In antenna theory, a phased array usually means an electronically scanned array, a computer-controlled array of antennas which creates a beam of radio waves that can be electronically steered to point in different directions without moving the antennas.In an array antenna, the radio frequency current from the transmitter is fed to the individual antennas with the correct phase relationship so that the radio waves from the separate antennas add together to increase the radiation in a desired direction, while cancelling to suppress radiation in undesired directions. In a phased array, the power from the transmitter is fed to the antennas through devices called phase shifters , controlled by a computer system, which can alter the phase electronically, thus steering the beam of radio waves to a different direction. Since the array must consist of many small antennas (sometimes thousands) to achieve high gain, phased arrays are mainly practical at the high frequency end of the radio spectrum, in the UHF and microwave bands, in which the antenna elements are conveniently small.
In radio engineering, an antenna is the interface between radio waves propagating through space and electric currents moving in metal conductors, used with a transmitter or receiver. In transmission, a radio transmitter supplies an electric current to the antenna's terminals, and the antenna radiates the energy from the current as electromagnetic waves. In reception, an antenna intercepts some of the power of a radio wave in order to produce an electric current at its terminals, that is applied to a receiver to be amplified. Antennas are essential components of all radio equipment.
An antenna array is a set of multiple connected antennas which work together as a single antenna, to transmit or receive radio waves. The individual antennas are usually connected to a single receiver or transmitter by feedlines that feed the power to the elements in a specific phase relationship. The radio waves radiated by each individual antenna combine and superpose, adding together to enhance the power radiated in desired directions, and cancelling to reduce the power radiated in other directions. Similarly, when used for receiving, the separate radio frequency currents from the individual antennas combine in the receiver with the correct phase relationship to enhance signals received from the desired directions and cancel signals from undesired directions. More sophisticated array antennas may have multiple transmitter or receiver modules, each connected to a separate antenna element or group of elements.
In electronics and telecommunications, a transmitter or radio transmitter is an electronic device which produces radio waves with an antenna. The transmitter itself generates a radio frequency alternating current, which is applied to the antenna. When excited by this alternating current, the antenna radiates radio waves.
Phased arrays were invented for use in military radar systems, to scan the radar beam quickly across the sky to detect planes and missiles. These phased array radar systems are now widely used, and phased arrays are spreading to civilian applications. The phased array principle is also used in acoustics, and phased arrays of acoustic transducers are used in medical ultrasound imaging scanners (phased array ultrasonics), oil and gas prospecting (reflection seismology), and military sonar systems.
Radar is a detection system that uses radio waves to determine the range, angle, or velocity of objects. It can be used to detect aircraft, ships, spacecraft, guided missiles, motor vehicles, weather formations, and terrain. A radar system consists of a transmitter producing electromagnetic waves in the radio or microwaves domain, a transmitting antenna, a receiving antenna and a receiver and processor to determine properties of the object(s). Radio waves from the transmitter reflect off the object and return to the receiver, giving information about the object's location and speed.
Acoustics is the branch of physics that deals with the study of all mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician while someone working in the field of acoustics technology may be called an acoustical engineer. The application of acoustics is present in almost all aspects of modern society with the most obvious being the audio and noise control industries.
A transducer is a device that converts energy from one form to another. Usually a transducer converts a signal in one form of energy to a signal in another.
The term "phased array" is also used to a lesser extent for unsteered array antennas in which the phase of the feed power and thus the radiation pattern of the antenna array is fixed.For example, AM broadcast radio antennas consisting of multiple mast radiators fed so as to create a specific radiation pattern are also called "phased arrays".
A mast radiator is a radio mast or tower in which the entire structure functions as an antenna. This design, first used in radiotelegraphy stations in the early 1900s, is commonly used for transmitting antennas operating at low frequencies, in the VLF, LF and MF ranges, in particular those used for AM broadcasting. The metal mast is electrically connected to the transmitter. Its base is usually mounted on a nonconductive support to insulate it from the ground. A mast radiator is a form of monopole antenna.
