Confusion is a symptom. It is a sign of a disease, and a reason for it can always be identified. Mild forms of confusion may pass for normal, but as they become more severe, affected individuals spend more time in unusual behavior.
Confused patients tend to sleep more, have difficulty sustaining conversation and respond with abrupt, brief, mechanical answers. Confusion is recognized by a combination of any of the following features:
1. The patient is awake.
2. The patient is disoriented.
3. The patient has impaired short term memory.
4. The patient has diminished intellectual capacity.
5. The patient exhibits bizarre and uncharacteristic behavior.
There are many dilfferent reasons for a person to appear confused. Some forms of confusion are readily curable, some are treatable and some are terminal. Thus, there should be a thorough search for a cause when confusion is first noticed.
Deciding which medical condition is responsible for the confusion challenges the best gerontologists. The clinical picture can be complicated by the simultaneous occurence of a combination of conditions in the same individual. For instance, the presence of dementia predisposes a person to depression
The Confusion is a novel by Neal Stephenson. It is the second volume in The Baroque Cycle.
The Confusion consists of two books, Bonanza and The Juncto which are "con-fused" together, so that one jumps back and forth between them as one reads through The Confusion. This is the only volume of the Baroque Cycle that is so confused; the novels contained in the other two volumes are read in order (comment taken from the book).
The title has several other meanings:
the cryptographic terms confusion and diffusion (several of the characters are involved in code-breaking)
the metallurgic term confusion, for the process of mingling two metals into an alloy (referring to the efforts of several characters involved in refining gold)
In 2005, The Confusion won the Locus Award, together with The System of the World.
in·co·her·ent
Pronunciation: \-Ént\
Function: adjective
Date: 1626
: lacking coherence: as a: lacking cohesion : loose b: lacking orderly continuity, arrangement, or relevance : inconsistent
c: lacking normal clarity or intelligibility in speech or thought
— in·co·her·ent·ly adverb
Coherence is the property of wave-like states that enables them to exhibit interference. It is also the parameter that quantifies the quality of the interference (also known as the degree of coherence). It was originally introduced in connection with Young’s double-slit experiment in optics but is now used in any field that involves waves, such as acoustics, electrical engineering, neuroscience, and quantum physics. In interference, at least two wave-like entities are combined and, depending on the relative phase between them, they can add constructively or subtract destructively. The degree of coherence is equal to the interference visibility, a measure of how perfectly the waves can cancel due to destructive interference. The property of coherence is the basis for commercial applications such as holography, the Sagnac gyroscope, radio antenna arrays, optical coherence tomography and telescope interferometers (astronomical optical interferometers and radio telescopes).
Contents [hide]
1 Coherence and correlation
2 Examples of wave-like states
3 Temporal coherence
3.1 The relationship between coherence time and bandwidth
3.2 Examples of temporal coherence
3.3 Measurement of temporal coherence
4 Spatial coherence
4.1 Examples of spatial coherence
5 Spectral coherence
5.1 Measurement of spectral coherence
6 Polarization coherence
7 Quantum coherence
8 See also
9 References
[edit] Coherence and correlation
The coherence of two waves follows from how well correlated the waves are as quantified by the cross-correlation function. The cross-correlation quantifies the ability to predict the value of the second wave by knowing the value of the first. As an example, consider two waves perfectly correlated for all times. At any time, if the first wave changes, the second will change in the same way. If combined they can exhibit complete constructive interference at all times. It follows that they are perfectly coherent. As will be discussed below, the second wave need not be a separate entity. It could be the first wave at a different time or position. In this case, sometimes called self-coherence, the measure of correlation is the autocorrelation function.
[edit] Examples of wave-like states
These states are unified by the fact that their behavior is described by a wave equation or some generalization thereof.
Waves in a rope (up and down) or slinky (compression and expansion)
Surface waves in a liquid
Electric signals (fields) in transmission cables
Sound
Radio and Microwaves
Light (optics)
Electrons, atoms, and any other object (as described by quantum physics)
In most of these systems, one can measure the wave directly. Consequently, its correlation with another wave can simply be calculated. However, in optics one can not measure the electric field directly as it oscillates much faster than any detector’s time resolution. Instead, we measure the intensity of the light. Most of the concepts involving coherence which will be introduced below were developed in the field of optics and then used in other fields. Therefore, many of the standard measurements of coherence are indirect measurements, even in fields where the wave can be measured directly.
[edit] Temporal coherence
Figure 1: The amplitude of a single frequency wave as a function of time t (red) and a copy of the same wave delayed by Ï(green). The coherence time of the wave is infinite since it is perfectly correlated with itself for all delays Ï.
