The Doppler effect (or the Doppler shift) is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. It is named after the Austrian physicist Christian Doppler, who described the phenomenon in 1842.
A common example of Doppler shift is the change of pitch heard when a vehicle sounding a horn approaches and recedes from an observer. Compared to the emitted frequency, the received frequency is higher during the approach, identical at the instant of passing by, and lower during the recession.
The reason for the Doppler effect is that when the source of the waves is moving towards the observer, each successive wave crest is emitted from a position closer to the observer than the crest of the previous wave. Therefore, each wave takes slightly less time to reach the observer than the previous wave. Hence, the time between the arrival of successive wave crests at the observer is reduced, causing an increase in the frequency. While they are traveling, the distance between successive wave fronts is reduced, so the waves "bunch together". Conversely, if the source of waves is moving away from the observer, each wave is emitted from a position farther from the observer than the previous wave, so the arrival time between successive waves is increased, reducing the frequency. The distance between successive wave fronts is then increased, so the waves "spread out".
For waves that propagate in a medium, such as sound waves, the velocity of the observer and of the source are relative to the medium in which the waves are transmitted. The total Doppler effect may therefore result from motion of the source, motion of the observer, or motion of the medium. Each of these effects is analyzed separately. For waves which do not require a medium, such as light or gravity in general relativity, only the relative difference in velocity between the observer and the source needs to be considered.
Doppler first proposed this effect in 1842 in his treatise "Über das farbige Licht der Doppelsterne und einiger anderer Gestirne des Himmels" (On the coloured light of the binary stars and some other stars of the heavens). The hypothesis was tested for sound waves by Buys Ballot in 1845.[p 1] He confirmed that the sound's pitch was higher than the emitted frequency when the sound source approached him, and lower than the emitted frequency when the sound source receded from him. Hippolyte Fizeau discovered independently the same phenomenon on electromagnetic waves in 1848 (in France, the effect is sometimes called "effet Doppler-Fizeau" but that name was not adopted by the rest of the world as Fizeau's discovery was six years after Doppler's proposal).[p 2]  In Britain, John Scott Russell made an experimental study of the Doppler effect (1848).[p 3]
In classical physics, where the speeds of source and the receiver relative to the medium are lower than the velocity of waves in the medium, the relationship between observed frequency and emitted frequency is given by:
The frequency is decreased if either is moving away from the other.
The above formula assumes that the source is either directly approaching or receding from the observer. If the source approaches the observer at an angle (but still with a constant velocity), the observed frequency that is first heard is higher than the object's emitted frequency. Thereafter, there is a monotonic decrease in the observed frequency as it gets closer to the observer, through equality when it is coming from a direction perpendicular to the relative motion (and was emitted at the point of closest approach; but when the wave is received, the source and observer will no longer be at their closest), and a continued monotonic decrease as it recedes from the observer. When the observer is very close to the path of the object, the transition from high to low frequency is very abrupt. When the observer is far from the path of the object, the transition from high to low frequency is gradual.
If the speeds and are small compared to the speed of the wave, the relationship between observed frequency and emitted frequency is approximately
|Observed frequency||Change in frequency|
To understand what happens, consider the following analogy. Someone throws one ball every second at a man. Assume that balls travel with constant velocity. If the thrower is stationary, the man will receive one ball every second. However, if the thrower is moving towards the man, he will receive balls more frequently because the balls will be less spaced out. The inverse is true if the thrower is moving away from the man. So it is actually the wavelength which is affected; as a consequence, the received frequency is also affected. It may also be said that the velocity of the wave remains constant whereas wavelength changes; hence frequency also changes.
With an observer stationary relative to the medium, if a moving source is emitting waves with an actual frequency (in this case, the wavelength is changed, the transmission velocity of the wave keeps constant note that the transmission velocity of the wave does not depend on the velocity of the source), then the observer detects waves with a frequency given by
A similar analysis for a moving observer and a stationary source (in this case, the wavelength keeps constant, but due to the motion, the rate at which the observer receives waves and hence the transmission velocity of the wave [with respect to the observer] is changed) yields the observed frequency:
These can be generalized into the equation that was presented in the previous section.