A passive phased array or passive electronically scanned array (PESA) is a phased array in which the antenna elements are connected to a single transmitter and/or receiver, as shown in the animation at top. PESAs are the most common type of phased array.
A passive electronically scanned array (PESA), also known as passive phased array, is a phased array antenna, that is an antenna in which the beam of radio waves can be electronically steered to point in different directions, in which all the antenna elements are connected to a single transmitter and/or receiver. This contrasts with an active electronically scanned array (AESA) antenna, which has a separate transmitter and/or receiver unit for each antenna element, all controlled by a computer. AESA is a more advanced, sophisticated versatile second-generation version of the original PESA phased array technology.
In radio communications, a radio receiver, also known as a receiver, wireless or simply radio is an electronic device that receives radio waves and converts the information carried by them to a usable form. It is used with an antenna. The antenna intercepts radio waves and converts them to tiny alternating currents which are applied to the receiver, and the receiver extracts the desired information. The receiver uses electronic filters to separate the desired radio frequency signal from all the other signals picked up by the antenna, an electronic amplifier to increase the power of the signal for further processing, and finally recovers the desired information through demodulation.
An active phased array or active electronically scanned array (AESA) is a phased array in which each antenna element has its own transmitter/receiver unit, all controlled by the computer. Active arrays are a more advanced, second-generation phased-array technology which are used in military applications; unlike PESAs they can radiate multiple beams of radio waves at multiple frequencies in different directions simultaneously.
An active electronically scanned array (AESA) is a type of phased array antenna, which is a computer-controlled array antenna in which the beam of radio waves can be electronically steered to point in different directions without moving the antenna. In the AESA, each antenna element is connected to a small solid-state transmit/receive module (TRM) under the control of a computer, which performs the functions of a transmitter and/or receiver for the antenna. This contrasts with a passive electronically scanned array (PESA), in which all the antenna elements are connected to a single transmitter and/or receiver through phase shifters under the control of the computer. AESA's main use is in radar, and these are known as active phased array radar (APAR).
A conformal antenna is a phased array in which the individual antennas, instead of being arranged in a flat plane, are mounted on a curved surface. The phase shifters compensate for the different path lengths of the waves due to the antenna elements' varying position on the surface, allowing the array to radiate a plane wave. Conformal antennas are used in aircraft and missiles, to integrate the antenna into the curving surface of the aircraft to reduce aerodynamic drag.
In radio communication and avionics a conformal antenna or conformal array is a flat radio antenna which is designed to conform or follow some prescribed shape, for example a flat curving antenna which is mounted on or embedded in a curved surface. Conformal antennas were developed in the 1980s as avionics antennas integrated into the curving skin of military aircraft to reduce aerodynamic drag, replacing conventional antenna designs which project from the aircraft surface. Military aircraft and missiles are the largest application of conformal antennas, but they are also used in some civilian aircraft, military ships and land vehicles. As the cost of the required processing technology comes down, they are being considered for use in civilian applications such as train antennas, car radio antennas, and cellular base station antennas, to save space and also to make the antenna less visually intrusive by integrating it into existing objects.
Phased array transmission was originally shown in 1905 by Nobel laureate Karl Ferdinand Braun who demonstrated enhanced transmission of radio waves in one direction.During World War II, Nobel laureate Luis Alvarez used phased array transmission in a rapidly steerable radar system for "ground-controlled approach", a system to aid in the landing of aircraft. At the same time, the GEMA in Germany built the Mammut 1. It was later adapted for radio astronomy leading to Nobel Prizes for Physics for Antony Hewish and Martin Ryle after several large phased arrays were developed at the University of Cambridge. This design is also used for radar, and is generalized in interferometric radio antennas.