Figure 2: The amplitude of a wave whose phase drifts significantly in time Ïc as a function of time t (red) and a copy of the same wave delayed by 2Ïc(green). At any particular time t the wave can interfere perfectly with its delayed copy. But, since half the time the red and green waves are in phase and half the time out of phase, when averaged over t any interference disappears at this delay.Temporal coherence is the measure of the average correlation between the value of a wave at any pair of times, separated by delay Ï. Temporal coherence tells us how monochromatic a source is. In other words, it characterizes how well a wave can interfere with itself at a different time. The delay over which the phase or amplitude wanders by a significant amount (and hence the correlation decreases by significant amount) is defined as the coherence time Ïc. At Ï=0 the degree of coherence is perfect whereas it drops significantly by delay Ïc. The coherence length Lc is defined as the distance the wave travels in time Ïc.
One should be careful not to confuse the coherence time with the time duration of the signal, nor the coherence length with the coherence area (see below).
[edit] The relationship between coherence time and bandwidth
Since period is the inverse of frequency, it follows that the faster a wave decorrelates (and hence the smaller Ïc is) the larger the range of frequencies Îf the wave contains. Thus there is a tradeoff:
.
In terms of wavelength (fλ = c) this relationship becomes,
Formally, this follows from the convolution theorem in mathematics, which relates the Fourier transform of the power spectrum (the intensity of each frequency) to its autocorrelation.
[edit] Examples of temporal coherence
We consider four examples of temporal coherence.
A wave containing only a single frequency (monochromatic) is perfectly correlated at all times according to the above relation. (See Figure 1)
Conversely, a wave whose phase drifts quickly will have a short coherence time. (See Figure 2)
Similarly, pulses (wave packets) of waves, which naturally have a broad range of frequencies, also have a short coherence time since the amplitude of the wave changes quickly. (See Figure 3)
Finally, white light, which has a very broad range of frequencies, is a wave which varies quickly in both amplitude and phase. Since it consequently has a very short coherence time (just 10 periods or so), it is often called incoherent.
The most monochromatic sources are usually lasers, and thus have the longest coherence lengths (up to hundreds of meters). For example, a stabilized helium-neon laser can produce light with coherence lengths in excess of 5 m. Not all lasers are monochromatic, however (e.g. for a Ti-sapphire laser, Îλ â 2 nm - 70 nm). LEDs are less monochromatic (Îλ â 50 nm) than the most monochromatic lasers, and tungsten filament lights are even less monochromatic (Îλ â 300 nm), and so these sources have shorter coherence times than the most monochromatic lasers.
Holography requires light with a long coherence time. In contrast, Optical coherence tomography uses light with a short coherence time.
[edit] Measurement of temporal coherence
Figure 3: The amplitude of a wavepacket whose amplitude changes significantly in time Ïc (red) and a copy of the same wave delayed by 2Ïc(green) plotted as a function of time t. At any particular time the red and green waves are uncorrelated; one oscillates while the other is constant and so there will be no interference at this delay. Another way of looking at this is the wavepackets are not overlapped in time and so at any particular time there is only one nonzero field so no interference can occur.
Figure 4: The time-averaged intensity (blue) detected at the output of an interferometer plotted as a function of delay Ï for the example waves in Figures 2 and 3. As the delay is changed by half a period, the interference switches between constructive and destructive. The black lines indicate the interference envelope, which gives the degree of coherence. Although the waves in Figures 2 and 3 have different time durations, they have the same coherence time.In optics, temporal coherence is measured in an interferometer such as the Michelson interferometer or Mach-Zehnder interferometer. In these devices, a wave is combined with a copy of itself that is delayed by time Ï. A detector measures the time-averaged intensity of the light exiting the interferometer. The resulting interference visibility (e.g. see Figure 4) gives the temporal coherence at delay Ï. Since for most natural light sources, the coherence time is much shorter than the time resolution of any detector, the detector itself does the time averaging. Consider the example shown in Figure 3. At a fixed delay, here 2Ïc, an infinitely fast detector would measure an intensity that fluctuates significantly over a time t equal to Ïc. In this case, to find the temporal coherence at 2Ïc, one would manually time-average the intensity.
[edit] Spatial coherence
In some systems, such as water waves or optics, wave-like states can extend over one or two dimensions. Spatial coherence describes the ability for two points in space, x1 and x2, in the extent of a wave to interfere, when averaged over time. More precisely, the spatial coherence is the cross-correlation between two points in a wave for all times. If a wave has only 1 value of amplitude over an infinite length, it is perfectly spatially coherent. The range of separation between the two points over which there is the significant interference is called the coherence area, Ac. This is the relevant type of coherence for the Young’s double-slit interferometer. It is also used in optical imaging systems and particularly in various types of astronomy telescopes. Sometimes people also use “spatial coherence” to refer to the visibility when a wave-like state is combined with a spatially shifted copy of itself.
[edit] Examples of spatial coherence
Figure 5: A plane wave with an infinite coherence length.Plane waves with an infinite coherence time have an infinite coherence area. See Figure 5.
A wave with distorted profile and with an infinite coherence time has an infinite coherence area. See Figure 6.
A wave with distorted profile and a finite coherence time has a finite coherence area. See Figure 7.
