element is 0.8 pF, it can be realized by 17 inter-digitated fingers, with the length of each finger of 5 mm and the gap between fingers of 0.2 mm. For the triangular grid array, the capacitor value between the element is 1 pF, it can be realized with 17 fingers, the length of each finger of 6 mm and the gap between fingers of 0.2mm.

The reflection coefficients for the C-ORA elements in an infinite array environment are shown in Fig. 4. The results are from simulations based on the optimized C-ORA designs with the parameter values given in Table 2. The performances for the C-ORA arrays with elements configured in both a square and triangular lattice are shown. They illustrate the main characteristics of the C-ORA design: providing a large frequency bandwidth (400MHz to 1.45GHz) operating over wide scan angles (± 45 ∘ from the zenith). It indicates that the aperture array based on C-ORA receptors of a planar structure has the ability for simultaneous measurements over large fractions of the sky (optical FoV over 200 deg 2 ) at the mid-frequency band of SKA.

The simulated active reflection coefficients in dB of C-ORA elements in infinite arrays, the arrays are scanned to wide angles

The same number of elements were used in both configurations of the finite array prototypes, so that the triangular grid array occupies a larger physical area than the square grid. Accordingly it is expected that the gain and hence sensitivity of the triangular grid array is higher than the square grid using the same number of elements. This is reflected in a narrower beam width for the triangular grid. Initial measurements are given in Fig. 5, which confirms the simulation results. It is stressed these are early measurements and do have significant measurement error due to site effects but nonetheless indicate the triangular grid approach is worthy of further investigation and refinement.

The C-ORA array based on square and triangular grid, measured radiation patterns of the 4x4 subarrays in the diagonal plane (D-plane) for the bore-sight reception

It reveals that approximately 13% total number of elements can be saved to achieve the same sensitivity with a triangular grid based C-ORA array. It is noted that the sidelobes for the triangular grid based array has no significant increase compared with that of the square based array even the element separation is greater. However, a 5-10 dB rise in cross polarization for the triangular grid array is observed compared to the square grid array. The triangular grid allows for larger separation between elements compared to a square grid without effecting the maximum scan performance limited by the occurrence of grating lobes. This makes it possible for the triangular grid to cover the same aperture area as the square grid but with less elements.

Log periodic dipole array

The Log Periodic Dipole Array (LPDA) for MFAA is essentially a progression of coplanar dipoles that increase size logarithmically as defined by a constant ratio. It is derived from the LPDA concept for SKA-LFAA [41]. Different to the Vivaldi and C-ORA mentioned above where the mutual coupling between the adjacent elements are effectively employed to yield the frequency bandwidth, the single LPDA element is designed to operate over the entire MFAA frequency band for sparse array geometry [42] and using a single ended LNA in the current version. This would deliver reduced power consumption with respect to a differential LNA (this may be important considering the antenna numbers for MFAA) and is relatively feasible for the MFAA bandwidth ratio - aprox. 3:1. A detailed trade-off study of matching/bandwidth/linearity between the differential option (typically more suited for wide bandwidths and better common mode rejection) and the single ended option will be done in the coming years. The small profile is sought to reduce the footprint of the antenna, and hence allow a higher frequency sampling if needed.

The current prototype design has 6 dipoles and its shape has been optimized using simulations in order to remain effective at the low end of the frequency band. It is noted that the overall element size is significantly smaller through iteration of design studies. The size of the current element model is 37.5 cm (W) × 37.5 cm (L) × 30 cm (H). The footprint of the LPDA for MFAA can be reduced further to allow the transition between the dense and sparse regimes, particularly at the high frequency. The main parameters for LPDA design is given in Table 3. Initial measurements on a 16 element LPDA array (1 tile) for the MFAA band with a sparse random configuration have been conducted at the Mullard Radio Astronomy Observatory, south of Cambridge, UK. The measured results on scattering parameters have a good agreement with the electromagnetic modeling, allowing further optimizations and characterizations for a greater scale investigation [43]. A larger array with 8 tiles, optical fiber output for the antennas and digital beam forming boards is currently been developed at Cambridge to continue the studies on the sparse array design and calibration. Furthermore, in collaboration with Cambridge Consultants Ltd., a mass production version of this antenna is being developed in order to reduce the unit cost and improve the life time of the design. The design model and the 16 element prototype tile is illustrated in Fig. 6.