An interesting effect was predicted by Lord Rayleigh in his classic book on sound: if the source is moving toward the observer at twice the speed of sound, a musical piece emitted by that source would be heard in correct time and tune, but backwards. The Doppler effect with sound is only clearly heard with objects moving at high speed, as change in frequency of musical tone involves a speed of around 40 meters per second, and smaller changes in frequency can easily be confused by changes in the amplitude of the sounds from moving emitters. Neil A Downie has demonstrated  how the Doppler effect can be made much more easily audible by using an ultrasonic (e.g. 40 kHz) emitter on the moving object. The observer then uses a heterodyne frequency converter, as used in many bat detectors, to listen to a band around 40 kHz. In this case, with the bat detector tuned to give frequency for the stationary emitter of 2000 Hz, the observer will perceive a frequency shift of a whole tone, 240 Hz, if the emitter travels at 2 meters per second.
The siren on a passing emergency vehicle will start out higher than its stationary pitch, slide down as it passes, and continue lower than its stationary pitch as it recedes from the observer. Astronomer John Dobson explained the effect thus:
The reason the siren slides is because it doesn't hit you.
In other words, if the siren approached the observer directly, the pitch would remain constant, at a higher than stationary pitch, until the vehicle hit him, and then immediately jump to a new lower pitch. Because the vehicle passes by the observer, the radial velocity does not remain constant, but instead varies as a function of the angle between his line of sight and the siren's velocity:
where is the angle between the object's forward velocity and the line of sight from the object to the observer.
The Doppler effect for electromagnetic waves such as light is of great use in astronomy and results in either a so-called redshift or blueshift. It has been used to measure the speed at which stars and galaxies are approaching or receding from us; that is, their radial velocities. This may be used to detect if an apparently single star is, in reality, a close binary, to measure the rotational speed of stars and galaxies, or to detect exoplanets. This redshift and blueshift happens on a very small scale. If an object is moving toward earth, there would not be a noticeable difference in visible light, to the unaided eye. 
Note that redshift is also used to measure the expansion of space, but that this is not truly a Doppler effect. Rather, redshifting due to the expansion of space is known as cosmological redshift, which can be derived purely from the Robertson-Walker metric under the formalism of General Relativity. Having said this, it also happens that there are detectable Doppler effects on cosmological scales, which, if incorrectly interpreted as cosmological in origin, lead to the observation of redshift-space distortions.
The use of the Doppler effect for light in astronomy depends on our knowledge that the spectra of stars are not homogeneous. They exhibit absorption lines at well defined frequencies that are correlated with the energies required to excite electrons in various elements from one level to another. The Doppler effect is recognizable in the fact that the absorption lines are not always at the frequencies that are obtained from the spectrum of a stationary light source. Since blue light has a higher frequency than red light, the spectral lines of an approaching astronomical light source exhibit a blueshift and those of a receding astronomical light source exhibit a redshift.
Among the nearby stars, the largest radial velocities with respect to the Sun are +308 km/s (BD-15°4041, also known as LHS 52, 81.7 light-years away) and −260 km/s (Woolley 9722, also known as Wolf 1106 and LHS 64, 78.2 light-years away). Positive radial velocity means the star is receding from the Sun, negative that it is approaching.
The Doppler effect is used in some types of radar, to measure the velocity of detected objects. A radar beam is fired at a moving target — e.g. a motor car, as police use radar to detect speeding motorists — as it approaches or recedes from the radar source. Each successive radar wave has to travel farther to reach the car, before being reflected and re-detected near the source. As each wave has to move farther, the gap between each wave increases, increasing the wavelength. In some situations, the radar beam is fired at the moving car as it approaches, in which case each successive wave travels a lesser distance, decreasing the wavelength. In either situation, calculations from the Doppler effect accurately determine the car's velocity. Moreover, the proximity fuze, developed during World War II, relies upon Doppler radar to detonate explosives at the correct time, height, distance, etc.
Because the doppler shift affects the wave incident upon the target as well as the wave reflected back to the radar, the change in frequency observed by a radar due to a target moving at relative velocity is twice that from the same target emitting a wave:
An echocardiogram can, within certain limits, produce an accurate assessment of the direction of blood flow and the velocity of blood and cardiac tissue at any arbitrary point using the Doppler effect. One of the limitations is that the ultrasound beam should be as parallel to the blood flow as possible. Velocity measurements allow assessment of cardiac valve areas and function, abnormal communications between the left and right side of the heart, leaking of blood through the valves (valvular regurgitation), and calculation of the cardiac output. Contrast-enhanced ultrasound using gas-filled microbubble contrast media can be used to improve velocity or other flow-related medical measurements.