A wave with finite coherence area is incident on a pinhole (small aperture). The wave will diffract out of the pinhole. Far from the pinhole the emerging spherical wavefronts are approximately flat. The coherence area is now infinite while the coherence length is unchanged. See Figure 8.
A wave with infinite coherence area is combined with a spatially-shifted copy of itself. Some sections in the wave interfere constructively and some will interfere destructively. Averaging over these sections, a detector with length D will measure reduced interference visibility. See Figure 9.
Consider a tungsten light-bulb filament. Different points in the filament emit light independently and have no fixed phase-relationship. In detail, at any point in time the profile of the emitted light is going to be distorted. The profile will change randomly over the coherence time Ïc. Since for a white-light source such as a light-bulb Ïc is small, the filament is considered a spatially incoherent source. In contrast, a radio antenna array, has large spatial coherence because antennas at opposite ends of the array emit with a fixed phase-relationship. Light waves produced by a laser often have high temporal and spatial coherence (though the degree of coherence depends strongly on the exact properties of the laser). Spatial coherence of laser beams also manifests itself as speckle patterns and diffraction fringes seen at the edges of shadow.
Holography requires temporally and spatially coherent light. Its inventor, Dennis Gabor, produced successful holograms more than ten years before lasers were invented. To produce coherent light he passed the monochromatic light from an emission line of a mercury-vapor lamp through a pinhole spatial filter.
Figure 6: A wave with a varying profile (wavefront) and infinite coherence length.
Figure 7: A wave with a varying profile (wavefront) and finite coherence length.
Figure 8: The wave with finite coherence length from Figure 7 is passed through a pinhole. The emerging wave has infinite coherence area. The coherence length (or coherence time) are unchanged by the pinhole.
Figure 9: The wave with infinite coherence length from Figure 6 is combined with a spatially shifted copy of itself. For example a misaligned Mach-Zehnder interferometer will do this. A detector will measure reduced visibility.
[edit] Spectral coherence
Figure 10: Waves of different frequencies (i.e. colors) interfere to form a pulse if they are coherent.
Figure 11: Spectrally incoherent light interferes to form continuous light with a randomly varying phase and amplitudeWaves of different frequencies (in light these are different colours) can interfere to form a pulse if they have a fixed relative phase-relationship (see Fourier transform). Conversely, if waves of different frequencies are not coherent, then, when combined, they create a wave that is continuous in time (e.g. white light or white noise). The temporal duration of the pulse Ît is limited by the spectral bandwidth of the light Îf according to:
,
which follows from the properties of the Fourier transform (for quantum particles it also follows from the Heisenberg uncertainty principle).
If the phase depends linearly on the frequency (i.e. ) then the pulse will have the minimum time duration for its bandwidth (a transform-limited pulse), otherwise it is chirped (see dispersion).
[edit] Measurement of spectral coherence
Measurement of the spectral coherence of light requires a nonlinear optical interferometer, such as an intensity optical correlator, frequency-resolved optical gating (FROG), or Spectral phase interferometry for direct electric-field reconstruction (SPIDER).
[edit] Polarization coherence
Light also has a polarization, which is the direction in which the electric field oscillates. Unpolarized light is composed of two equally intense incoherent light waves with orthogonal polarizations. The electric field of the unpolarized light wanders in every direction and changes in phase over the coherence time of the two light waves. A polarizer rotated to any angle will always transmit half the incident intensity when averaged over time.
If the electric field wanders by a smaller amount the light will be partially polarized so that at some angle, the polarizer will transmit more than half the intensity. If a wave is combined with an orthogonally polarized copy of itself delayed by less than the coherence time, partially polarized light is created.
The polarization of a light beam is represented by a vector in the Poincare sphere. For polarized light the end of the vector lies on the surface of the sphere, whereas the vector has zero length for unpolarized light. The vector for partially polarized light lies within the sphere.
[edit] Quantum coherence
In quantum mechanics, all objects have wave-like properties (see de Broglie waves). For instance, in Young's double-slit experiment electrons can be used in the place of light waves. Each electron can go through either slit and hence has two paths that it can take to a particular final position. In quantum mechanics these two paths interfere. If there is destructive interference, the electron never arrives at that particular position. This ability to interfere is called quantum coherence.
The quantum description of perfectly coherent paths is called a pure state, in which the two paths are combined in a superposition. The correlation between the two particles exceeds what would be predicted for classical correlation alone (see Bell's inequalities). If this two-particle system is decohered (which would occur in a measurement via Einselection), then there is no longer any phase relationship between the two states. The quantum description of imperfectly coherent paths is called a mixed state, described by a density matrix and is entirely analogous to a classical system of mixed probabilities (the correlations are classical).
Large-scale (macroscopic) quantum coherence leads to very amazing phenomena. For instance, the laser, superconductivity, and superfluidity are examples of highly coherent quantum systems. One example that shows the amazing possibilities of macroscopic quantum coherence is the Schrödinger's cat thought experiment. Another example of quantum coherence is in a Bose-Einstein condensate. Here, all the atoms that make up the condensate are in-phase. They are thus all described by a single quantum wavefunction. Their behavior is communal and inseparable until the coherence is destroyed.