In 2004, Caltech researchers demonstrated the first integrated silicon-based phased array receiver at 24GHz with 8 elements GHz.. This was followed by their demonstration of a CMOS 24GHz phased array transmitter in 2005 and a fully integrated 77GHz phased array transceiver with integrated antennas in 2006 by the Caltech team. In 2007, DARPA researchers announced a 16 element phased array radar antenna which was also integrated with all the necessary circuits on a single silicon chip and operated at 30–50
The relative amplitudes of—and constructive and destructive interference effects among—the signals radiated by the individual antennas determine the effective radiation pattern of the array. A phased array may be used to point a fixed radiation pattern, or to scan rapidly in azimuth or elevation. Simultaneous electrical scanning in both azimuth and elevation was first demonstrated in a phased array antenna at Hughes Aircraft Company, California in 1957.
In broadcast engineering, phased arrays are used by many AM broadcast radio stations to enhance signal strength and therefore coverage in the city of license, while minimizing interference to other areas. Due to the differences between daytime and nighttime ionospheric propagation at mediumwave frequencies, it is common for AM broadcast stations to change between day (groundwave) and night (skywave) radiation patterns by switching the phase and power levels supplied to the individual antenna elements (mast radiators) daily at sunrise and sunset. For shortwave broadcasts many stations use arrays of horizontal dipoles. A common arrangement uses 16 dipoles in a 4×4 array. Usually this is in front of a wire grid reflector. The phasing is often switchable to allow Beam steering in azimuth and sometimes elevation.
More modest phased array longwire antenna systems may be employed by private radio enthusiasts to receive longwave, mediumwave (AM) and shortwave radio broadcasts from great distances.
On VHF, phased arrays are used extensively for FM broadcasting. These greatly increase the antenna gain, magnifying the emitted RF energy toward the horizon, which in turn greatly increases a station's broadcast range. In these situations, the distance to each element from the transmitter is identical, or is one (or other integer) wavelength apart. Phasing the array such that the lower elements are slightly delayed (by making the distance to them longer) causes a downward beam tilt, which is very useful if the antenna is quite high on a radio tower.
Other phasing adjustments can increase the downward radiation in the far field without tilting the main lobe, creating null fill to compensate for extremely high mountaintop locations, or decrease it in the near field, to prevent excessive exposure to those workers or even nearby homeowners on the ground. The latter effect is also achieved by half-wave spacing – inserting additional elements halfway between existing elements with full-wave spacing. This phasing achieves roughly the same horizontal gain as the full-wave spacing; that is, a five-element full-wave-spaced array equals a nine- or ten-element half-wave-spaced array.
Phased array radar systems are also used by warships of many navies. Because of the rapidity with which the beam can be steered, phased array radars allow a warship to use one radar system for surface detection and tracking (finding ships), air detection and tracking (finding aircraft and missiles) and missile uplink capabilities. Before using these systems, each surface-to-air missile in flight required a dedicated fire-control radar, which meant that radar-guided weapons could only engage a small number of simultaneous targets. Phased array systems can be used to control missiles during the mid-course phase of the missile's flight. During the terminal portion of the flight, continuous-wave fire control directors provide the final guidance to the target. Because the radar beam is electronically steered, phased array systems can direct radar beams fast enough to maintain a fire control quality track on many targets simultaneously while also controlling several in-flight missiles.
The AN/SPY-1 phased array radar, part of the Aegis Combat System deployed on modern U.S. cruisers and destroyers, "is able to perform search, track and missile guidance functions simultaneously with a capability of over 100 targets."Likewise, the Thales Herakles phased array multi-function radar used in service with France, Russia and Singapore has a track capacity of 200 targets and is able to achieve automatic target detection, confirmation and track initiation in a single scan, while simultaneously providing mid-course guidance updates to the MBDA Aster missiles launched from the ship. The German Navy and the Royal Dutch Navy have developed the Active Phased Array Radar System (APAR). The MIM-104 Patriot and other ground-based antiaircraft systems use phased array radar for similar benefits.