Although "Doppler" has become synonymous with "velocity measurement" in medical imaging, in many cases it is not the frequency shift (Doppler shift) of the received signal that is measured, but the phase shift (when the received signal arrives).[p 4]
Velocity measurements of blood flow are also used in other fields of medical ultrasonography, such as obstetric ultrasonography and neurology. Velocity measurement of blood flow in arteries and veins based on Doppler effect is an effective tool for diagnosis of vascular problems like stenosis.
Instruments such as the laser Doppler velocimeter (LDV), and acoustic Doppler velocimeter (ADV) have been developed to measure velocities in a fluid flow. The LDV emits a light beam and the ADV emits an ultrasonic acoustic burst, and measure the Doppler shift in wavelengths of reflections from particles moving with the flow. The actual flow is computed as a function of the water velocity and phase. This technique allows non-intrusive flow measurements, at high precision and high frequency.
Developed originally for velocity measurements in medical applications (blood flow), Ultrasonic Doppler Velocimetry (UDV) can measure in real time complete velocity profile in almost any liquids containing particles in suspension such as dust, gas bubbles, emulsions. Flows can be pulsating, oscillating, laminar or turbulent, stationary or transient. This technique is fully non-invasive.
Fast moving satellites can have a Doppler shift of dozens of kilohertz relative to a ground station. The speed, thus magnitude of Doppler effect, changes due to earth curvature. Dynamic Doppler compensation, where the frequency of a signal is changed progressively during transmission, is used so the satellite receives a constant frequency signal.
Doppler shift of the direct path can be estimated by the following formula :
where is the velocity of the mobile station, is the wave length of the carrier, is the elevation angle of the satellite and is the driving direction with respect to the satellite.
The additional Doppler shift due to the satellite moving can be described as:
where is the relative speed of the satellite.
The Leslie speaker, most commonly associated with and predominantly used with the famous Hammond organ, takes advantage of the Doppler effect by using an electric motor to rotate an acoustic horn around a loudspeaker, sending its sound in a circle. This results at the listener's ear in rapidly fluctuating frequencies of a keyboard note.
A laser Doppler vibrometer (LDV) is a non-contact instrument for measuring vibration. The laser beam from the LDV is directed at the surface of interest, and the vibration amplitude and frequency are extracted from the Doppler shift of the laser beam frequency due to the motion of the surface.
During the segmentation of vertebrate embryos, waves of gene expression sweep across the presomitic mesoderm, the tissue from which the precursors of the vertebrae (somites) are formed. A new somite is formed upon arrival of a wave at the anterior end of the presomitic mesoderm. In zebrafish, it has been shown that the shortening of the presomitic mesoderm during segmentation leads to a Doppler effect as the anterior end of the tissue moves into the waves. This Doppler effect contributes to the period of segmentation.[p 5]
Since 1968 scientists such as Victor Veselago have speculated about the possibility of an inverse Doppler effect. The size of the Doppler shift depends on the refractive index of the medium a wave is traveling through. But some materials are capable of negative refraction, which should lead to a Doppler shift that works in a direction opposite that of a conventional Doppler shift. The experiment that claimed to have detected this effect was conducted by Nigel Seddon and Trevor Bearpark in Bristol, United Kingdom in 2003.[p 6]
Media related to Doppler effect at Wikimedia Commons
30 Foot Fall (styled as 30footFALL) is an American punk rock band that began in Houston, Texas.71 Aquilae
71 Aquilae (abbreviated 71 Aql) is a binary star in the equatorial constellation of Aquila. 71 Aquilae is its Flamsteed designation though it also bears the Bayer designation l Aquilae. The apparent visual magnitude of the system is 4.33, making it bright enough to be viewed by the naked eye. It has an annual parallax shift of 9.67 mas, which equates to a physical distance of 340 light-years (100 parsecs) from Earth, give or take a 30 light-year margin of error. At this distance, the brightness of the system is diminished by 0.065 in visual magnitude from extinction caused by interstellar gas and dust.This is a spectroscopic binary system where the presence of an orbiting companion is revealed by shifts in the spectral lines caused by the Doppler effect. The primary component is a giant star with a stellar classification of G8 III. The secondary is following a circular orbit with a period of 205.2 days.Automatic target recognition
Automatic target recognition (ATR) is the ability for an algorithm or device to recognize targets or other objects based on data obtained from sensors.
