Plasma (physics)

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Plasma_(physics) 

Plasma (from Ancient Greek πλάσμα (plásma) 'moldable substance') is one of four fundamental states of matter (the other three being solid, liquid, and gas) characterized by the presence of a significant portion of charged particles in any combination of ions or electrons. It is the most abundant form of ordinary matter in the universe, mostly in stars (including the Sun), but also dominating the rarefied intracluster medium and intergalactic medium. Plasma can be artificially generated, for example, by heating a neutral gas or subjecting it to a strong electromagnetic field.

The presence of charged particles makes plasma electrically conductive, with the dynamics of individual particles and macroscopic plasma motion governed by collective electromagnetic fields and very sensitive to externally applied fields. The response of plasma to electromagnetic fields is used in many modern devices and technologies, such as plasma televisions or plasma etching.

Depending on temperature and density, a certain number of neutral particles may also be present, in which case plasma is called partially ionized. Neon signs and lightning are examples of partially ionized plasmas. Unlike the phase transitions between the other three states of matter, the transition to plasma is not well defined and is a matter of interpretation and context. Whether a given degree of ionization suffices to call a substance "plasma" depends on the specific phenomenon being considered.

Early history

Plasma was first identified in laboratory by Sir William Crookes. Crookes presented a lecture on what he called "radiant matter" to the British Association for the Advancement of Science, in Sheffield, on Friday, 22 August 1879. Systematic studies of plasma began with the research of Irving Langmuir and his colleagues in the 1920s. Langmuir also introduced the term "plasma" as a description of ionized gas in 1928:

Except near the electrodes, where there are sheaths containing very few electrons, the ionized gas contains ions and electrons in about equal numbers so that the resultant space charge is very small. We shall use the name plasma to describe this region containing balanced charges of ions and electrons.

Lewi Tonks and Harold Mott-Smith, both of whom worked with Langmuir in the 1920s, recall that Langmuir first used the term by analogy with the blood plasma. Mott-Smith recalls, in particular, that the transport of electrons from thermionic filaments reminded Langmuir of "the way blood plasma carries red and white corpuscles and germs."

Definitions

The fourth state of matter

Plasma is called the fourth state of matter after solid, liquid, and gas. It is a state of matter in which an ionized substance becomes highly electrically conductive to the point that long-range electric and magnetic fields dominate its behaviour.

Plasma is typically an electrically quasineutral medium of unbound positive and negative particles (i.e., the overall charge of a plasma is roughly zero). Although these particles are unbound, they are not "free" in the sense of not experiencing forces. Moving charged particles generate electric currents, and any movement of a charged plasma particle affects and is affected by the fields created by the other charges. In turn, this governs collective behaviour with many degrees of variation.

Plasma is distinct from the other states of matter. In particular, describing a low-density plasma as merely an "ionized gas" is wrong and misleading, even though it is similar to the gas phase in that both assume no definite shape or volume. The following table summarizes some principal differences:

State Property	Gas	Plasma
Interactions	Short-range: Two-particle (binary) collisions are the rule.	Long-range: Collective motion of particles is ubiquitous in plasma, resulting in various waves and other types of collective phenomena.
Electrical conductivity	Very low: Gases are excellent insulators up to electric field strengths of tens of kilovolts per centimetre.	Very high: For many purposes, the conductivity of a plasma may be treated as infinite.
Independently acting species	One: All gas particles behave in a similar way, largely influenced by collisions with one another and by gravity.	Two or more: Electrons and ions possess different charges and vastly different masses, so that they behave differently in many circumstances, with various types of plasma-specific waves and instabilities emerging as a result.

Ideal plasma

Three factors define an ideal plasma:

• The plasma approximation: The plasma approximation applies when the plasma parameter Λ, representing the number of charge carriers within the Debye sphere is much higher than unity. It can be readily shown that this criterion is equivalent to smallness of the ratio of the plasma electrostatic and thermal energy densities. Such plasmas are called weakly coupled.
• Bulk interactions: The Debye length is much smaller than the physical size of the plasma. This criterion means that interactions in the bulk of the plasma are more important than those at its edges, where boundary effects may take place. When this criterion is satisfied, the plasma is quasineutral.
• Collisionlessness: The electron plasma frequency (measuring plasma oscillations of the electrons) is much larger than the electron–neutral collision frequency. When this condition is valid, electrostatic interactions dominate over the processes of ordinary gas kinetics. Such plasmas are called collisionless.

Non-neutral plasma

Main article: Non-neutral plasmas

The strength and range of the electric force and the good conductivity of plasmas usually ensure that the densities of positive and negative charges in any sizeable region are equal ("quasineutrality"). A plasma with a significant excess of charge density, or, in the extreme case, is composed of a single species, is called a non-neutral plasma. In such a plasma, electric fields play a dominant role. Examples are charged particle beams, an electron cloud in a Penning trap and positron plasmas.