Phased arrays are used in naval sonar, in active (transmit and receive) and passive (receive only) and hull-mounted and towed array sonar.
The MESSENGER spacecraft was a space probe mission to the planet Mercury (2011–2015). This was the first deep-space mission to use a phased-array antenna for communications. The radiating elements are circularly-polarized, slotted waveguides. The antenna, which uses the X band, used 26 radiative elements and can gracefully degrade.
The National Severe Storms Laboratory has been using a SPY-1A phased array antenna, provided by the US Navy, for weather research at its Norman, Oklahoma facility since April 23, 2003. It is hoped that research will lead to a better understanding of thunderstorms and tornadoes, eventually leading to increased warning times and enhanced prediction of tornadoes. Current project participants include the National Severe Storms Laboratory and National Weather Service Radar Operations Center, Lockheed Martin, United States Navy, University of Oklahoma School of Meteorology, School of Electrical and Computer Engineering, and Atmospheric Radar Research Center, Oklahoma State Regents for Higher Education, the Federal Aviation Administration, and Basic Commerce and Industries. The project includes research and development, future technology transfer and potential deployment of the system throughout the United States. It is expected to take 10 to 15 years to complete and initial construction was approximately $25 million.A team from Japan's RIKEN Advanced Institute for Computational Science (AICS) has begun experimental work on using phased-array radar with a new algorithm for instant weather forecasts.
Within the visible or infrared spectrum of electromagnetic waves it is possible to construct optical phased arrays. They are used in wavelength multiplexers and filters for telecommunication purposes,laser beam steering, and holography. Synthetic array heterodyne detection is an efficient method for multiplexing an entire phased array onto a single element photodetector. The dynamic beam forming in an optical phased array transmitter can be used to electronically raster or vector scan images without using lenses or mechanically moving parts in a lensless projector. Optical phased array receivers have been demonstrated to be able to act as lensless cameras by selectively looking at different directions.
OneWeb and Starlink are two low-earth orbit satellite constellations which are under construction as of 2019. They are designed to provide broadband internet connectivity to consumers; the user terminals of both systems will use phased array antennas.
By 2014, phased array antennas were integrated into RFID systems to increase the area of coverage of a single system by 100% to 76,200 m2 (820,000 sq ft) while still using traditional passive UHF tags.
A phased array of acoustic transducers, denominated airborne ultrasound tactile display (AUTD), was developed in 2008 at the University of Tokyo's Shinoda Lab to induce tactile feedback.This system was demonstrated to enable a user to interactively manipulate virtual holographic objects.
This section does not cite any sources . (December 2016) (Learn how and when to remove this template message)
Mathematically a phased array is an example of N-slit diffraction, in which the radiation field at the receiving point is the result of the coherent addition of N point sources in a line. Since each individual antenna acts as a slit, emitting radio waves, their diffraction pattern can be calculated by adding the phase shift φ to the fringing term.
We will begin from the N-slit diffraction pattern derived on the diffraction formalism page, with slits of equal size and spacing .
Now, adding a φ term to the fringe effect in the second term yields:
Taking the square of the wave function gives us the intensity of the wave.
Now space the emitters a distance apart. This distance is chosen for simplicity of calculation but can be adjusted as any scalar fraction of the wavelength.
As sine achieves its maximum at , we set the numerator of the second term = 1.
Thus as N gets large, the term will be dominated by the term. As sine can oscillate between −1 and 1, we can see that setting will send the maximum energy on an angle given by
Additionally, we can see that if we wish to adjust the angle at which the maximum energy is emitted, we need only to adjust the phase shift φ between successive antennas. Indeed, the phase shift corresponds to the negative angle of maximum signal.
A similar calculation will show that the denominator is minimized by the same factor.
This section does not cite any sources . (December 2016) (Learn how and when to remove this template message)
There are two main types of beamformers. These are time domain beamformers and frequency domain beamformers.