Coherence is the property of wave-like states that enables them to exhibit interference. It is also the parameter that quantifies the quality of the interference (also known as the degree of coherence). It was originally introduced in connection with Young’s double-slit experiment in optics but is now used in any field that involves waves, such as acoustics, electrical engineering, neuroscience, and quantum physics. In interference, at least two wave-like entities are combined and, depending on the relative phase between them, they can add constructively or subtract destructively. The degree of coherence is equal to the interference visibility, a measure of how perfectly the waves can cancel due to destructive interference. The property of coherence is the basis for commercial applications such as holography, the Sagnac gyroscope, radio antenna arrays, optical coherence tomography and telescope interferometers (astronomical optical interferometers and radio telescopes).
Contents [hide]
1 Coherence and correlation
2 Examples of wave-like states
3 Temporal coherence
3.1 The relationship between coherence time and bandwidth
3.2 Examples of temporal coherence
3.3 Measurement of temporal coherence
4 Spatial coherence
4.1 Examples of spatial coherence
5 Spectral coherence
5.1 Measurement of spectral coherence
6 Polarization coherence
7 Quantum coherence
8 See also
9 References
[edit] Coherence and correlation
The coherence of two waves follows from how well correlated the waves are as quantified by the cross-correlation function. The cross-correlation quantifies the ability to predict the value of the second wave by knowing the value of the first. As an example, consider two waves perfectly correlated for all times. At any time, if the first wave changes, the second will change in the same way. If combined they can exhibit complete constructive interference at all times. It follows that they are perfectly coherent. As will be discussed below, the second wave need not be a separate entity. It could be the first wave at a different time or position. In this case, sometimes called self-coherence, the measure of correlation is the autocorrelation function.
[edit] Examples of wave-like states
These states are unified by the fact that their behavior is described by a wave equation or some generalization thereof.
Waves in a rope (up and down) or slinky (compression and expansion)
Surface waves in a liquid
Electric signals (fields) in transmission cables
Sound
Radio and Microwaves
Light (optics)
Electrons, atoms, and any other object (as described by quantum physics)
In most of these systems, one can measure the wave directly. Consequently, its correlation with another wave can simply be calculated. However, in optics one can not measure the electric field directly as it oscillates much faster than any detector’s time resolution. Instead, we measure the intensity of the light. Most of the concepts involving coherence which will be introduced below were developed in the field of optics and then used in other fields. Therefore, many of the standard measurements of coherence are indirect measurements, even in fields where the wave can be measured directly.
[edit] Temporal coherence
Figure 1: The amplitude of a single frequency wave as a function of time t (red) and a copy of the same wave delayed by Ï(green). The coherence time of the wave is infinite since it is perfectly correlated with itself for all delays Ï.
Figure 2: The amplitude of a wave whose phase drifts significantly in time Ïc as a function of time t (red) and a copy of the same wave delayed by 2Ïc(green). At any particular time t the wave can interfere perfectly with its delayed copy. But, since half the time the red and green waves are in phase and half the time out of phase, when averaged over t any interference disappears at this delay.Temporal coherence is the measure of the average correlation between the value of a wave at any pair of times, separated by delay Ï. Temporal coherence tells us how monochromatic a source is. In other words, it characterizes how well a wave can interfere with itself at a different time. The delay over which the phase or amplitude wanders by a significant amount (and hence the correlation decreases by significant amount) is defined as the coherence time Ïc. At Ï=0 the degree of coherence is perfect whereas it drops significantly by delay Ïc. The coherence length Lc is defined as the distance the wave travels in time Ïc.
One should be careful not to confuse the coherence time with the time duration of the signal, nor the coherence length with the coherence area (see below).
[edit] The relationship between coherence time and bandwidth
Since period is the inverse of frequency, it follows that the faster a wave decorrelates (and hence the smaller Ïc is) the larger the range of frequencies Îf the wave contains. Thus there is a tradeoff:
.
In terms of wavelength (fλ = c) this relationship becomes,
Formally, this follows from the convolution theorem in mathematics, which relates the Fourier transform of the power spectrum (the intensity of each frequency) to its autocorrelation.
[edit] Examples of temporal coherence
We consider four examples of temporal coherence.
A wave containing only a single frequency (monochromatic) is perfectly correlated at all times according to the above relation. (See Figure 1)
Conversely, a wave whose phase drifts quickly will have a short coherence time. (See Figure 2)
Similarly, pulses (wave packets) of waves, which naturally have a broad range of frequencies, also have a short coherence time since the amplitude of the wave changes quickly. (See Figure 3)
Finally, white light, which has a very broad range of frequencies, is a wave which varies quickly in both amplitude and phase. Since it consequently has a very short coherence time (just 10 periods or so), it is often called incoherent.