The LPDA designed for SKA MFAA at University of Cambridge


Strictly, the three-dimensional shape of the reflector is called a paraboloid. A parabola is the two-dimensional figure. (The distinction is like that between a sphere and a circle.) However, in informal language, the word parabola and its associated adjective parabolic are often used in place of paraboloid and paraboloidal.

The parabolic reflector functions due to the geometric properties of the paraboloidal shape: any incoming ray that is parallel to the axis of the dish will be reflected to a central point, or "focus". (For a geometrical proof, click here.) Because many types of energy can be reflected in this way, parabolic reflectors can be used to collect and concentrate energy entering the reflector at a particular angle. Similarly, energy radiating from the focus to the dish can be transmitted outward in a beam that is parallel to the axis of the dish.

In contrast with spherical reflectors, which suffer from a spherical aberration that becomes stronger as the ratio of the beam diameter to the focal distance becomes larger, parabolic reflectors can be made to accommodate beams of any width. However, if the incoming beam makes a non-zero angle with the axis (or if the emitting point source is not placed in the focus), parabolic reflectors suffer from an aberration called coma. This is primarily of interest in telescopes because most other applications do not require sharp resolution off the axis of the parabola.

The precision to which a parabolic dish must be made in order to focus energy well depends on the wavelength of the energy. If the dish is wrong by a quarter of a wavelength, then the reflected energy will be wrong by a half wavelength, which means that it will interfere destructively with energy that has been reflected properly from another part of the dish. To prevent this, the dish must be made correctly to within about 1 / 20 of a wavelength. The wavelength range of visible light is between about 400 and 700 nanometres (nm), so in order to focus all visible light well, a reflector must be correct to within about 20 nm. For comparison, the diameter of a human hair is usually about 50,000 nm, so the required accuracy for a reflector to focus visible light is about 2500 times less than the diameter of a hair. For example, the flaw in the Hubble Space Telescope mirror (too flat by about 2,200 nm at its perimeter) caused severe spherical aberration until corrected with COSTAR. [2]

Microwaves, such as are used for satellite-TV signals, have wavelengths of the order of ten millimetres, so dishes to focus these waves can be wrong by half a millimetre or so and still perform well.

Focus-balanced reflector Edit

It is sometimes useful if the centre of mass of a reflector dish coincides with its focus. This allows it to be easily turned so it can be aimed at a moving source of light, such as the Sun in the sky, while its focus, where the target is located, is stationary. The dish is rotated around axes that pass through the focus and around which it is balanced. If the dish is symmetrical and made of uniform material of constant thickness, and if F represents the focal length of the paraboloid, this "focus-balanced" condition occurs if the depth of the dish, measured along the axis of the paraboloid from the vertex to the plane of the rim of the dish, is 1.8478 times F. The radius of the rim is 2.7187 F. [a] The angular radius of the rim as seen from the focal point is 72.68 degrees.

Scheffler reflector Edit

The focus-balanced configuration (see above) requires the depth of the reflector dish to be greater than its focal length, so the focus is within the dish. This can lead to the focus being difficult to access. An alternative approach is exemplified by the Scheffler Reflector, named after its inventor, Wolfgang Scheffler. This is a paraboloidal mirror which is rotated about axes that pass through its centre of mass, but this does not coincide with the focus, which is outside the dish. If the reflector were a rigid paraboloid, the focus would move as the dish turns. To avoid this, the reflector is flexible, and is bent as it rotates so as to keep the focus stationary. Ideally, the reflector would be exactly paraboloidal at all times. In practice, this cannot be achieved exactly, so the Scheffler reflector is not suitable for purposes that require high accuracy. It is used in applications such as solar cooking, where sunlight has to be focused well enough to strike a cooking pot, but not to an exact point. [3]

Off-axis reflectors Edit

A circular paraboloid is theoretically unlimited in size. Any practical reflector uses just a segment of it. Often, the segment includes the vertex of the paraboloid, where its curvature is greatest, and where the axis of symmetry intersects the paraboloid. However, if the reflector is used to focus incoming energy onto a receiver, the shadow of the receiver falls onto the vertex of the paraboloid, which is part of the reflector, so part of the reflector is wasted. This can be avoided by making the reflector from a segment of the paraboloid which is offset from the vertex and the axis of symmetry. For example, in the above diagram the reflector could be just the part of the paraboloid between the points P1 and P3. The receiver is still placed at the focus of the paraboloid, but it does not cast a shadow onto the reflector. The whole reflector receives energy, which is then focused onto the receiver. This is frequently done, for example, in satellite-TV receiving dishes, and also in some types of astronomical telescope (e.g., the Green Bank Telescope, the James Webb Space Telescope).