A graduated attenuation window is sometimes applied across the face of the array to improve side-lobe suppression performance, in addition to the phase shift.
Time domain beamformer works by introducing time delays. The basic operation is called "delay and sum". It delays the incoming signal from each array element by a certain amount of time, and then adds them together. The most common kind of time domain beam former is serpentine waveguide. Active phased array designs use individual delay lines that are switched on and off. Yttrium iron garnet phase shifters vary the phase delay using the strength of a magnetic field.
There are two different types of frequency domain beamformers.
The first type separates the different frequency components that are present in the received signal into multiple frequency bins (using either a Discrete Fourier transform (DFT) or a filterbank). When different delay and sum beamformers are applied to each frequency bin, the result is that the main lobe simultaneously points in multiple different directions at each of the different frequencies. This can be an advantage for communication links, and is used with the SPS-48 radar.
The other type of frequency domain beamformer makes use of Spatial Frequency. Discrete samples are taken from each of the individual array elements. The samples are processed using a DFT. The DFT introduces multiple different discrete phase shifts during processing. The outputs of the DFT are individual channels that correspond with evenly spaced beams formed simultaneously. A 1-dimensional DFT produces a fan of different beams. A 2-dimensional DFT produces beams with a pineapple configuration.
These techniques are used to create two kinds of phased array.
There are two further sub-categories that modify the kind of dynamic array or fixed array.
Each array element incorporates an adjustable phase shifter that are collectively used to move the beam with respect to the array face.
Dynamic phased array require no physical movement to aim the beam. The beam is moved electronically. This can produce antenna motion fast enough to use a small pencil-beam to simultaneously track multiple targets while searching for new targets using just one radar set (track while search).
As an example, an antenna with a 2 degree beam with a pulse rate of 1 kHz will require approximately 8 seconds to cover an entire hemisphere consisting of 8,000 pointing positions. This configuration provides 12 opportunities to detect a 1,000 m/s (2,200 mph; 3,600 km/h) vehicle over a range of 100 km (62 mi), which is suitable for military applications.[ citation needed ]
The position of mechanically steered antennas can be predicted, which can be used to create electronic countermeasures that interfere with radar operation. The flexibility resulting from phased array operation allows beams to be aimed at random locations, which eliminates this vulnerability. This is also desirable for military applications.
Fixed phased array antennas are typically used to create an antenna with a more desirable form factor than the conventional parabolic reflector or cassegrain reflector. Fixed phased arrays incorporate fixed phase shifters. For example, most commercial FM Radio and TV antenna towers use a collinear antenna array, which is a fixed phased array of dipole elements.
In radar applications, this kind of phased array is physically moved during the track and scan process. There are two configurations.
The SPS-48 radar uses multiple transmit frequencies with a serpentine delay line along the left side of the array to produce vertical fan of stacked beams. Each frequency experiences a different phase shift as it propagates down the serpentine delay line, which forms different beams. A filter bank is used to split apart the individual receive beams. The antenna is mechanically rotated.
Semi-active radar homing uses monopulse radar that relies on a fixed phased array to produce multiple adjacent beams that measure angle errors. This form factor is suitable for gimbal mounting in missile seekers.
Active electronically-scanned arrays (AESA) elements incorporate transmit amplification with phase shift in each antenna element (or group of elements). Each element also includes receive pre-amplification. The phase shifter setting is the same for transmit and receive.
Active phased array do not require phase reset after the end of the transmit pulse, which is compatible with Doppler radar and pulse-Doppler radar.
Passive phased arrays typically use large amplifiers that produce all of the microwave transmit signal for the antenna. Phase shifters typically consist of waveguide elements controlled by magnetic field, voltage gradient, or equivalent technology.