The most monochromatic sources are usually lasers, and thus have the longest coherence lengths (up to hundreds of meters). For example, a stabilized helium-neon laser can produce light with coherence lengths in excess of 5 m. Not all lasers are monochromatic, however (e.g. for a Ti-sapphire laser, Îλ â 2 nm - 70 nm). LEDs are less monochromatic (Îλ â 50 nm) than the most monochromatic lasers, and tungsten filament lights are even less monochromatic (Îλ â 300 nm), and so these sources have shorter coherence times than the most monochromatic lasers.
Holography requires light with a long coherence time. In contrast, Optical coherence tomography uses light with a short coherence time.
[edit] Measurement of temporal coherence
Figure 3: The amplitude of a wavepacket whose amplitude changes significantly in time Ïc (red) and a copy of the same wave delayed by 2Ïc(green) plotted as a function of time t. At any particular time the red and green waves are uncorrelated; one oscillates while the other is constant and so there will be no interference at this delay. Another way of looking at this is the wavepackets are not overlapped in time and so at any particular time there is only one nonzero field so no interference can occur.
Figure 4: The time-averaged intensity (blue) detected at the output of an interferometer plotted as a function of delay Ï for the example waves in Figures 2 and 3. As the delay is changed by half a period, the interference switches between constructive and destructive. The black lines indicate the interference envelope, which gives the degree of coherence. Although the waves in Figures 2 and 3 have different time durations, they have the same coherence time.In optics, temporal coherence is measured in an interferometer such as the Michelson interferometer or Mach-Zehnder interferometer. In these devices, a wave is combined with a copy of itself that is delayed by time Ï. A detector measures the time-averaged intensity of the light exiting the interferometer. The resulting interference visibility (e.g. see Figure 4) gives the temporal coherence at delay Ï. Since for most natural light sources, the coherence time is much shorter than the time resolution of any detector, the detector itself does the time averaging. Consider the example shown in Figure 3. At a fixed delay, here 2Ïc, an infinitely fast detector would measure an intensity that fluctuates significantly over a time t equal to Ïc. In this case, to find the temporal coherence at 2Ïc, one would manually time-average the intensity.
[edit] Spatial coherence
In some systems, such as water waves or optics, wave-like states can extend over one or two dimensions. Spatial coherence describes the ability for two points in space, x1 and x2, in the extent of a wave to interfere, when averaged over time. More precisely, the spatial coherence is the cross-correlation between two points in a wave for all times. If a wave has only 1 value of amplitude over an infinite length, it is perfectly spatially coherent. The range of separation between the two points over which there is the significant interference is called the coherence area, Ac. This is the relevant type of coherence for the Young’s double-slit interferometer. It is also used in optical imaging systems and particularly in various types of astronomy telescopes. Sometimes people also use “spatial coherence” to refer to the visibility when a wave-like state is combined with a spatially shifted copy of itself.
[edit] Examples of spatial coherence
Figure 5: A plane wave with an infinite coherence length.Plane waves with an infinite coherence time have an infinite coherence area. See Figure 5.
A wave with distorted profile and with an infinite coherence time has an infinite coherence area. See Figure 6.
A wave with distorted profile and a finite coherence time has a finite coherence area. See Figure 7.
A wave with finite coherence area is incident on a pinhole (small aperture). The wave will diffract out of the pinhole. Far from the pinhole the emerging spherical wavefronts are approximately flat. The coherence area is now infinite while the coherence length is unchanged. See Figure 8.
A wave with infinite coherence area is combined with a spatially-shifted copy of itself. Some sections in the wave interfere constructively and some will interfere destructively. Averaging over these sections, a detector with length D will measure reduced interference visibility. See Figure 9.
Consider a tungsten light-bulb filament. Different points in the filament emit light independently and have no fixed phase-relationship. In detail, at any point in time the profile of the emitted light is going to be distorted. The profile will change randomly over the coherence time Ïc. Since for a white-light source such as a light-bulb Ïc is small, the filament is considered a spatially incoherent source. In contrast, a radio antenna array, has large spatial coherence because antennas at opposite ends of the array emit with a fixed phase-relationship. Light waves produced by a laser often have high temporal and spatial coherence (though the degree of coherence depends strongly on the exact properties of the laser). Spatial coherence of laser beams also manifests itself as speckle patterns and diffraction fringes seen at the edges of shadow.
Holography requires temporally and spatially coherent light. Its inventor, Dennis Gabor, produced successful holograms more than ten years before lasers were invented. To produce coherent light he passed the monochromatic light from an emission line of a mercury-vapor lamp through a pinhole spatial filter.
Figure 6: A wave with a varying profile (wavefront) and infinite coherence length.
Figure 7: A wave with a varying profile (wavefront) and finite coherence length.
Figure 8: The wave with finite coherence length from Figure 7 is passed through a pinhole. The emerging wave has infinite coherence area. The coherence length (or coherence time) are unchanged by the pinhole.
Figure 9: The wave with infinite coherence length from Figure 6 is combined with a spatially shifted copy of itself. For example a misaligned Mach-Zehnder interferometer will do this. A detector will measure reduced visibility.