Dusty plasma

Main article: Dusty plasma

A dusty plasma contains tiny charged particles of dust (typically found in space). The dust particles acquire high charges and interact with each other. A plasma that contains larger particles is called grain plasma. Under laboratory conditions, dusty plasmas are also called complex plasmas.

Properties and parameters

Artist's rendition of the Earth's plasma fountain, showing oxygen, helium, and hydrogen ions that gush into space from regions near the Earth's poles. The faint yellow area shown above the north pole represents gas lost from Earth into space; the green area is the aurora borealis, where plasma energy pours back into the atmosphere.

Density and ionization degree

For plasma to exist, ionization is necessary. The term "plasma density" by itself usually refers to the electron density ${\displaystyle n_e}$, that is, the number of charge-contributing electrons per unit volume. The degree of ionization ${\displaystyle \alpha }$ is defined as fraction of neutral particles that are ionized:

$${\displaystyle \alpha =\frac{n_i}{n_i+n_n},}$$

where ${\displaystyle n_i}$ is the ion density and ${\displaystyle n_n}$ the neutral density (in number of particles per unit volume). In the case of fully ionized matter, ${\displaystyle \alpha =1}$. Because of the quasineutrality of plasma, the electron and ion densities are related by ${\displaystyle n_e=⟨Z_i⟩n_i}$, where ${\displaystyle ⟨Z_i⟩}$ is the average ion charge (in units of the elementary charge).

Temperature

Plasma temperature, commonly measured in kelvin or electronvolts, is a measure of the thermal kinetic energy per particle. High temperatures are usually needed to sustain ionization, which is a defining feature of a plasma. The degree of plasma ionization is determined by the electron temperature relative to the ionization energy (and more weakly by the density). In thermal equilibrium, the relationship is given by the Saha equation. At low temperatures, ions and electrons tend to recombine into bound states—atoms—and the plasma will eventually become a gas.

In most cases, the electrons and heavy plasma particles (ions and neutral atoms) separately have a relatively well-defined temperature; that is, their energy distribution function is close to a Maxwellian even in the presence of strong electric or magnetic fields. However, because of the large difference in mass between electrons and ions, their temperatures may be different, sometimes significantly so. This is especially common in weakly ionized technological plasmas, where the ions are often near the ambient temperature while electrons reach thousands of kelvin. The opposite case is the z-pinch plasma where the ion temperature may exceed that of electrons.

See also: Nonthermal plasma and Anisothermal plasma

Plasma potential

Lightning as an example of plasma present at Earth's surface: Typically, lightning discharges 30 kiloamperes at up to 100 megavolts, and emits radio waves, light, X- and even gamma rays. Plasma temperatures can approach 30000 K and electron densities may exceed 10²⁴ m⁻³.

Since plasmas are very good electrical conductors, electric potentials play an important role. The average potential in the space between charged particles, independent of how it can be measured, is called the "plasma potential", or the "space potential". If an electrode is inserted into a plasma, its potential will generally lie considerably below the plasma potential due to what is termed a Debye sheath. The good electrical conductivity of plasmas makes their electric fields very small. This results in the important concept of "quasineutrality", which says the density of negative charges is approximately equal to the density of positive charges over large volumes of the plasma (${\displaystyle n_e=⟨Z⟩n_i}$), but on the scale of the Debye length, there can be charge imbalance. In the special case that double layers are formed, the charge separation can extend some tens of Debye lengths.

The magnitude of the potentials and electric fields must be determined by means other than simply finding the net charge density. A common example is to assume that the electrons satisfy the Boltzmann relation: $${\displaystyle n_e\propto \exp (e\mathrm{\Phi }/k_{\text{B}}{T}_e).}$$

Differentiating this relation provides a means to calculate the electric field from the density: $${\displaystyle \overrightarrow{E}=\frac{k_{\text{B}}{T}_e}{e}\frac{\mathrm{\nabla }{n}_e}{n_e}.}$$

It is possible to produce a plasma that is not quasineutral. An electron beam, for example, has only negative charges. The density of a non-neutral plasma must generally be very low, or it must be very small, otherwise, it will be dissipated by the repulsive electrostatic force.

