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66-478: Normally, signals in the microwave frequency range travel in straight lines, and so are limited to line-of-sight applications, in which the receiver can be 'seen' by the transmitter. Communication distances are limited by the visual horizon to around 48–64 kilometres (30–40 mi). Troposcatter allows microwave communication beyond the horizon. It was developed in the 1950s and used for military communications until communications satellites largely replaced it in

132-415: A burning glass . Parabolic reflectors are popular for use in creating optical illusions . These consist of two opposing parabolic mirrors, with an opening in the center of the top mirror. When an object is placed on the bottom mirror, the mirrors create a real image , which is a virtually identical copy of the original that appears in the opening. The quality of the image is dependent upon the precision of

198-430: A hemisphere ( 2 3 π R 2 D , {\textstyle ({\frac {2}{3}}\pi R^{2}D,} where D = R ) , {\textstyle D=R),} and a cone ( 1 3 π R 2 D ) . {\textstyle ({\frac {1}{3}}\pi R^{2}D).} π R 2 {\textstyle \pi R^{2}}

264-471: A parabola revolving around its axis. The parabolic reflector transforms an incoming plane wave travelling along the axis into a spherical wave converging toward the focus. Conversely, a spherical wave generated by a point source placed in the focus is reflected into a plane wave propagating as a collimated beam along the axis. Parabolic reflectors are used to collect energy from a distant source (for example sound waves or incoming star light). Since

330-447: A few voice channels. Troposcatter systems have evolved over the years. With communication satellites used for long-distance communication links, current troposcatter systems are employed over shorter distances than previous systems, use smaller antennas and amplifiers, and have much higher bandwidth capabilities. Typical distances are between 50 and 250 kilometres (31 and 155 mi), though greater distances can be achieved depending on

396-416: A mirror that was parabolic would correct spherical aberration as well as the chromatic aberration seen in refracting telescopes . The design he came up with bears his name: the " Gregorian telescope "; but according to his own confession, Gregory had no practical skill and he could find no optician capable of actually constructing one. Isaac Newton knew about the properties of parabolic mirrors but chose

462-420: A narrow beam of radio waves for point-to-point communications in satellite dishes and microwave relay stations, and to locate aircraft, ships, and vehicles in radar sets. In acoustics , parabolic microphones are used to record faraway sounds such as bird calls , in sports reporting, and to eavesdrop on private conversations in espionage and law enforcement. Strictly, the three-dimensional shape of

528-570: A number of parts of the world, including: As well as the permanent networks detailed above, there have been many tactical transportable systems produced by several countries: The U.S. Army and Air Force use tactical tropospheric scatter systems developed by Raytheon for long haul communications. The systems come in two configurations, the original "heavy tropo", and a newer "light tropo" configuration exist. The systems provide four multiplexed group channels and trunk encryption, and 16 or 32 local analog phone extensions. The U.S. Marine Corps also uses

594-573: 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 . Microwaves, such as are used for satellite-TV signals, have wavelengths of

660-416: A spherical shape for his Newtonian telescope mirror to simplify construction. Lighthouses also commonly used parabolic mirrors to collimate a point of light from a lantern into a beam, before being replaced by more efficient Fresnel lenses in the 19th century. In 1888, Heinrich Hertz , a German physicist, constructed the world's first parabolic reflector antenna. The most common modern applications of

726-501: Is a consequence of a circular segment of earth profile that blocks off long-distance communications. Since the vacuum line of sight passes at varying heights over the Earth, the propagating radio wave encounters slightly different propagation conditions over the path. Assuming a perfect sphere with no terrain irregularity, the distance to the horizon from a high altitude transmitter (i.e., line of sight) can readily be calculated. Let R be

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792-462: 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

858-457: Is composed of a conductor that completely surrounds an area on all sides, top, and bottom. Electromagnetic radiation is blocked where the wavelength is longer than any gaps. For example, mobile telephone signals are blocked in windowless metal enclosures that approximate a Faraday cage, such as elevator cabins, and parts of trains, cars, and ships. The same problem can affect signals in buildings with extensive steel reinforcement. The radio horizon