[edit] Spectral coherence
Figure 10: Waves of different frequencies (i.e. colors) interfere to form a pulse if they are coherent.
Figure 11: Spectrally incoherent light interferes to form continuous light with a randomly varying phase and amplitudeWaves of different frequencies (in light these are different colours) can interfere to form a pulse if they have a fixed relative phase-relationship (see Fourier transform). Conversely, if waves of different frequencies are not coherent, then, when combined, they create a wave that is continuous in time (e.g. white light or white noise). The temporal duration of the pulse Ît is limited by the spectral bandwidth of the light Îf according to:
,
which follows from the properties of the Fourier transform (for quantum particles it also follows from the Heisenberg uncertainty principle).
If the phase depends linearly on the frequency (i.e. ) then the pulse will have the minimum time duration for its bandwidth (a transform-limited pulse), otherwise it is chirped (see dispersion).
[edit] Measurement of spectral coherence
Measurement of the spectral coherence of light requires a nonlinear optical interferometer, such as an intensity optical correlator, frequency-resolved optical gating (FROG), or Spectral phase interferometry for direct electric-field reconstruction (SPIDER).
[edit] Polarization coherence
Light also has a polarization, which is the direction in which the electric field oscillates. Unpolarized light is composed of two equally intense incoherent light waves with orthogonal polarizations. The electric field of the unpolarized light wanders in every direction and changes in phase over the coherence time of the two light waves. A polarizer rotated to any angle will always transmit half the incident intensity when averaged over time.
If the electric field wanders by a smaller amount the light will be partially polarized so that at some angle, the polarizer will transmit more than half the intensity. If a wave is combined with an orthogonally polarized copy of itself delayed by less than the coherence time, partially polarized light is created.
The polarization of a light beam is represented by a vector in the Poincare sphere. For polarized light the end of the vector lies on the surface of the sphere, whereas the vector has zero length for unpolarized light. The vector for partially polarized light lies within the sphere.
[edit] Quantum coherence
In quantum mechanics, all objects have wave-like properties (see de Broglie waves). For instance, in Young's double-slit experiment electrons can be used in the place of light waves. Each electron can go through either slit and hence has two paths that it can take to a particular final position. In quantum mechanics these two paths interfere. If there is destructive interference, the electron never arrives at that particular position. This ability to interfere is called quantum coherence.
The quantum description of perfectly coherent paths is called a pure state, in which the two paths are combined in a superposition. The correlation between the two particles exceeds what would be predicted for classical correlation alone (see Bell's inequalities). If this two-particle system is decohered (which would occur in a measurement via Einselection), then there is no longer any phase relationship between the two states. The quantum description of imperfectly coherent paths is called a mixed state, described by a density matrix and is entirely analogous to a classical system of mixed probabilities (the correlations are classical).
Large-scale (macroscopic) quantum coherence leads to very amazing phenomena. For instance, the laser, superconductivity, and superfluidity are examples of highly coherent quantum systems. One example that shows the amazing possibilities of macroscopic quantum coherence is the Schrödinger's cat thought experiment. Another example of quantum coherence is in a Bose-Einstein condensate. Here, all the atoms that make up the condensate are in-phase. They are thus all described by a single quantum wavefunction. Their behavior is communal and inseparable until the coherence is destroyed.
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Dictionary.com Unabridged (v 1.1) - Cite This Source - Share This
in·co·her·ent /ËɪnkoÊËhɪÉrÉnt, -ËhÉr-/ Pronunciation Key - Show Spelled Pronunciation[in-koh-heer-uhnt, -her-] Pronunciation Key - Show IPA Pronunciation
–adjective 1. without logical or meaningful connection; disjointed; rambling: an incoherent sentence.
2. characterized by such thought or language, as a person: incoherent with rage.
3. not coherent or cohering: an incoherent mixture.
4. lacking physical cohesion; loose: incoherent dust.
5. lacking unity or harmony of elements: an incoherent public.
6. lacking congruity of parts; uncoordinated.
7. different or incompatible by nature, as things.
8. Physics. (of a wave) having a low degree of coherence. Compare coherent (def. 4).
--------------------------------------------------------------------------------
[Origin: 1620–30; in-3 + coherent]
—Related forms
in·co·her·ent·ly, adverb
—Synonyms 1. confused, irrational, muddled.
Dictionary.com Unabridged (v 1.1)
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2006.
American Heritage Dictionary - Cite This Source - Share This in·co·her·ent (Än'kÅ-hîr'Ént) Pronunciation Key
adj.
Lacking cohesion, connection, or harmony; not coherent: incoherent fragments of a story.
Unable to think or express one's thoughts in a clear or orderly manner: incoherent with grief.
in'co·her'ent·ly adv., in'co·her'ent·ness n.