Magnetization

The existence of charged particles causes the plasma to generate, and be affected by, magnetic fields. Plasma with a magnetic field strong enough to influence the motion of the charged particles is said to be magnetized. A common quantitative criterion is that a particle on average completes at least one gyration around the magnetic-field line before making a collision, i.e., ${\displaystyle {\nu }_{\mathrm{c}\mathrm{e}}/{\nu }_{\mathrm{c}\mathrm{o}\mathrm{l}\mathrm{l}}>1}$, where ${\displaystyle {\nu }_{\mathrm{c}\mathrm{e}}}$ is the electron gyrofrequency and ${\displaystyle {\nu }_{\mathrm{c}\mathrm{o}\mathrm{l}\mathrm{l}}}$ is the electron collision rate. It is often the case that the electrons are magnetized while the ions are not. Magnetized plasmas are anisotropic, meaning that their properties in the direction parallel to the magnetic field are different from those perpendicular to it. While electric fields in plasmas are usually small due to the plasma high conductivity, the electric field associated with a plasma moving with velocity ${\displaystyle \mathbf{v}}$ in the magnetic field ${\displaystyle \mathbf{B}}$ is given by the usual Lorentz formula ${\displaystyle \mathbf{E}=-\mathbf{v}\times \mathbf{B}}$, and is not affected by Debye shielding.

Mathematical descriptions

The complex self-constricting magnetic field lines and current paths in a field-aligned Birkeland current that can develop in a plasma.

Main article: Plasma modeling

To completely describe the state of a plasma, all of the particle locations and velocities that describe the electromagnetic field in the plasma region would need to be written down. However, it is generally not practical or necessary to keep track of all the particles in a plasma. Therefore, plasma physicists commonly use less detailed descriptions, of which there are two main types:

Fluid model

Fluid models describe plasmas in terms of smoothed quantities, like density and averaged velocity around each position (see Plasma parameters). One simple fluid model, magnetohydrodynamics, treats the plasma as a single fluid governed by a combination of Maxwell's equations and the Navier–Stokes equations. A more general description is the two-fluid plasma, where the ions and electrons are described separately. Fluid models are often accurate when collisionality is sufficiently high to keep the plasma velocity distribution close to a Maxwell–Boltzmann distribution. Because fluid models usually describe the plasma in terms of a single flow at a certain temperature at each spatial location, they can neither capture velocity space structures like beams or double layers, nor resolve wave-particle effects.

Kinetic model

Kinetic models describe the particle velocity distribution function at each point in the plasma and therefore do not need to assume a Maxwell–Boltzmann distribution. A kinetic description is often necessary for collisionless plasmas. There are two common approaches to kinetic description of a plasma. One is based on representing the smoothed distribution function on a grid in velocity and position. The other, known as the particle-in-cell (PIC) technique, includes kinetic information by following the trajectories of a large number of individual particles. Kinetic models are generally more computationally intensive than fluid models. The Vlasov equation may be used to describe the dynamics of a system of charged particles interacting with an electromagnetic field. In magnetized plasmas, a gyrokinetic approach can substantially reduce the computational expense of a fully kinetic simulation.

Plasma science and technology

Plasmas are studied by the vast academic field of plasma science or plasma physics, including several sub-disciplines such as space plasma physics.

Plasmas can appear in nature in various forms and locations, with a few examples given in the following table:

Common forms of plasma

Artificially produced	Terrestrial plasmas	Space and astrophysical plasmas
In plasma displays, including TV screens. Inside fluorescent lamps (low energy lighting), neon signs Rocket exhaust and ion thrusters The area in front of a spacecraft's heat shield during re-entry into the atmosphere Plasmas in fusion energy research Plasma globe (sometimes called plasma sphere or plasma ball) Laser-produced plasmas (LPP), found when high power lasers interact with materials	Lightning The magnetosphere contains plasma in the Earth's surrounding space environment The ionosphere The polar aurorae Upper-atmospheric lightning, including sprites, blue jets, blue starters, gigantic jets, ELVESs St. Elmo's fire Fire (if sufficiently hot)	Stars (plasmas heated by nuclear fusion) The solar wind The interplanetary medium (space between planets) The interstellar medium (space between star systems) The Intergalactic medium (space between galaxies) Accretion disks Interstellar nebulae

Space and astrophysics

Further information: Astrophysical plasma

Plasmas are by far the most common phase of ordinary matter in the universe, both by mass and by volume.

Above the Earth's surface, the ionosphere is a plasma, and the magnetosphere contains plasma. Within our Solar System, interplanetary space is filled with the plasma expelled via the solar wind, extending from the Sun's surface out to the heliopause. Furthermore, all the distant stars, and much of interstellar space or intergalactic space is also filled with plasma, albeit at very low densities. Astrophysical plasmas are also observed in accretion disks around stars or compact objects like white dwarfs, neutron stars, or black holes in close binary star systems. Plasma is associated with ejection of material in astrophysical jets, which have been observed with accreting black holes or in active galaxies like M87's jet that possibly extends out to 5,000 light-years.