Accurate off-axis reflectors, for use in solar furnaces and other non-critical applications, can be made quite simply by using a rotating furnace, in which the container of molten glass is offset from the axis of rotation. To make less accurate ones, suitable as satellite dishes, the shape is designed by a computer, then multiple dishes are stamped out of sheet metal.

Off-axis-reflectors heading from medium latitudes to a geostationary TV satellite somewhere above the equator stand steeper than a coaxial reflector. The effect is, that the arm to hold the dish can be shorter and snow tends less to accumulate in (the lower part of) the dish.

3.5 Radio Telescopes

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 e ⁢ ( θ , ϕ ) of any antenna averaged over all directions ( θ , ϕ ) is (Equation 3.41 )

so large peak collecting areas imply extremely directive antennas at short wavelengths. Only at long wavelengths ( λ > 1 m) is it feasible to construct sensitive antennas from reasonable numbers of small, nearly isotropic elements such as dipoles. Jansky’s λ ≈ 15 -m “wire” antenna (Figure 1.7 ) is an array of phased dipoles. It produces a wide fan beam near the horizon but has a large collecting area because λ 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 and Wilson [81] to show that the zenith antenna temperature of the Bell Labs horn (Figure 3.19 ) was 3.5 K higher at ν ≈ 4 GHz than expected—the first detection of the cosmic microwave background radiation.

Figure 3.19: The horn antenna at Bell Labs, Holmdel, NJ used by Penzias and Wilson to discover the 3 K cosmic microwave background radiation in 1965. Reprinted with permission of Alcatel-Lucent USA Inc.

The aperture of a waveguide horn is not blocked by any feed-support structure, so it is also easier to calculate the gain of a horn antenna from first principles than to calculate the gain of a partially blocked reflecting antenna. 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 secondary calibration sources whose flux densities relative to that of Cas A are known in advance. The painstaking 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. [6] .

Figure 3.20: The 140-foot (43-m) telescope in Green Bank, WV is the largest telescope with an equatorial mount. Image credit: NRAO/AUI/NSF.

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 consequences:

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.

Radiation from the Sun and artificial sources of radio frequency interference (RFI) far from the main beam will be mixed with the desired signal.

Radio telescopes are so large that paraboloids with high f / D ratios are impractical typically f / D ≈ 0.4 . Thus radio “dishes” are relatively deep, as shown in Figure 3.20 . 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 that can fit into the tiny focal circle.

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 altitude or elevation angle (two names for the angle above the horizon). The 140-foot telescope in Green Bank is unique among large radio telescopes in having an equatorial mount (Figure 3.20 ). The advantage of a equatorial 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. (The hour angle is the angle past the meridian, measured in hours. The meridian is the great circle passing through the north pole, south pole, and zenith.) 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 equatorial mount is mechanical—the sloped hour-angle yoke and polar axle with its huge tail bearing are very difficult to build and support.

Figure 3.21: 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 at the secondary focus f 2 just above the vertex of the paraboloid. The angle 2 ⁢ θ 1 subtended by the main reflector viewed from the prime focus is much larger than the angle 2 ⁢ θ 2 subtended by the subreflector viewed from the secondary focus, so Cassegrain feeds have to be much larger than primary feeds.

Figure 3.20 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. A subreflector system has some advantages over a prime-focus system:

The magnifying subreflector can multiply the effective f / D ratio values of f / D ∼ 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 trade-off between high aperture efficiency and low sidelobes.

Receivers can be 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 be nutated (rocked back and forth) rapidly to switch the beam between two adjacent positions on the sky. Such differential observations in time and space can be used to remove receiver baseline drift in time and large-scale spatial fluctuations of 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.

A subreflector system has some disadvantages:

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 with frequency period Δ ⁢ ν ≈ c / ( 2 ⁢ f ) in the observed spectra of strong continuum radio sources. These ripples can be minimized by alternately defocusing the subreflector radially by ± λ / 8 and averaging the data from both subreflector positions.

A Cassegrain subreflector blocks the prime-focus position, so prime-focus feeds cannot be used when the Cassegrain subreflector is in position.