924-462: 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. The whole reflector receives energy, which

990-457: 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)

1056-540: Is referred to as the "radio horizon". In practice, the propagation characteristics of these radio waves vary substantially depending on the exact frequency and the strength of the transmitted signal (a function of both the transmitter and the antenna characteristics). Broadcast FM radio, at comparatively low frequencies of around 100 MHz, are less affected by the presence of buildings and forests. Low-powered microwave transmitters can be foiled by tree branches, or even heavy rain or snow. The presence of objects not in

1122-421: 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

1188-433: Is the locus of points at which direct rays from an antenna are tangential to the surface of the Earth. If the Earth were a perfect sphere without an atmosphere, the radio horizon would be a circle. The radio horizon of the transmitting and receiving antennas can be added together to increase the effective communication range. Radio wave propagation is affected by atmospheric conditions, ionospheric absorption , and

1254-681: Is the aperture area of the dish, the area enclosed by the rim, which is proportional to the amount of sunlight the reflector dish can intercept. The area of the concave surface of the dish can be found using the area formula for a surface of revolution which gives A = π R 6 D 2 ( ( R 2 + 4 D 2 ) 3 / 2 − R 3 ) {\textstyle A={\frac {\pi R}{6D^{2}}}\left((R^{2}+4D^{2})^{3/2}-R^{3}\right)} . providing D ≠ 0 {\textstyle D\neq 0} . The fraction of light reflected by

1320-411: Is the focal length, D {\textstyle D} is the depth of the dish (measured along the axis of symmetry from the vertex to the plane of the rim), and R {\textstyle R} is the radius of the dish from the center. All units used for the radius, focal point and depth must be the same. If two of these three quantities are known, this equation can be used to calculate

1386-550: 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

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1452-454: Is usually chosen to be 4 ⁄ 3 . That means that the maximum service range increases by 15%. for h in metres and d in kilometres; or for h in feet and d in miles. But in stormy weather, k may decrease to cause fading in transmission. (In extreme cases k can be less than 1.) That is equivalent to a hypothetical decrease in Earth radius and an increase of Earth bulge. For example, in normal weather conditions,

1518-762: The British Telecom (BT) North Sea oil communications network, required higher capacity ‘information’ channels than were available using HF (high frequency – 3 MHz to 30 MHz ) radio signals, before satellite technology was available. The BT systems, based at Scousburgh in the Shetland Islands , Mormond Hill in Aberdeenshire and Row Brow near Scarborough , were capable of transmitting and receiving 156 analogue ( 4 kHz bandwidth) channels of data and telephony to / from North Sea oil production platforms, using frequency-division multiplexing (FDMX) to combine

1584-455: The Siege of Syracuse . This seems unlikely to be true, however, as the claim does not appear in sources before the 2nd century CE, and Diocles does not mention it in his book. Parabolic mirrors and reflectors were also studied extensively by the physicist Roger Bacon in the 13th century AD. James Gregory , in his 1663 book Optica Promota (1663), pointed out that a reflecting telescope with

1650-427: The natural logarithm of x , i.e. its logarithm to base " e ". The volume of the dish is given by 1 2 π R 2 D , {\textstyle {\frac {1}{2}}\pi R^{2}D,} where the symbols are defined as above. This can be compared with the formulae for the volumes of a cylinder ( π R 2 D ) , {\textstyle (\pi R^{2}D),}

1716-402: The shortwave bands between approximately 1 and 30 MHz, can be refracted back to Earth by the ionosphere , called skywave or "skip" propagation, thus giving radio transmissions in this range a potentially global reach. However, at frequencies above 30 MHz ( VHF and higher) and in lower levels of the atmosphere, neither of these effects are significant. Thus, any obstruction between