Artificial plasmas

Most artificial plasmas are generated by the application of electric and/or magnetic fields through a gas. Plasma generated in a laboratory setting and for industrial use can be generally categorized by:

• The type of power source used to generate the plasma—DC, AC (typically with radio frequency (RF)) and microwave
• The pressure they operate at—vacuum pressure (< 10 mTorr or 1 Pa), moderate pressure (≈1 Torr or 100 Pa), atmospheric pressure (760 Torr or 100 kPa)
• The degree of ionization within the plasma—fully, partially, or weakly ionized
• The temperature relationships within the plasma—thermal plasma (${\displaystyle T_e=T_i=T_{\text{gas}}}$), non-thermal or "cold" plasma (${\displaystyle T_e\gg T_i=T_{\text{gas}}}$)
• The electrode configuration used to generate the plasma
• The magnetization of the particles within the plasma—magnetized (both ion and electrons are trapped in Larmor orbits by the magnetic field), partially magnetized (the electrons but not the ions are trapped by the magnetic field), non-magnetized (the magnetic field is too weak to trap the particles in orbits but may generate Lorentz forces)

Generation of artificial plasma

Artificial plasma produced in air by a Jacob's Ladder

Just like the many uses of plasma, there are several means for its generation. However, one principle is common to all of them: there must be energy input to produce and sustain it. For this case, plasma is generated when an electric current is applied across a dielectric gas or fluid (an electrically non-conducting material) as can be seen in the adjacent image, which shows a discharge tube as a simple example (DC used for simplicity).

The potential difference and subsequent electric field pull the bound electrons (negative) toward the anode (positive electrode) while the cathode (negative electrode) pulls the nucleus. As the voltage increases, the current stresses the material (by electric polarization) beyond its dielectric limit (termed strength) into a stage of electrical breakdown, marked by an electric spark, where the material transforms from being an insulator into a conductor (as it becomes increasingly ionized). The underlying process is the Townsend avalanche, where collisions between electrons and neutral gas atoms create more ions and electrons (as can be seen in the figure on the right). The first impact of an electron on an atom results in one ion and two electrons. Therefore, the number of charged particles increases rapidly (in the millions) only "after about 20 successive sets of collisions", mainly due to a small mean free path (average distance travelled between collisions).

Electric arc

Cascade process of ionization. Electrons are "e−", neutral atoms "o", and cations "+".

Avalanche effect between two electrodes. The original ionization event liberates one electron, and each subsequent collision liberates a further electron, so two electrons emerge from each collision: the ionizing electron and the liberated electron.

Electric arc is a continuous electric discharge between two electrodes, similar to lightning. With ample current density, the discharge forms a luminous arc, where the inter-electrode material (usually, a gas) undergoes various stages — saturation, breakdown, glow, transition, and thermal arc. The voltage rises to its maximum in the saturation stage, and thereafter it undergoes fluctuations of the various stages, while the current progressively increases throughout. Electrical resistance along the arc creates heat, which dissociates more gas molecules and ionizes the resulting atoms. Therefore, the electrical energy is given to electrons, which, due to their great mobility and large numbers, are able to disperse it rapidly by elastic collisions to the heavy particles.

Examples of industrial plasma

Plasmas find applications in many fields of research, technology and industry, for example, in industrial and extractive metallurgy, surface treatments such as plasma spraying (coating), etching in microelectronics, metal cutting and welding; as well as in everyday vehicle exhaust cleanup and fluorescent/luminescent lamps, fuel ignition, and even in supersonic combustion engines for aerospace engineering.

Low-pressure discharges

• Glow discharge plasmas: non-thermal plasmas generated by the application of DC or low frequency RF (<100 kHz) electric field to the gap between two metal electrodes. Probably the most common plasma; this is the type of plasma generated within fluorescent light tubes.
• Capacitively coupled plasma (CCP): similar to glow discharge plasmas, but generated with high frequency RF electric fields, typically 13.56 MHz. These differ from glow discharges in that the sheaths are much less intense. These are widely used in the microfabrication and integrated circuit manufacturing industries for plasma etching and plasma enhanced chemical vapor deposition.
• Cascaded arc plasma source: a device to produce low temperature (≈1eV) high density plasmas (HDP).
• Inductively coupled plasma (ICP): similar to a CCP and with similar applications but the electrode consists of a coil wrapped around the chamber where plasma is formed.
• Wave heated plasma: similar to CCP and ICP in that it is typically RF (or microwave). Examples include helicon discharge and electron cyclotron resonance (ECR).