Target recognition was initially done by using an audible representation of the received signal, where a trained operator who would decipher that sound to classify the target illuminated by the radar. While these trained operators had success, automated methods have been developed and continue to be developed that allow for more accuracy and speed in classification. ATR can be used to identify man made objects such as ground and air vehicles as well as for biological targets such as animals, humans, and vegetative clutter. This can be useful for everything from recognizing an object on a battlefield to filtering out interference caused by large flocks of birds on Doppler weather radar.
Possible military applications include a simple identification system such as an IFF transponder, and is used in other applications such as unmanned aerial vehicles and cruise missiles. There has been more and more interest shown in using ATR for domestic applications as well. Research has been done into using ATR for border security, safety systems to identify objects or people on a subway track, automated vehicles, and many others.Christian Doppler
Christian Andreas Doppler (; German: [ˈdɔplɐ]; 29 November 1803 – 17 March 1853) was an Austrian mathematician and physicist. He is celebrated for his principle — known as the Doppler effect — that the observed frequency of a wave depends on the relative speed of the source and the observer. He used this concept to explain the color of binary stars.Differential Doppler effect
The Differential Doppler effect occurs when light is emitted from a rotating source.
In circumstellar environments it describes the difference in photons arriving at orbiting dust particles. Photons that originate from the limb that is rotating away from the particle are red-shifted, while photons emitted from the limb rotating toward the particle are blue-shifted.Doppler
Doppler may refer to:
Doppler (surname), a surname and a list of people with the name
Christian Doppler (1803–1853), Austrian mathematician and physicist
Doppler (building), a building in Amazon.com's corporate headquarters
Doppler (crater), a lunar impact crater
Doppler (novel), a novel by Erlend Loe
3905 Doppler, an asteroid
Doppler, the mascot of the WNBA's Seattle StormDoppler echocardiography
Doppler echocardiography is a procedure that uses Doppler ultrasonography to examine the heart. An echocardiogram uses high frequency sound waves to create an image of the heart while the use of Doppler technology allows determination of the speed and direction of blood flow by utilizing the Doppler effect.
An echocardiogram can, within certain limits, produce accurate assessment of the direction of blood flow and the velocity of blood and cardiac tissue at any arbitrary point using the Doppler effect. One of the limitations is that the ultrasound beam should be as parallel to the blood flow as possible. Velocity measurements allow assessment of cardiac valve areas and function, any abnormal communications between the left and right side of the heart, any leaking of blood through the valves (valvular regurgitation), calculation of the cardiac output and calculation of E/A ratio (a measure of diastolic dysfunction). Contrast-enhanced ultrasound-using gas-filled microbubble contrast media can be used to improve velocity or other flow-related medical measurements.
An advantage of Doppler echocardiography is that it can be used to measure blood flow within the heart without invasive procedures such as cardiac catheterization.
In addition, with slightly different filter/gain settings, the method can measure tissue velocities by tissue Doppler echocardiography. The combination of flow and tissue velocities can be used for estimating left ventricular filling pressure, although only under certain conditions.Although "Doppler" has become synonymous with "velocity measurement" in medical imaging, in many cases it is not the frequency shift (Doppler shift) of the received signal that is measured, but the phase shift (when the received signal arrives). However, the calculation result will end up identical.
This procedure is frequently used to examine children's hearts for heart disease because there is no age or size requirement.Doppler radar
A Doppler radar is a specialized radar that uses the Doppler effect to produce velocity data about objects at a distance. It does this by bouncing a microwave signal off a desired target and analyzing how the object's motion has altered the frequency of the returned signal. This variation gives direct and highly accurate measurements of the radial component of a target's velocity relative to the radar. Doppler radars are used in aviation, sounding satellites, Major League Baseball's StatCast system, meteorology, radar guns, radiology and healthcare (fall detection and risk assessment, nursing or clinic purpose), and bistatic radar (surface-to-air missiles).