1782-420: The 1970s. Because the troposphere is turbulent and has a high proportion of moisture, the tropospheric scatter radio signals are refracted and consequently only a tiny proportion of the transmitted radio energy is collected by the receiving antennas. Frequencies of transmission around 2 GHz are best suited for tropospheric scatter systems as at this frequency the wavelength of the signal interacts well with

1848-474: 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. 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

1914-410: The atmosphere and obstructions with material and generally cannot travel over the horizon or behind obstacles. In contrast to line-of-sight propagation, at low frequency (below approximately 3  MHz ) due to diffraction , radio waves can travel as ground waves , which follow the contour of the Earth. This enables AM radio stations to transmit beyond the horizon. Additionally, frequencies in

1980-487: The atmosphere with height ( vertical pressure variation ) is to bend ( refract ) radio waves down towards the surface of the Earth. This results in an effective Earth radius , increased by a factor around 4 ⁄ 3 . This k -factor can change from its average value depending on weather. The previous vacuum distance analysis does not consider the effect of atmosphere on the propagation path of RF signals. In fact, RF signals do not propagate in straight lines: Because of

2046-401: 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

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2112-449: The channels. Because of the nature of the turbulence in the troposphere, quadruple diversity propagation paths were used to ensure 99.98% reliability of the service, equating to about 3 minutes of downtime due to propagation drop out per month. The quadruple space and polarisation diversity systems needed two separate dish antennas (spaced several metres apart) and two differently polarised feed horns – one using vertical polarisation,

2178-423: The climate, terrain, and data rate required. Typical antenna sizes range from 1.2 to 12 metres (3 ft 11 in to 39 ft 4 in) while typical amplifier sizes range from 10 W to 2 kW . Data rates over 20 Mbit/s can be achieved with today's technology. Tropospheric scatter is a fairly secure method of propagation as dish alignment is critical, making it extremely difficult to intercept

2244-402: The direct line-of-sight can cause diffraction effects that disrupt radio transmissions. For the best propagation, a volume known as the first Fresnel zone should be free of obstructions. Reflected radiation from the surface of the surrounding ground or salt water can also either cancel out or enhance the direct signal. This effect can be reduced by raising either or both antennas further from

2310-474: 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,

2376-467: The dish, from a light source in the focus, is given by 1 − arctan ⁡ R D − F π {\textstyle 1-{\frac {\arctan {\frac {R}{D-F}}}{\pi }}} , where F , {\displaystyle F,} D , {\displaystyle D,} and R {\displaystyle R} are defined as above. The parabolic reflector functions due to

2442-476: The dish. The principle of parabolic reflectors has been known since classical antiquity , when the mathematician Diocles described them in his book On Burning Mirrors and proved that they focus a parallel beam to a point. Archimedes in the third century BCE studied paraboloids as part of his study of hydrostatic equilibrium , and it has been claimed that he used reflectors to set the Roman fleet alight during

2508-648: The equivalent: P = R 2 2 D {\textstyle P={\frac {R^{2}}{2D}}} ) and Q = P 2 + R 2 {\textstyle Q={\sqrt {P^{2}+R^{2}}}} , where F , D , and R are defined as above. The diameter of the dish, measured along the surface, is then given by: R Q P + P ln ⁡ ( R + Q P ) {\textstyle {\frac {RQ}{P}}+P\ln \left({\frac {R+Q}{P}}\right)} , where ln ⁡ ( x ) {\textstyle \ln(x)} means

2574-406: 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

2640-410: 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

2706-407: The ground: The reduction in loss achieved is known as height gain . See also Non-line-of-sight propagation for more on impairments in propagation. It is important to take into account the curvature of the Earth for calculation of line-of-sight paths from maps, when a direct visual fix cannot be made. Designs for microwave formerly used 4 ⁄ 3  Earth radius to compute clearances along

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2772-421: The height h is given in metres, and distance d in kilometres, If the height h is given in feet, and the distance d in statute miles, In the case, when there are two stations involve, e.g. a transmit station on ground with a station height h and a receive station in the air with a station height H , the line of sight distance can be calculated as follows: The usual effect of the declining pressure of