Atmospheric pressure

• Arc discharge: this is a high power thermal discharge of very high temperature (≈10,000 K). It can be generated using various power supplies. It is commonly used in metallurgical processes. For example, it is used to smelt minerals containing Al₂O₃ to produce aluminium.
• Corona discharge: this is a non-thermal discharge generated by the application of high voltage to sharp electrode tips. It is commonly used in ozone generators and particle precipitators.
• Dielectric barrier discharge (DBD): this is a non-thermal discharge generated by the application of high voltages across small gaps wherein a non-conducting coating prevents the transition of the plasma discharge into an arc. It is often mislabeled "Corona" discharge in industry and has similar application to corona discharges. A common usage of this discharge is in a plasma actuator for vehicle drag reduction. It is also widely used in the web treatment of fabrics. The application of the discharge to synthetic fabrics and plastics functionalizes the surface and allows for paints, glues and similar materials to adhere. The dielectric barrier discharge was used in the mid-1990s to show that low temperature atmospheric pressure plasma is effective in inactivating bacterial cells. This work and later experiments using mammalian cells led to the establishment of a new field of research known as plasma medicine. The dielectric barrier discharge configuration was also used in the design of low temperature plasma jets. These plasma jets are produced by fast propagating guided ionization waves known as plasma bullets.
• Capacitive discharge: this is a nonthermal plasma generated by the application of RF power (e.g., 13.56 MHz) to one powered electrode, with a grounded electrode held at a small separation distance on the order of 1 cm. Such discharges are commonly stabilized using a noble gas such as helium or argon.
• "Piezoelectric direct discharge plasma:" is a nonthermal plasma generated at the high side of a piezoelectric transformer (PT). This generation variant is particularly suited for high efficient and compact devices where a separate high voltage power supply is not desired.

MHD converters

Main articles: magnetohydrodynamic converter, magnetohydrodynamic generator, and magnetohydrodynamic drive

See also: Electrothermal instability

A world effort was triggered in the 1960s to study magnetohydrodynamic converters in order to bring MHD power conversion to market with commercial power plants of a new kind, converting the kinetic energy of a high velocity plasma into electricity with no moving parts at a high efficiency. Research was also conducted in the field of supersonic and hypersonic aerodynamics to study plasma interaction with magnetic fields to eventually achieve passive and even active flow control around vehicles or projectiles, in order to soften and mitigate shock waves, lower thermal transfer and reduce drag.

Such ionized gases used in "plasma technology" ("technological" or "engineered" plasmas) are usually weakly ionized gases in the sense that only a tiny fraction of the gas molecules are ionized. These kinds of weakly ionized gases are also nonthermal "cold" plasmas. In the presence of magnetics fields, the study of such magnetized nonthermal weakly ionized gases involves resistive magnetohydrodynamics with low magnetic Reynolds number, a challenging field of plasma physics where calculations require dyadic tensors in a 7-dimensional phase space. When used in combination with a high Hall parameter, a critical value triggers the problematic electrothermal instability which limited these technological developments.

Complex plasma phenomena

Although the underlying equations governing plasmas are relatively simple, plasma behaviour is extraordinarily varied and subtle: the emergence of unexpected behaviour from a simple model is a typical feature of a complex system. Such systems lie in some sense on the boundary between ordered and disordered behaviour and cannot typically be described either by simple, smooth, mathematical functions, or by pure randomness. The spontaneous formation of interesting spatial features on a wide range of length scales is one manifestation of plasma complexity. The features are interesting, for example, because they are very sharp, spatially intermittent (the distance between features is much larger than the features themselves), or have a fractal form. Many of these features were first studied in the laboratory, and have subsequently been recognized throughout the universe. Examples of complexity and complex structures in plasmas include:

Filamentation

Striations or string-like structures are seen in many plasmas, like the plasma ball, the aurora, lightning, electric arcs, solar flares, and supernova remnants. They are sometimes associated with larger current densities, and the interaction with the magnetic field can form a magnetic rope structure. (See also Plasma pinch)

Filamentation also refers to the self-focusing of a high power laser pulse. At high powers, the nonlinear part of the index of refraction becomes important and causes a higher index of refraction in the center of the laser beam, where the laser is brighter than at the edges, causing a feedback that focuses the laser even more. The tighter focused laser has a higher peak brightness (irradiance) that forms a plasma. The plasma has an index of refraction lower than one, and causes a defocusing of the laser beam. The interplay of the focusing index of refraction, and the defocusing plasma makes the formation of a long filament of plasma that can be micrometers to kilometers in length. One interesting aspect of the filamentation generated plasma is the relatively low ion density due to defocusing effects of the ionized electrons. (See also Filament propagation)

Impermeable plasma

Impermeable plasma is a type of thermal plasma which acts like an impermeable solid with respect to gas or cold plasma and can be physically pushed. Interaction of cold gas and thermal plasma was briefly studied by a group led by Hannes Alfvén in 1960s and 1970s for its possible applications in insulation of fusion plasma from the reactor walls. However, later it was found that the external magnetic fields in this configuration could induce kink instabilities in the plasma and subsequently lead to an unexpectedly high heat loss to the walls.

In 2013, a group of materials scientists reported that they have successfully generated stable impermeable plasma with no magnetic confinement using only an ultrahigh-pressure blanket of cold gas. While spectroscopic data on the characteristics of plasma were claimed to be difficult to obtain due to the high pressure, the passive effect of plasma on synthesis of different nanostructures clearly suggested the effective confinement. They also showed that upon maintaining the impermeability for a few tens of seconds, screening of ions at the plasma-gas interface could give rise to a strong secondary mode of heating (known as viscous heating) leading to different kinetics of reactions and formation of complex nanomaterials.