The geometry of a symmetrical radio telescope with a Cassegrain subreflector is shown in Figure 3.21 . 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

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 2 ⁢ a . 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 the diameter of the subreflector as needed to intercept rays from the edge of the primary and the height of the secondary focus on the z -axis. The magnification provided by the subreflector is

M = tan ⁡ ( θ 1 / 2 ) tan ⁡ ( θ 2 / 2 ) , (3.147)

where θ 1 is the half angle subtended by the primary viewed from f 1 and θ 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 ⁢ θ 2 at f 2 so a feed horn several wavelengths in diameter is required to illuminate it properly.

The Parkes 210-foot (since renamed to 64-m) telescope (Figure 3.22 ) 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.

Elevation-dependent gravitational deformations degrade the short-wavelength performance of tilting reflectors. The deformations can be controlled by designing the backup structure so that the deformed surface remains paraboloidal. The deformations cause the focal point to shift slightly in elevation, but this shift can be accommodated by moving the feed slightly to track the focus. The first large homologous telescope deliberately designed to deform this way is the 100-m telescope (Figure 3.23 ) of the Max Planck Institut für Radioastronomie (MPIfR) near Effelsberg, Germany. Despite its huge size, its passive surface remains accurate enough to work at wavelengths as short as λ = 7 mm over a range of elevations.

Figure 3.23: The 100-m telescope near Effelsberg, Germany. The first deliberately homologous telescope, it works to λ ∼ 7 mm. Note the large Gregorian subreflector above the prime focus. Photo by Matthias Kadler.

The 100-m telescope has a concave Gregorian subreflector above the prime focus. The geometry of a symmetric Gregorian system is shown in Figure 3.24 . 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

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 2 ⁢ a . The distance between the foci is 2 ⁢ ( a 2 - b 2 ) 1 / 2 .

Figure 3.24: 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 the 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 at the secondary focus f 2 just above the vertex of the paraboloid.

The Arecibo radio telescope (Figures 8.2 and 3.25 ) was originally designed as a radar facility to study the ionosphere via Thomson scattering of 430 MHz ( λ = 70 cm) radio waves by free electrons. Thermal motions of truly free electrons would greatly Doppler broaden the bandwidth of the radar echo and lower the received signal-to-noise ratio, 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, H i 21-cm line observations of galaxies, and other observations that need high sensitivity.

Figure 3.25: 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 secondary mirror and tertiary correcting mirror, illuminated by waveguide horn feeds. The carriage houses can move along tracks at the bottom of the azimuth arm to change the zenith angle of the beam.

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 Figure 3.25 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 and permit 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 and keep it away from the warm and noisy ground.

A spherical reflector focuses a distant point source onto a radial line segment, so a radial line feed (see Figure 3.25 ) up to 96 feet long is needed to illuminate the entire aperture efficiently from the prime focus. The line feed is a slotted waveguide tapered to control the group velocity (Equation 3.143 ) and phase up radiation arriving from all over the reflector. However, long slotted-waveguide line feeds are inherently narrowband, and ohmic losses in the long slotted waveguide increase the system temperature significantly at short wavelengths. The “golf ball” under the feed arm at Arecibo (Figure 3.25 ) houses an enormous Gregorian subreflector and a tertiary reflector that allow low-noise wideband point feeds to illuminate an ellipse about 200 m by 225 m in size on the main reflector.

Figure 3.26: 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 (dotted curve) whose diameter is 208 m. The inner edge of the GBT reflector 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 (Figure 3.27 ) at this height.

The 100-m Robert C. Byrd Green Bank Telescope (GBT) (Figure 8.1 ) is the successor to the collapsed 300-foot telescope in Green Bank, and it incorporates a number of new design features to optimize its sensitivity and short-wavelength performance.

The actual reflector is a 110 m × 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 H i emission from the Galaxy.

Figure 3.27: The concave Gregorian subreflector just above the prime focus of the GBT images sources onto conical horn feeds extending through the top of the rectangular 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: NRAO/AUI/NSF.

The vertical cross section of the GBT plotted in Figure 3.26 shows how the offset Gregorian subreflector does not block any radiation falling onto the primary reflector. The Gregorian subreflector is above the prime focus at f 1 , so prime-focus operation is possible by raising a swinging boom carrying the prime-focus feeds into position below the subreflector, although this temporarily blocks the Gregorian subreflector. 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, equipment rooms, and an elevator. 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 (Figure 3.27 ). Because 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 < ν ⁢ ( GHz ) < 100 can fit into the receiver cabin simultaneously and are available for use on short notice.