2838-410: The moist, turbulent areas of the troposphere, improving signal-to-noise ratios . Prior to World War II , prevailing radio physics theory predicted a relationship between frequency and diffraction that suggested radio signals would follow the curvature of the Earth, but that the strength of the effect would fall off rapidly and especially at higher frequencies. In spite of this widespread belief, during

2904-448: The order of ten millimetres, so dishes to focus these waves can be wrong by half a millimetre or so and still perform well. 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

2970-540: The other using horizontal polarisation. This ensured that at least one signal path was open at any one time. The signals from the four different paths were recombined in the receiver where a phase corrector removed the phase differences of each signal. Phase differences were caused by the different path lengths of each signal from transmitter to receiver. Once phase corrected, the four signals could be combined additively. The tropospheric scatter phenomenon has been used to build both civilian and military communication links in

3036-499: The parabolic reflector are in satellite dishes , reflecting telescopes , radio telescopes , parabolic microphones , solar cookers , and many lighting devices such as spotlights , car headlights , PAR lamps and LED housings. The Olympic Flame is traditionally lit at Olympia, Greece , using a parabolic reflector concentrating sunlight , and is then transported to the venue of the Games. Parabolic mirrors are one of many shapes for

3102-441: The path. Although the frequencies used by mobile phones (cell phones) are in the line-of-sight range, they still function in cities. This is made possible by a combination of the following effects: The combination of all these effects makes the mobile phone propagation environment highly complex, with multipath effects and extensive Rayleigh fading . For mobile phone services, these problems are tackled using: A Faraday cage

3168-414: The presence of obstructions, for example mountains or trees. Simple formulas that include the effect of the atmosphere give the range as: The simple formulas give a best-case approximation of the maximum propagation distance, but are not sufficient to estimate the quality of service at any location. In telecommunications , Earth bulge refers to the effect of earth's curvature on radio propagation. It

3234-423: The principles of reflection are reversible, parabolic reflectors can also be used to collimate radiation from an isotropic source into a parallel beam . In optics , parabolic mirrors are used to gather light in reflecting telescopes and solar furnaces , and project a beam of light in flashlights , searchlights , stage spotlights , and car headlights . In radio , parabolic antennas are used to radiate

3300-518: The radius of the Earth and h be the altitude of a telecommunication station. The line of sight distance d of this station is given by the Pythagorean theorem ; The altitude of the station h is much smaller than the radius of the Earth R. Therefore, h 2 {\displaystyle h^{2}} can be neglected compared with 2 ⋅ R ⋅ h {\displaystyle 2\cdot R\cdot h} . Thus: If

3366-466: 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 . If a parabola is positioned in Cartesian coordinates with its vertex at the origin and its axis of symmetry along

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3432-448: The refractive effects of atmospheric layers, the propagation paths are somewhat curved. Thus, the maximum service range of the station is not equal to the line of sight vacuum distance. Usually, a factor k is used in the equation above, modified to be k  > 1 means geometrically reduced bulge and a longer service range. On the other hand, k  < 1 means a shorter service range. Under normal weather conditions, k

3498-490: The rim is 2.7187  F . The angular radius of the rim as seen from the focal point is 72.68 degrees. 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

3564-478: The same calculations used during the war, the Federal Communications Commission (FCC) arranged frequency allocations for the new VHF and UHF channels to avoid interference between stations. To everyone's surprise, interference was common, even between widely separated stations. As a result, licenses for new stations were put on hold in what is known as the "television freeze" of 1948. Bell Labs

3630-465: The same device, albeit an older version. Line-of-sight propagation Line-of-sight propagation is a characteristic of electromagnetic radiation or acoustic wave propagation which means waves can only travel in a direct visual path from the source to the receiver without obstacles. Electromagnetic transmission includes light emissions traveling in a straight line . The rays or waves may be diffracted , refracted , reflected, or absorbed by