Partly because of its common use by television meteorologists in on-air weather reporting, the specific term "Doppler Radar" has erroneously become popularly synonymous with the type of radar used in meteorology. Most modern weather radars use the pulse-Doppler technique to examine the motion of precipitation, but it is only a part of the processing of their data. So, while these radars use a highly specialized form of Doppler radar, the term is much broader in its meaning and its applications.Doppler ultrasonography
Doppler ultrasonography is medical ultrasonography that employs the Doppler effect to generate imaging of the movement of tissues and body fluids (usually blood), and their relative velocity to the probe. By calculating the frequency shift of a particular sample volume, for example flow in an artery or a jet of blood flow over a heart valve, its speed and direction can be determined and visualized. Color Doppler or color flow Doppler is the presentation of the velocity by color scale. Color Doppler images are generally combined with grayscale (B-mode) images to display duplex ultrasonography images, allowing for simultaneous visualization of the anatomy of the area.
This is particularly useful in cardiovascular studies (sonography of the vascular system and heart) and essential in many areas such as determining reverse blood flow in the liver vasculature in portal hypertension.Dopplr
Dopplr was a free social networking service, launched in 2007, that allowed users to create itineraries of their travel plans and spot correlations with their contacts' travel plans in order to arrange meetings at any point on their journey. Additional features included allowing the user to calculate the carbon footprint their journeys have produced. The site was named after Christian Doppler, discoverer of the Doppler effect. The company was based in the "Silicon Roundabout" area of London.E-VSB
E-VSB or Enhanced VSB is an optional enhancement to the original ATSC Standards that use the 8VSB modulation system used for transmission of digital television. It is intended for improving reception where signals are weaker, including fringe reception areas, and on portable devices such as handheld televisions or mobile phones. It does not cause problems to older receivers, but they cannot take advantage of its features. E-VSB was approved by the ATSC committee in 2004. However, it has been implemented by few stations or manufacturers.For mobile applications, ATSC suffers significant signal degradation caused by the Doppler effect. Additionally, low-power handheld receivers are usually equipped with smaller antennas. These have a poor signal-to-noise ratio, which is disruptive to digital signals. The E-VSB standard provides for Reed-Solomon forward error correction to alleviate the data corruption caused by these issues.
Additionally, the standard can use either the MPEG-4 AVC or VC-1 video codecs. As these codecs have higher video compression than the original MPEG-2, they require less bandwidth.
As 8VSB lacks both link adaptation and hierarchical modulation of DVB, which would allow the SDTV part of an HDTV signal (or the LDTV part of SDTV) to be received even in fringe reception areas where signal strength is low, E-VSB yields a similar benefit. However, E-VSB places a significant processing overhead on the receiver, as well as a significant transmission overhead on the broadcaster's total bitrate. These are not a problem with DVB-H.
A-VSB is a different and, as of July 2008, unapproved addition to ATSC, which is also designed to send programming to mobile devices, and to allow for single-frequency networks. It is one of several proposals for ATSC-M/H, the as-yet undecided standard for mobile broadcasting via ATSC.Ives–Stilwell experiment
The Ives–Stilwell experiment tested the contribution of relativistic time dilation to the Doppler shift of light. The result was in agreement with the formula for the transverse Doppler effect and was the first direct, quantitative confirmation of the time dilation factor. Since then many Ives–Stilwell type experiments have been performed with increased precision. Together with the Michelson–Morley and Kennedy–Thorndike experiments it forms one of the fundamental tests of special relativity theory. Other tests confirming the relativistic Doppler effect are the Mössbauer rotor experiment and modern Ives–Stilwell experiments.
Both time dilation and the relativistic Doppler effect were predicted by Albert Einstein in his seminal 1905 paper.