Efficient coding hypothesis

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Efficient_coding_hypothesis 

The efficient coding hypothesis was proposed by Horace Barlow in 1961 as a theoretical model of sensory coding in the brain. Within the brain, neurons communicate with one another by sending electrical impulses referred to as action potentials or spikes. One goal of sensory neuroscience is to decipher the meaning of these spikes in order to understand how the brain represents and processes information about the outside world.

Barlow hypothesized that the spikes in the sensory system formed a neural code for efficiently representing sensory information. By efficient it is understood that the code minimized the number of spikes needed to transmit a given signal. This is somewhat analogous to transmitting information across the internet, where different file formats can be used to transmit a given image. Different file formats require different numbers of bits for representing the same image at a given distortion level, and some are better suited for representing certain classes of images than others. According to this model, the brain is thought to use a code which is suited for representing visual and audio information which is representative of an organism's natural environment .

Labeled Neuron

Efficient coding and information theory

The development of Barlow's hypothesis was influenced by information theory introduced by Claude Shannon only a decade before. Information theory provides a mathematical framework for analyzing communication systems. It formally defines concepts such as information, channel capacity, and redundancy. Barlow's model treats the sensory pathway as a communication channel where neuronal spiking is an efficient code for representing sensory signals. The spiking code aims to maximize available channel capacity by minimizing the redundancy between representational units. H. Barlow was not the first to introduce the idea. It already appears in a 1954 article written by F. Attneave.

A key prediction of the efficient coding hypothesis is that sensory processing in the brain should be adapted to natural stimuli. Neurons in the visual (or auditory) system should be optimized for coding images (or sounds) representative of those found in nature. Researchers have shown that filters optimized for coding natural images lead to filters which resemble the receptive fields of simple-cells in V1. In the auditory domain, optimizing a network for coding natural sounds leads to filters which resemble the impulse response of cochlear filters found in the inner ear.

Constraints on the visual system

Due to constraints on the visual system such as the number of neurons and the metabolic energy required for "neural activities", the visual processing system must have an efficient strategy for transmitting as much information as possible. Information must be compressed as it travels from the retina back to the visual cortex. While the retinal receptors can receive information at 10^9 bit/s, the optic nerve, which is composed of 1 million ganglion cells transmitting at 1 bit/sec, only has a transmission capacity of 10^6 bit/s. Further reduction occurs that limits the overall transmission to 40 bit/s which results in inattentional blindness. Thus, the hypothesis states that neurons should encode information as efficiently as possible in order to maximize neural resources. For example, it has been shown that visual data can be compressed up to 20 fold without noticeable information loss.

Evidence suggests that our visual processing system engages in bottom-up selection. For example, inattentional blindness suggests that there must be data deletion early on in the visual pathway. This bottom-up approach allows us to respond to unexpected and salient events more quickly and is often directed by attentional selection. This also gives our visual system the property of being goal-directed. Many have suggested that the visual system is able to work efficiently by breaking images down into distinct components. Additionally, it has been argued that the visual system takes advantage of redundancies in inputs in order to transmit as much information as possible while using the fewest resources.

Evolution-based neural system

Simoncelli and Olshausen outline the three major concepts that are assumed to be involved in the development of systems neuroscience:

1. an organism has specific tasks to perform
2. neurons have capabilities and limitations
3. an organism is in a particular environment.

One assumption used in testing the Efficient Coding Hypothesis is that neurons must be evolutionarily and developmentally adapted to the natural signals in their environment. The idea is that perceptual systems will be the quickest when responding to "environmental stimuli". The visual system should cut out any redundancies in the sensory input.

Natural images and statistics

Central to Barlow's hypothesis is information theory, which when applied to neuroscience, argues that an efficiently coding neural system "should match the statistics of the signals they represent". Therefore, it is important to be able to determine the statistics of the natural images that are producing these signals. Researchers have looked at various components of natural images including luminance contrast, color, and how images are registered over time. They can analyze the properties of natural scenes via digital cameras, spectrophotometers, and range finders.

Researchers look at how luminance contrasts are spatially distributed in an image: the luminance contrasts are highly correlated the closer they are in measurable distance and less correlated the farther apart the pixels are. Independent component analysis (ICA) is an algorithm system that attempts to "linearly transform given (sensory) inputs into independent outputs (synaptic currents) ". ICA eliminates the redundancy by decorrelating the pixels in a natural image. Thus the individual components that make up the natural image are rendered statistically independent. However, researchers have thought that ICA is limited because it assumes that the neural response is linear, and therefore insufficiently describes the complexity of natural images. They argue that, despite what is assumed under ICA, the components of the natural image have a "higher-order structure" that involves correlations among components. Instead, researchers have now developed temporal independent component analysis (TICA), which better represents the complex correlations that occur between components in a natural image. Additionally, a "hierarchical covariance model" developed by Karklin and Lewicki expands on sparse coding methods and can represent additional components of natural images such as "object location, scale, and texture".