3696-414: The service range of a station at an altitude of 1500 m with respect to receivers at sea level can be found as, Parabolic reflector A parabolic (or paraboloid or paraboloidal ) reflector (or dish or mirror ) is a reflective surface used to collect or project energy such as light , sound , or radio waves . Its shape is part of a circular paraboloid , that is, the surface generated by

3762-457: The signals, especially if transmitted across open water, making them highly attractive to military users. Military systems have tended to be ‘thin-line’ tropo – so called because only a narrow bandwidth ‘information’ channel was carried on the tropo system; generally up to 32 analogue ( 4 kHz bandwidth) channels. Modern military systems are "wideband" as they operate 4-16 Mbit/s digital data channels. Civilian troposcatter systems, such as

3828-555: The system they felt it might be useful for a new communications network in Labrador and took one of the systems there for cold weather testing. In 1954 the results from both test series were complete and construction began on the first troposcatter system, the Pole Vault system that linked Pinetree Line radar systems along the coast of Labrador . Using troposcatter reduced the number of stations from 50 microwave relays scattered through

3894-420: The third. A more complex calculation is needed to find the diameter of the dish measured along its surface . This is sometimes called the "linear diameter", and equals the diameter of a flat, circular sheet of material, usually metal, which is the right size to be cut and bent to make the dish. Two intermediate results are useful in the calculation: P = 2 F {\textstyle P=2F} (or

3960-467: The tiny amount that was reflected was useful if combined with powerful transmitters and very sensitive receivers. In 1952, Bell began experiments with Lincoln Labs , the MIT-affiliated radar research lab. Using Lincoln's powerful microwave transmitters and Bell's sensitive receivers, they built several experimental systems to test a variety of frequencies and weather effects. When Bell Canada heard of

4026-630: The transmit power is available at the receiver. This demands the use of antennas with extremely large antenna gain . The original Pole Vault system used large parabolic reflector dish antennas, but these were soon replaced by billboard antennas which were somewhat more robust, an important quality given that these systems were often found in harsh locales. Paths were established at distances over 1,000 kilometres (620 mi). They required antennas ranging from 9 to 36 metres (30 to 118 ft) and amplifiers ranging from 1 kW to 50 kW . These were analogue systems which were capable of transmitting

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4092-463: The transmitting antenna ( transmitter ) and the receiving antenna ( receiver ) will block the signal, just like the light that the eye may sense. Therefore, since the ability to visually see a transmitting antenna (disregarding the limitations of the eye's resolution) roughly corresponds to the ability to receive a radio signal from it, the propagation characteristic at these frequencies is called "line-of-sight". The farthest possible point of propagation

4158-523: The war there were numerous incidents in which high-frequency radar signals were able to detect targets at ranges far beyond the theoretical calculations. In spite of these repeated instances of anomalous range, the matter was never seriously studied. In the immediate post-war era, the limitation on television construction was lifted in the United States and millions of sets were sold. This drove an equally rapid expansion of new television stations. Based on

4224-635: The wilderness to only 10, all located at the radar stations. In spite of their higher unit costs, the new network cost half as much to build as a relay system. Pole Vault was quickly followed by similar systems like White Alice , relays on the Mid-Canada Line and the DEW Line , and during the 1960s, across the Atlantic Ocean and Europe as part of NATO 's ACE High system. The propagation losses are very high; only about one trillionth (10 × 10 ^ ) of

4290-488: The y-axis, so the parabola opens upward, its equation is 4 f y = x 2 {\textstyle 4fy=x^{2}} , where f {\textstyle f} is its focal length. (See " Parabola#In a cartesian coordinate system ".) Correspondingly, the dimensions of a symmetrical paraboloidal dish are related by the equation: 4 F D = R 2 {\textstyle 4FD=R^{2}} , where F {\textstyle F}

4356-476: Was among the many organizations that began studying this effect, and concluded it was a previously unknown type of reflection off the tropopause . This was limited to higher frequencies, in the UHF and microwave bands, which is why it had not been seen prior to the war when these frequencies were beyond the ability of existing electronics. Although the vast majority of the signal went through the troposphere and on to space,

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