The main reflector is supported by a backup structure that deforms homologously to ensure good efficiency at wavelengths as short as λ = 2 cm. The active reflecting surface consists of approximately two thousand panels, each about 2 m 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 continuously correct the overall shape of the surface. Photogrammetry was used to measure the surface at the rigging elevation (the elevation at which the surface was originally set). 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 rms surface error is only σ ≈ 0.2 ⁢ mm and the GBT has a high surface efficiency at wavelengths as short as λ ≈ 3 mm.

The 30-m IRAM (Institut de Radioastronomie Millimétrique) telescope (Figure 3.28 ) is the largest telescope operating at 3, 2, 1, and 0.8 mm. Its rms surface error is only 55 ⁢ μ ⁢ m , and its pointing accuracy is about 1 arcsec.

1.2. Types of Astronomical Antennas

This chapter discusses different types of astronomical antennas. The pattern of the pencil-beam antenna has one main lobe or maximum with a single-output terminal pair or a few main lobes each with its own separate output. The output at a single terminal pair corresponds to one main lobe for only one sense of polarization: linear, circular, or elliptical. The most common antenna used for radio astronomy is the parabolic reflector with the feed horn or dipole located at the parabolic focus. One principal advantage of this antenna is the ease with which the receiver may be coupled to it. The input terminals are at the feed horn or dipole. Operation over a wide range of wavelengths is simple changing from one band of wavelengths to another requires only the change of the feed. The multi-element interferometer consists of a number of two-element interferometers operating simultaneously. The outputs of all the antenna elements are combined in pairs and recorded at the same time. The result is a system that can complete the aperture synthesis for a given region of the sky in a time shorter than that required by a simple two-element telescope.

The hydrogen epoch of reionization array dish III: measuring chromaticity of prototype element with reflectometry

Spectral structures due to the instrument response is the current limiting factor for the experiments attempting to detect the redshifted 21 cm signal from the Epoch of Reionization (EoR). Recent advances in the delay spectrum methodology for measuring the redshifted 21 cm EoR power spectrum brought new attention to the impact of an antenna’s frequency response on the viability of making this challenging measurement. The delay spectrum methodology provides a somewhat straightforward relationship between the time-domain response of an instrument that can be directly measured and the power spectrum modes accessible to a 21 cm EoR experiment. In this paper, we derive the explicit relationship between antenna reflection coefficient (S11) measurements made by a Vector Network Analyzer (VNA) and the extent of additional foreground contaminations in delay space. In the light of this mathematical framework, we examine the chromaticity of a prototype antenna element that will constitute the Hydrogen Epoch of Reionization Array (HERA) between 100 and 200 MHz. These reflectometry measurements exhibit additional structures relative to electromagnetic simulations, but we find that even without any further design improvement, such an antenna element will support measuring spatial k modes with line-of-sight components of k > 0.2h Mpc − 1 . We also find that when combined with the powerful inverse covariance weighting method used in optimal quadratic estimation of redshifted 21 cm power spectra the HERA prototype elements can successfully measure the power spectrum at spatial modes as low as k > 0.1h Mpc − 1 . This work represents a major step toward understanding the HERA antenna element and highlights a straightforward method for characterizing instrument response for future experiments designed to detect the 21 cm EoR power spectrum.

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Design of a 7m Davies-Cotton Cherenkov telescope mount for the high energy section of the Cherenkov Telescope Array

The Cherenkov Telescope Array is the next generation ground-based observatory for the study of very-high-energy gamma-rays. It will provide an order of magnitude more sensitivity and greater angular resolution than present systems as well as an increased energy range (20 GeV to 300 TeV). For the high energy portion of this range, a relatively large area has to be covered by the array. For this, the construction of ∼7 m diameter Cherenkov telescopes is an option under study. We have proposed an innovative design of a Davies-Cotton mount for such a telescope, within Cherenkov Telescope Array specifications, and evaluated its mechanical and optical performance. The mount is a reticulated-type structure with steel tubes and tensioned wires, designed in three main parts to be assembled on site. In this work we show the structural characteristics of the mount and the optical aberrations at the focal plane for three options of mirror facet size caused by mount deformations due to wind and gravity.