(Download Now or Buy the Book) The American Heritage® Dictionary of the English Language, Fourth Edition
Copyright © 2006 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
WordNet - Cite This Source - Share This incoherent
adjective
1. without logical or meaningful connection; "a turgid incoherent presentation" [ant: coherent]
2. (physics) of waves having no stable definite or stable phase relation [ant: coherent]
3. unable to express yourself clearly or fluently; "felt tongue-tied with embarrassment"; "incoherent with grief"
WordNet® 3.0, © 2006 by Princeton University.
Kernerman English Multilingual Dictionary (Beta Version) - Cite This Source - Share This
incoherent [inkouËhiÉrÉnt] adjective
talking, writing etc in a way which is not easy to follow
Example: He was quite incoherent with rage. Arabic: Ù
ÙتÙÙÙÙÙÙÙØ ØºÙر Ù
ÙتÙÙ
اسÙÙ
Chinese (Simplified): æ æ¡çç, è¯æ 伦次ç
Chinese (Traditional): ç¡æ¢çç, èªç¡å«æ¬¡ç
Czech: bez sebe
Danish: usammenhængende
Dutch: onsamenhangend
Estonian: segane, seosetu
Finnish: sekava
French: incohérent
German: zusammenhangslos
Greek: αÏÏ
νάÏÏηÏοÏ
Hungarian: összefüggéstelen, zavaros
Icelandic: ruglinslegur, samhengislaus
Indonesian: sulit dipahami
Italian: incoerente
Japanese: ä¸è²«ããªã
Korean: ì¡°ë¦¬ê° ìì§ ìë
Latvian: nesakarīgs
Lithuanian: (kalbantis) be sÄ
ryšio, padrikai
Norwegian: usammenhengende, uklar
Polish: chaotyczny
Portuguese (Brazil): incoerente
Portuguese (Portugal): incoerente
Romanian: incoerent
Russian: беÑÑвÑзнÑй
Slovak: nesúvislý, bez seba
Slovenian: nepovezan
Spanish: incoherente
Swedish: osammanhängande
Turkish: ne söylediÄi anlaÅılmaz, abuk sabuk
Kernerman English Multilingual Dictionary (Beta Version), © 2000-2006 K Dictionaries Ltd.
Merriam-Webster's Medical Dictionary - Cite This Source - Share This
Main Entry: in·co·her·ent
Pronunciation: -&nt
Function: adjective
: lacking clarity or intelligibility usually by reason of some emotional stress —in·co·her·ent·ly adverb
Merriam-Webster's Medical Dictionary, © 2002 Merriam-Webster, Inc.
On-line Medical Dictionary - Cite This Source - Share This
incoherent
incoherent: in CancerWEB's On-line Medical Dictionary
On-line Medical Dictionary, © 1997-98 Academic Medical Publishing & CancerWEB
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41 results for: unclear
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Roget's New Millennium⢠Thesaurus - Cite This Source - Share This
Main Entry: ambiguous
Part of Speech: adjective
Definition: unclear
Synonyms: cryptic, doubtful, dubious, enigmatic, enigmatical, equivocal, inconclusive, indefinite, indeterminate, inexplicit, obscure, opaque, puzzling, questionable, tenebrous, uncertain, unclear, unintelligible, vague
Antonyms: certain, clear, definite, explicit, lucid, unequivocal
Notes: ambiguous is vague by accident or intent; equivocal is vague by intent
Source: Roget's New Millennium⢠Thesaurus, First Edition (v 1.3.1)
Copyright © 2007 by Lexico Publishing Group, LLC. All rights reserved.
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Main Entry: baffling
Part of Speech: adjective
Definition: puzzling
Synonyms: abstruse, bewildering, beyond one, confusing, difficult to understand, enigmatic, hard to understand, incomprehensible, mystifying, over one's head, perplexing, unclear, unfathomable
Antonyms: clear, comprehensible
Source: Roget's New Millennium⢠Thesaurus, First Edition (v 1.3.1)
Copyright © 2007 by Lexico Publishing Group, LLC. All rights reserved.
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Main Entry: borderline
Part of Speech: adjective
Definition: inexact
Synonyms: ambiguous, ambivalent, doubtful, dubitable, equivocal, indecisive, indefinite, indeterminate, marginal, open, problematic, uncertain, unclear, undecided, unsettled
Antonyms: absolute, certain, decisive, definite, exact
Source: Roget's New Millennium⢠Thesaurus, First Edition (v 1.3.1)
Copyright © 2007 by Lexico Publishing Group, LLC. All rights reserved.
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Main Entry: cryptic
Part of Speech: adjective
Definition: secret
Synonyms: Delphian, Delphic, abstruse, ambiguous, apocryphal, arcane, cabalistic, cryptic, dark, enigmatic, equivocal, esoteric, evasive, hidden, incomprehensible, inexplicable, murky, mysterious, mystic, mystical, mystifying, occult, opaque, oracular, perplexing, puzzling, recondite, secretive, strange, tenebrous, unclear, unfathomable, uninformative, vague, veiled
Antonyms: clear, obvious, open, plain, straightforward
Notes: cryptic coloration helps conceal an animal; phaneric coloration makes an animal stand out
Source: Roget's New Millennium⢠Thesaurus, First Edition (v 1.3.1)
Copyright © 2007 by Lexico Publishing Group, LLC. All rights reserved.