Einstein subsequently (1907) suggested an experiment based on the measurement of the relative frequencies of light perceived as arriving from a light source in motion with respect to the observer, and he calculated the additional Doppler shift due to time dilation. This effect was later called "transverse Doppler effect" (TDE), since such experiments were initially imagined to be conducted at right angles with respect to the moving source, in order to avoid the influence of the longitudinal Doppler shift. Eventually, Herbert E. Ives and G. R. Stilwell (referring to time dilation as following from the theory of Lorentz and Larmor) gave up the idea of measuring this effect at right angles. They used rays in longitudinal direction and found a way to separate the much smaller TDE from the much bigger longitudinal Doppler effect. The experiment was performed in 1938 and it was reprised several times (see, e.g.). Similar experiments were conducted several times with increased precision, for example by Otting (1939), Mandelberg et al. (1962),
Hasselkamp et al. (1979), and Botermann et al.Photoacoustic Doppler effect
The photoacoustic Doppler effect, as its name implies, is one specific kind of Doppler effect, which occurs when an intensely modulated light wave induces a photoacoustic wave on moving particles with a specific frequency. The observed frequency shift is a good indicator of the velocity of the illuminated moving particles. A potential biomedical application is measuring blood flow.
Specifically, when an intensity modulated light wave is exerted on a localized medium, the resulting heat can induce an alternating and localized pressure change. This periodic pressure change generates an acoustic wave with a specific frequency. Among various factors that determine this frequency, the velocity of the heated area and thus the moving particles in this area can induce a frequency shift proportional to the relative motion. Thus, from the perspective of an observer, the observed frequency shift can be used to derive the velocity of illuminated moving particles.Radar gun
A radar speed gun (also radar gun and speed gun) is a device used to measure the speed of moving objects. It is used in law-enforcement to measure the speed of moving vehicles and is often used in professional spectator sport, for things such as the measurement of bowling speeds in cricket, speed of pitched baseballs, athletes and tennis serves.
A radar speed gun is a Doppler radar unit that may be hand-held, vehicle-mounted or static. It measures the speed of the objects at which it is pointed by detecting a change in frequency of the returned radar signal caused by the Doppler effect, whereby the frequency of the returned signal is increased in proportion to the object's speed of approach if the object is approaching, and lowered if the object is receding. Such devices are frequently used for speed limit enforcement, although more modern LIDAR speed gun instruments, which use pulsed laser light instead of radar, began to replace radar guns during the first decade of the twenty-first century, because of limitations associated with small radar systems.Redshift
In physics, redshift is a phenomenon where electromagnetic radiation (such as light) from an object undergoes an increase in wavelength. Whether or not the radiation is visible, "redshift" means an increase in wavelength, equivalent to a decrease in wave frequency and photon energy, in accordance with, respectively, the wave and quantum theories of light.
Neither the emitted nor perceived light is necessarily red; instead, the term refers to the human perception of longer wavelengths as red, which is at the section of the visible spectrum with the longest wavelengths. Examples of redshifting are a gamma ray perceived as an X-ray, or initially visible light perceived as radio waves. The opposite of a redshift is a blueshift, where wavelengths shorten and energy increases. However, redshift is a more common term and sometimes blueshift is referred to as negative redshift.
There are three main causes of red (and blue shifts) in astronomy and cosmology:
Objects move apart (or closer together) in space. This is an example of the Doppler effect.
Space itself expands, causing objects to become separated without changing their positions in space. This is known as cosmological redshift. All sufficiently distant light sources (generally more than a few million light years away) show redshift corresponding to the rate of increase in their distance from Earth, known as Hubble's Law.
Gravitational redshift is a relativistic effect observed due to strong gravitational fields, which distort spacetime and exert a force on light and other particles.Knowledge of redshifts and blueshifts has been used to develop several terrestrial technologies such as Doppler radar and radar guns. Redshifts are also seen in the spectroscopic observations of astronomical objects. Its value is represented by the letter z.
A special relativistic redshift formula (and its classical approximation) can be used to calculate the redshift of a nearby object when spacetime is flat. However, in many contexts, such as black holes and Big Bang cosmology, redshifts must be calculated using general relativity. Special relativistic, gravitational, and cosmological redshifts can be understood under the umbrella of frame transformation laws. There exist other physical processes that can lead to a shift in the frequency of electromagnetic radiation, including scattering and optical effects; however, the resulting changes are distinguishable from true redshift and are not generally referred to as such (see section on physical optics and radiative transfer).Relativistic Doppler effect
The relativistic Doppler effect is the change in frequency (and wavelength) of light, caused by the relative motion of the source and the observer (as in the classical Doppler effect), when taking into account effects described by the special theory of relativity.