The phase shift process used with passive phased arrays typically puts the receive beam and transmit beam into diagonally opposite quadrants. The sign of the phase shift must be inverted after the transmit pulse is finished and before the receive period begins to place the receive beam into the same location as the transmit beam. That requires a phase impulse that degrades sub-clutter visibility performance on Doppler radar and Pulse-Doppler radar. As an example, Yttrium iron garnet phase shifters must be changed after transmit pulse quench and before receiver processing starts to align transmit and receive beams. That impulse introduces FM noise that degrades clutter performance.
Passive phased array design is used in the AEGIS Combat System.for direction-of-arrival estimation.
In the field of antenna design the term radiation pattern refers to the directional (angular) dependence of the strength of the radio waves from the antenna or other source.
A waveform is a variable that varies with time, usually representing a voltage or current.
In electromagnetics, an antenna's power gain or simply gain is a key performance number which combines the antenna's directivity and electrical efficiency. In a transmitting antenna, the gain describes how well the antenna converts input power into radio waves headed in a specified direction. In a receiving antenna, the gain describes how well the antenna converts radio waves arriving from a specified direction into electrical power. When no direction is specified, "gain" is understood to refer to the peak value of the gain, the gain in the direction of the antenna's main lobe. A plot of the gain as a function of direction is called the radiation pattern.
Synchrotron radiation is the electromagnetic radiation emitted when charged particles are accelerated radially, i.e., when they are subject to an acceleration perpendicular to their velocity. It is produced, for example, in synchrotrons using bending magnets, undulators and/or wigglers. If the particle is non-relativistic, then the emission is called cyclotron emission. If, on the other hand, the particles are relativistic, sometimes referred to as ultrarelativistic, the emission is called synchrotron emission. Synchrotron radiation may be achieved artificially in synchrotrons or storage rings, or naturally by fast electrons moving through magnetic fields. The radiation produced in this way has a characteristic polarization and the frequencies generated can range over the entire electromagnetic spectrum which is also called continuum radiation.
In optics, a Fabry–Pérot interferometer (FPI) or etalon is typically made of a transparent plate with two reflecting surfaces, or two parallel highly reflecting mirrors. Its transmission spectrum as a function of wavelength exhibits peaks of large transmission corresponding to resonances of the etalon. It is named after Charles Fabry and Alfred Perot, who developed the instrument in 1899. Etalon is from the French étalon, meaning "measuring gauge" or "standard".
In radio and telecommunications a dipole antenna or doublet is the simplest and most widely used class of antenna. The dipole is any one of a class of antennas producing a radiation pattern approximating that of an elementary electric dipole with a radiating structure supporting a line current so energized that the current has only one node at each end. A dipole antenna commonly consists of two identical conductive elements such as metal wires or rods. The driving current from the transmitter is applied, or for receiving antennas the output signal to the receiver is taken, between the two halves of the antenna. Each side of the feedline to the transmitter or receiver is connected to one of the conductors. This contrasts with a monopole antenna, which consists of a single rod or conductor with one side of the feedline connected to it, and the other side connected to some type of ground. A common example of a dipole is the "rabbit ears" television antenna found on broadcast television sets.
A sensor array is a group of sensors, usually deployed in a certain geometry pattern, used for collecting and processing electromagnetic or acoustic signals. The advantage of using a sensor array over using a single sensor lies in the fact that an array adds new dimensions to the observation, helping to estimate more parameters and improve the estimation performance. For example an array of radio antenna elements used for beamforming can increase antenna gain in the direction of the signal while decreasing the gain in other directions, i.e., increasing signal-to-noise ratio (SNR) by amplifying the signal coherently. Another example of sensor array application is to estimate the direction of arrival of impinging electromagnetic waves. The related processing method is called array signal processing. Application examples of array signal processing include radar/sonar, wireless communications, seismology, machine condition monitoring, astronomical observations fault diagnosis, etc.