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Main Entry: difficult
Part of Speech: adjective 2
Definition: complicated
Synonyms: abstract, abstruse, baffling, bewildering, complex, confounding, confusing, dark, deep, delicate, enigmatic, enigmatical, entangled, esoteric, formidable, hard, hidden, inexplicable, intricate, involved, knotty, labyrinthine, loose, meandering, mysterious, mystical, mystifying, nice, obscure, obstinate, paradoxical, perplexing, problematical, profound, puzzling, rambling, subtle, tangled, thorny, ticklish, troublesome, unclear, unfathomable, unintelligible, vex
Antonyms: simple, straightforward, uncomplicated
Source: Roget's New Millennium⢠Thesaurus, First Edition (v 1.3.1)
Copyright © 2007 by Lexico Publishing Group, LLC. All rights reserved.
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Main Entry: dim
Part of Speech: adjective 1
Definition: darkish
Synonyms: blah, bleary, blurred, caliginous, cloudy, dark, dingy, dreary, dull, dusk, dusky, faded, faint, flat, fuzzy, gloomy, gray, grey, indistinct, lackluster, lightless, mat, monotone, monotonous, murky, muted, obscured, opaque, overcast, pale, poorly lit, shadowy, sullied, tarnished, tenebrous, unclear, unilluminated, vague, weak
Antonyms: blinding, bright, brilliant, illuminated, shining, sunny
Source: Roget's New Millennium⢠Thesaurus, First Edition (v 1.3.1)
Copyright © 2007 by Lexico Publishing Group, LLC. All rights reserved.
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Main Entry: dubious
Part of Speech: adjective 1
Definition: doubtful
Synonyms: arguable, chancy, debatable, diffident, disputable, dubitable, equivocal, farfetched, fishy*, fly-by-night*, hesitant, iffy*, improbable, indecisive, moot, mootable, open, perplexed, problematic, questionable, reluctant, shady, skeptical, suspect, suspicious, trustless, unassured, uncertain, unclear, unconvinced, undecided, undependable, unlikely, unreliable, unsure, untrustworthy, untrusty, wavering
Antonyms: certain, definite, indisputable, positive, sure
Notes: a person is capable of doubting, whereas a thing is dubitable; dubious, unlike doubtful, carries the connotation of suspicion
Source: Roget's New Millennium⢠Thesaurus, First Edition (v 1.3.1)
Copyright © 2007 by Lexico Publishing Group, LLC. All rights reserved.
* = informal or slang
Roget's New Millennium⢠Thesaurus - Cite This Source - Share This
Main Entry: dubious
Part of Speech: adjective 2
Definition: vague
Synonyms: ambiguous, debatable, disinclined, doubtful, equivocal, indefinite, indeterminate, mistrustful, obscure, open, problematic, problematical, skeptical, unclear, undecided, unsettled
Antonyms: clear, decided, settled, unambiguous, unequivocal
Notes: a person is capable of doubting, whereas a thing is dubitable; dubious, unlike doubtful, carries the connotation of suspicion
Source: Roget's New Millennium⢠Thesaurus, First Edition (v 1.3.1)
Copyright © 2007 by Lexico Publishing Group, LLC. All rights reserved.
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Main Entry: equivocal
Part of Speech: adjective
Definition: doubtful
Synonyms: ambiguous, ambivalent, amphibological, borderline, clouded*, disreputable, dubious, evasive, fishy*, hazy*, indefinite, indeterminate, indistinct, misleading, mixed feelings, oblique, obscure, open, problematic, puzzling, questionable, suspect, suspicious, tenebrous, uncertain, unclear, undecided, unexplicit, unintelligible, vague
Antonyms: certain, clear, definite, obvious, plain, unequivocal, unquestionable
Notes: ambiguous is vague by accident or intent; equivocal is vague by intent
Source: Roget's New Millennium⢠Thesaurus, First Edition (v 1.3.1)
Copyright © 2007 by Lexico Publishing Group, LLC. All rights reserved.
* = informal or slang
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Main Entry: evasive
Part of Speech: adjective
Definition: deceitful
Synonyms: ambiguous, cagey, casuistic, casuistical, cunning, deceptive, devious, dissembling, elusive, elusory, equivocating, false, fugitive, greasy, indirect, intangible, jivey, lying, misleading, oblique, prevaricating, shifty, shuffling, slippery, sly, sophistical, stonewalling*, tricky, unclear, vague
Antonyms: candid, direct, forthright, honest, straight, straightforward, unambiguous
Notes: elusive is used when what is being avoided is physical capture or apprehension, whereas evasive is used when what is being avoided is direct or relevant response to a verbal challenge
Source: Roget's New Millennium⢠Thesaurus, First Edition (v 1.3.1)
Copyright © 2007 by Lexico Publishing Group, LLC. All rights reserved.
* = informal or slang
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