The relativistic Doppler effect is different from the non-relativistic Doppler effect as the equations include the time dilation effect of special relativity and do not involve the medium of propagation as a reference point. They describe the total difference in observed frequencies and possess the required Lorentz symmetry.
Astronomers know of three sources of redshift/blueshift: Doppler shifts; gravitational redshifts (due to light exiting a gravitational field); and cosmological expansion (where space itself stretches). This article concerns itself only with Doppler shifts.Relativistic beaming
Relativistic beaming (also known as Doppler beaming, Doppler boosting, or the headlight effect) is the process by which relativistic effects modify the apparent luminosity of emitting matter that is moving at speeds close to the speed of light. In an astronomical context, relativistic beaming commonly occurs in two oppositely-directed relativistic jets of plasma that originate from a central compact object that is accreting matter. Accreting compact objects and relativistic jets are invoked to explain the following observed phenomena: x-ray binaries, gamma-ray bursts, and, on a much larger scale, active galactic nuclei (AGN). (Quasars are also associated with an accreting compact object, but are thought to be merely a particular variety of AGN.)
Beaming (short for relativistic beaming) affects the apparent brightness of a moving object just as a lighthouse affects the appearance of its light source: the light source appears dim or unseen to a ship except when the rotating lighthouse beacon is directed towards a ship, where it then appears very bright. This so-called lighthouse effect illustrates how important the direction of motion (relative to the observer) is in relativistic beaming: consider a blob of gas emitting electromagnetic radiation that is moving relative to the observer. If the gas is moving towards the observer then it will be brighter than if it were at rest, but if the gas isn't moving towards the observer it may (in some cases) appear much fainter than if it were at rest. The importance of this effect in astronomy is illustrated by comparing the AGN jets detected in the galaxy M87 and 3C31 (see figures on the right). The twin jets in M87 show how beaming affects their appearance when one jet moves almost directly towards Earth and the other jet moves in the opposite direction; while M87's jet moving towards Earth is clearly visible to telescopes (the long and thin blue-ish feature in the top image) and is many times brighter due to beaming, M87's other jet is moving away from us and is, due to beaming, so much fainter than the jet directed towards us that it is rendered invisible. 3C31 is different from M87 because both jets (labeled in the figure directly below M87's image) are directed at roughly right angles to our line of sight and are therefore subject to the same amount of beaming. Thus, unlike the case of M87, both of 3C31's jets are visible. The jet displayed on the upper part of the image of 3C31 is actually pointing slightly more in Earth's direction than the other jet and is therefore the brighter of the two.Relativistically moving objects are beamed due to a variety of physical effects. Light aberration causes most of the photons to be emitted along the object's direction of motion. The Doppler effect changes the energy of the photons by red- or blueshifting them. Finally, time intervals as measured by clocks moving alongside the emitting object are different from those measured by an observer on Earth due to time dilation and photon arrival time effects. How all of these effects modify the brightness, or apparent luminosity, of a moving object is determined by the equation describing the relativistic Doppler effect (which is why relativistic beaming is also known as Doppler beaming).Spectral resolution
The spectral resolution of a spectrograph, or, more generally, of a frequency spectrum, is a measure of its ability to resolve features in the electromagnetic spectrum. It is usually denoted by , and is closely related to the resolving power of the spectrograph, defined as
where is the smallest difference in wavelengths that can be distinguished at a wavelength of . For example, the Space Telescope Imaging Spectrograph (STIS) can distinguish features 0.17 nm apart at a wavelength of 1000 nm, giving it a resolution of 0.17 nm and a resolving power of about 5,900. An example of a high resolution spectrograph is the Cryogenic High-Resolution IR Echelle Spectrograph (CRIRES) installed at ESO's Very Large Telescope, which has a spectral resolving power of up to 100,000.Wave vector
In physics, a wave vector (also spelled wavevector) is a vector which helps describe a wave. Like any vector, it has a magnitude and direction, both of which are important: Its magnitude is either the wavenumber or angular wavenumber of the wave (inversely proportional to the wavelength), and its direction is ordinarily the direction of wave propagation (but not always, see below).
In the context of special relativity the wave vector can also be defined as a four-vector.