The chromatic spectrum as it comes from natural light, but also as it is reflected off of "natural materials", can be easily characterized with principal components analysis (PCA). Because the cones are absorbing a specific amount of photons from the natural image, researchers can use cone responses as a way of describing the natural image. Researchers have found that the three classes of cone receptors in the retina can accurately code natural images and that color is decorrelated already in the LGN.Time has also been modeled. Natural images transform over time, and we can use these transformations to see how the visual input changes over time.

A padegogical review of efficient coding in visual processing --- efficient spatial coding, color coding, temporal/motion coding, stereo coding, and the combination of them --- is in chapter 3 of the book "Understanding vision: theory, models, and data". It explains how efficient coding is realized when input noise makes redundancy reduction no longer adequate, and how efficient coding methods in different situations are related to each other or different from each other.

Hypotheses for testing the efficient coding hypothesis

If neurons are encoding according to the efficient coding hypothesis then individual neurons must be expressing their full output capacity. Before testing this hypothesis it is necessary to define what is considered to be a neural response. Simoncelli and Olshausen suggest that an efficient neuron needs to be given a maximal response value so that we can measure if a neuron is efficiently meeting the maximum level. Secondly, a population of neurons must not be redundant in transmitting signals and must be statistically independent. If the efficient coding hypothesis is accurate, researchers should observe is that there is sparsity in the neuron responses: that is, only a few neurons at a time should fire for an input.

Methodological approaches for testing the hypotheses

One approach is to design a model for early sensory processing based on the statistics of a natural image and then compare this predicted model to how real neurons actually respond to the natural image. The second approach is to measure a neural system responding to a natural environment, and analyze the results to see if there are any statistical properties to this response. A third approach is to derive the necessary and sufficient conditions under which an observed neural computation is efficient, and test whether empirical stimulus statistics satisfy them.

Examples of these approaches

1. Predicted model approach

In one study by Doi et al. in 2012, the researchers created a predicted response model of the retinal ganglion cells that would be based on the statistics of the natural images used, while considering noise and biological constraints. They then compared the actual information transmission as observed in real retinal ganglion cells to this optimal model to determine the efficiency. They found that the information transmission in the retinal ganglion cells had an overall efficiency of about 80% and concluded that "the functional connectivity between cones and retinal ganglion cells exhibits unique spatial structure...consistent with coding efficiency.

A study by van Hateren and Ruderman in 1998 used ICA to analyze video-sequences and compared how a computer analyzed the independent components of the image to data for visual processing obtained from a cat in DeAngelis et al. 1993. The researchers described the independent components obtained from a video sequence as the "basic building blocks of a signal", with the independent component filter (ICF) measuring "how strongly each building block is present". They hypothesized that if simple cells are organized to pick out the "underlying structure" of images over time then cells should act like the independent component filters. They found that the ICFs determined by the computer were similar to the "receptive fields" that were observed in actual neurons.

Primary visual cortex location on the right side of the figure

2. Analyzing actual neural system in response to natural images

In a report in Science from 2000, William E. Vinje and Jack Gallant outlined a series of experiments used to test elements of the efficient coding hypothesis, including a theory that the non-classical receptive field (nCRF) decorrelates projections from the primary visual cortex. To test this, they took recordings from the V1 neurons in awake macaques during "free viewing of natural images and conditions" that simulated natural vision conditions. The researchers hypothesized that the V1 uses sparse code, which is minimally redundant and "metabolically more efficient".

They also hypothesized that interactions between the classical receptive field (CRF) and the nCRF produced this pattern of sparse coding during the viewing of these natural scenes. In order to test this, they created eye-scan paths and also extracted patches that ranged in size from 1-4 times the diameter of the CRF. They found that the sparseness of the coding increased with the size of the patch. Larger patches encompassed more of the nCRF—indicating that the interactions between these two regions created sparse code. Additionally as stimulus size increased, so did the sparseness. This suggests that the V1 uses sparse code when natural images span the entire visual field. The CRF was defined as the circular area surrounding the locations where stimuli evoked action potentials. They also tested to see if stimulation of the nCRF increased the independence of the responses from the V1 neurons by randomly selecting pairs of neurons. They found that indeed, the neurons were more greatly decoupled upon stimulation of the nCRF.