An acousto-optic modulator (AOM), also called a Bragg cell, uses the acousto-optic effect to diffract and shift the frequency of light using sound waves. They are used in lasers for Q-switching, telecommunications for signal modulation, and in spectroscopy for frequency control. A piezoelectric transducer is attached to a material such as glass. An oscillating electric signal drives the transducer to vibrate, which creates sound waves in the material. These can be thought of as moving periodic planes of expansion and compression that change the index of refraction. Incoming light scatters off the resulting periodic index modulation and interference occurs similar to Bragg diffraction. The interaction can be thought of as a three-wave mixing process resulting in Sum-frequency generation or Difference-frequency generation between phonons and photons.
In electromagnetics, directivity is a parameter of an antenna or optical system which measures the degree to which the radiation emitted is concentrated in a single direction. It measures the power density the antenna radiates in the direction of its strongest emission, versus the power density radiated by an ideal isotropic radiator radiating the same total power.
Position angle, usually abbreviated PA, is the convention for measuring angles on the sky in astronomy. The International Astronomical Union defines it as the angle measured relative to the north celestial pole (NCP), turning positive into the direction of the right ascension. In the standard (non-flipped) images this is a counterclockwise measure relative to the axis into the direction of positive declination.
Cylindrical multipole moments are the coefficients in a series expansion of a potential that varies logarithmically with the distance to a source, i.e., as . Such potentials arise in the electric potential of long line charges, and the analogous sources for the magnetic potential and gravitational potential.
Phase-comparison monopulse describes a technique that can be used in radar and direction finding applications to accurately estimate the direction of arrival of a signal from the phase difference of the signal measured on two separated antennas.
Diffraction processes affecting waves are amenable to quantitative description and analysis. Such treatments are applied to a wave passing through one or more slits whose width is specified as a proportion of the wavelength. Numerical approximations may be used, including the Fresnel and Fraunhofer approximations.
Clutter is a term used for unwanted echoes in electronic systems, particularly in reference to radars. Such echoes are typically returned from ground, sea, rain, animals/insects, chaff and atmospheric turbulences, and can cause serious performance issues with radar systems.
Radar engineering details are technical details pertaining to the components of a radar and their ability to detect the return energy from moving scatterers — determining an object's position or obstruction in the environment. This includes field of view in terms of solid angle and maximum unambiguous range and velocity, as well as angular, range and velocity resolution. Radar sensors are classified by application, architecture, radar mode, platform, and propagation window.
The contrast transfer function (CTF) mathematically describes how aberrations in a transmission electron microscope (TEM) modify the image of a sample. This contrast transfer function (CTF) sets the resolution of high-resolution transmission electron microscopy (HRTEM), also known as phase contrast TEM.
In optics, the Fraunhofer diffraction equation is used to model the diffraction of waves when the diffraction pattern is viewed at a long distance from the diffracting object, and also when it is viewed at the focal plane of an imaging lens.
The Eckert IV projection is an equal-area pseudocylindrical map projection. The length of the polar lines is half that of the equator, and lines of longitude are semiellipses, or portions of ellipses. It was first described by Max Eckert in 1906 as one of a series of three pairs of pseudocylindrical projections. In each pair, the meridians have the same shape, and the odd-numbered projection has equally spaced parallels, whereas the even-numbered projection has parallels spaced to preserve area. The pair to Eckert IV is the Eckert III projection.
The Two-Rays Ground Reflected Model is a radio propagation model which predicts the path losses between a transmitting antenna and a receiving antenna when they are in LOS. Generally, the two antenna each have different height. The received signal having two components, the LOS component and the multipath component formed predominantly by a single ground reflected wave.
In physics and engineering, the radiative heat transfer from one surface to another is the equal to the difference of incoming and outgoing radiation from the first surface. In general, the heat transfer between surfaces is governed by temperature, surface emissivity properties and the geometry of the surfaces. The relation for heat transfer can be written as an integral equation with boundary conditions based upon surface conditions. Kernel functions can be useful in approximating and solving this integral equation.
|Wikimedia Commons has media related to Phased arrays .|