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Computing Antenna Patterns

The next step is to understand how to compute the power pattern of a given telescope. Consider a parabolic reflecting telescope being fed by a feed at the focus. The radiation from the feed reflects off the telescope and is beamed off into space (Figure 3.12). If one knew the radiation pattern of the feed, then from geometric optics (i.e. simple ray tracing, see Chapter 19) one could then calculate the electric field on the plane across the mouth of the telescope (the `aperture plane'). How does the field very far away from the telescope lookslike? If the telescope surface were infinitely large, then the electric field in the aperture plane is simply a plane wave, and since a plane wave remains a plane wave on propagation through free space, the far field is simply a plane wave traveling along the axis of the reflector. The power pattern is an infinitely narrow spike, zero everywhere except along the axis. Real telescopes are however finite in size, and this results in diffraction. The rigorous solution to the diffraction problem is to find the appropriate Green's function for the geometry, this is often impossible in practise and various approximations are necessary. The most commonly used one is Kirchoff's scalar diffraction theory. However, for our purposes, it is more than sufficient to simply use Huygen's principle.

Huygen's principle states that each point in a wave front can be regarded as an imaginary source. The wave at any other point can then be computed by adding together the contributions from each of these point sources. For example consider a one dimensional aperture, of length with the electric field distribution (`aperture illumination') . The field at a point P(R, ) (Figure 3.13) due to a point source at a distance x from the center of the aperture is (if is much greater than ) is:

Where is simply the difference in path length between the path from the center of the aperture to the point P and the path from point to point P. Since the wave from point has a shorter path length, it arrives at point P at an earlier phase. The total electric field at P is:

where and and x is now measured in units of wavelength. The shape of the distribution is clearly independent of R, and hence the unnormalized power pattern is just:

The region in which the field pattern is no longer dependent on the distance from the antenna is called the far field region . The integral operation in equation (3.5.13) is called the Fourier transform . is the Fourier transform of , which is often denoted as . The Fourier transform has many interresting properties, some of which are listed below (see also Section 2.5).

The Fourier transform is an invertible operation if

If then . This means that an antenna beam can be steered across the sky simply by introducing the appropriate linear phase gradient in the aperture illumination.

This is merely a restatement of power conservation. The LHS is the power outflow from the antenna as measured in the far field region, the RHS is the power outflow from the antenna as measured at the aperture plane.

With this background we are now in a position to determine the maximum effective aperture of a reflecting telescope. For a 2D aperture with aperture illumination , from equation (3.4.10)

But the field pattern is just the normalized far field electric field strength, i.e.

and from Parseval's theorem,

substituting in equation (3.5.14) using equations (3.5.15), 3.5.16 gives,

Note that since and are in units of wavelength, so is . however is in physical units. Uniform illumination gives the maximum possible aperture efficiency (i.e. 1), because if the illumination is tapered then the entire available aperture is not being used.

As a concrete example, consider a 1D uniformly illuminated aperture of length . The far field is then

and the normalized field pattern is

  1. the width of a function is inversely proportional to width of its transform ( so large antennas will have small beams and small antennas will have large beams), and
  2. any sharp discontinuities in the function will give rise to sidelobes (`ringing') in the fourier transform.

Figure 3.14 shows a plot of the the power and field patterns for a 700 ft, uniformly illuminated aperture at 2380 MHz.

Aperture illumination design hence involves the following following tradeoffs (see also Chapter 19):

    A more tapered illumination will have a broader main beam (or equivalently smaller effective aperture) but also lower side lobes than uniform illumination.

Another important issue in aperture illumination is the amount of aperture blockage. The feed antenna is usually suspended over the reflecting surface (see Figure 3.3) and blocks out part of the aperture. If the illumination is tapered, then the central part of the aperture has the highest illumination and blocking out this region could have a drastic effect on the power pattern. Consider again a 1D uniformly illuminated aperture of length l with the central portion of length blocked out. The far field of this aperture is (from the linearity of fourier transforms) just the difference between the far field of an aperture of length and an aperture of length d, i.e.

or the normalized field pattern is:

The field pattern of the ``missing'' part of the aperture has a broad main beam (since ). Subtracting this from the pattern due to the entire aperture will give a resultant pattern with very high sidelobes. In Figure 3.15 the solid curve is the pattern due to the entire aperture, the dotted line is the pattern of the blocked part and the dark curve is the resultant pattern. (This is for a 100ft blockage of a 700 ft aperture at 2380 MHz). Aperture blockage has to be minimized for a `clean' beam, many telescopes have feeds offset from the reflecting surface altogether to eliminate all blockage.

Watch the video: 50 What is Granularity level (September 2022).