In conclusion, the experiments of Vinje and Gallant showed that the V1 uses sparse code by employing both the CRF and nCRF when viewing natural images, with the nCRF showing a definitive decorrelating effect on neurons which may increase their efficiency by increasing the amount of independent information they carry. They propose that the cells may represent the individual components of a given natural scene, which may contribute to pattern recognition

Another study done by Baddeley et al. had shown that firing-rate distributions of cat visual area V1 neurons and monkey inferotemporal (IT) neurons were exponential under naturalistic conditions, which implies optimal information transmission for a fixed average rate of firing. A subsequent study of monkey IT neurons found that only a minority were well described by an exponential firing distribution. De Polavieja later argued that this discrepancy was due to the fact that the exponential solution is correct only for the noise-free case, and showed that by taking noise into consideration, one could account for the observed results.

A study by Dan, Attick, and Reid in 1996 used natural images to test the hypothesis that early on in the visual pathway, incoming visual signals will be decorrelated to optimize efficiency. This decorrelation can be observed as the '"whitening" of the temporal and spatial power spectra of the neuronal signals". The researchers played natural image movies in front of cats and used a multielectrode array to record neural signals. This was achieved by refracting the eyes of the cats and then contact lenses being fitted into them. They found that in the LGN, the natural images were decorrelated and concluded, "the early visual pathway has specifically adapted for efficient coding of natural visual information during evolution and/or development".

Extensions

One of the implications of the efficient coding hypothesis is that the neural coding depends upon the statistics of the sensory signals. These statistics are a function of not only the environment (e.g., the statistics of the natural environment), but also the organism's behavior (e.g., how it moves within that environment). However, perception and behavior are closely intertwined in the perception-action cycle. For example, the process of vision involves various kinds of eye movements. An extension to the efficient coding hypothesis called active efficient coding (AEC) extends efficient coding to active perception. It hypothesizes that biological agents optimize not only their neural coding, but also their behavior to contribute to an efficient sensory representation of the environment. Along these lines, models for the development of active binocular vision, active visual tracking, and accommodation control have been proposed.

The brain has limited resources to process information, in vision this is manifested as the visual attentional bottleneck. The bottleneck forces the brain to select only a small fraction of visual input information for further processing, as merely coding information efficiently is no longer sufficient. A subsequent theory, V1 Saliency Hypothesis, has been developed on exogenous attentional selection of visual input information for further processing guided by a bottom-up saliency map in the primary visual cortex.

Criticisms

Researchers should consider how the visual information is used: The hypothesis does not explain how the information from a visual scene is used—which is the main purpose of the visual system. It seems necessary to understand why we are processing image statistics from the environment because this may be relevant to how this information is ultimately processed. However, some researchers may see the irrelevance of the purpose of vision in Barlow's theory as an advantage for designing experiments.

Some experiments show correlations between neurons: When considering multiple neurons at a time, recordings "show correlation, synchronization, or other forms of statistical dependency between neurons". However, it is relevant to note that most of these experiments did not use natural stimuli to provoke these responses: this may not fit in directly to the efficient coding hypothesis because this hypothesis is concerned with natural image statistics. In his review article Simoncelli notes that perhaps we can interpret redundancy in the Efficient Coding Hypothesis a bit differently: he argues that statistical dependency could be reduced over "successive stages of processing", and not just in one area of the sensory pathway. Yet, recordings by Hung et al. at the end of the visual pathway also show strong layer-dependent correlations to naturalistic objects and in ongoing activity. They showed that redundancy of neighboring neurons (i.e. a 'manifold' representation) benefits learning of complex shape features and that network anisotropy/inhomogeneity is a stronger predictor than noise redundancy of encoding/decoding efficiency.

Observed redundancy: A comparison of the number of retinal ganglion cells to the number of neurons in the primary visual cortex shows an increase in the number of sensory neurons in the cortex as compared to the retina. Simoncelli notes that one major argument of critics in that higher up in the sensory pathway there are greater numbers of neurons that handle the processing of sensory information so this should seem to produce redundancy. However, this observation may not be fully relevant because neurons have different neural coding. In his review, Simoncelli notes "cortical neurons tend to have lower firing rates and may use a different form of code as compared to retinal neurons". Cortical Neurons may also have the ability to encode information over longer periods of time than their retinal counterparts. Experiments done in the auditory system have confirmed that redundancy is decreased.

Difficult to test: Estimation of information-theoretic quantities requires enormous amounts of data, and is thus impractical for experimental verification. Additionally, informational estimators are known to be biased. However, some experimental success has occurred.

Need well-defined criteria for what to measure: This criticism illustrates one of the most fundamental issues of the hypothesis. Here, assumptions are made about the definitions of both the inputs and the outputs of the system. The inputs into the visual system are not completely defined, but they are assumed to be encompassed in a collection of natural images. The output must be defined to test the hypothesis, but variability can occur here too based on the choice of which type of neurons to measure, where they are located and what type of responses, such as firing rate or spike times are chosen to be measured.

How to take noise into account: Some argue that experiments that ignore noise, or other physical constraints on the system are too simplistic. However, some researchers have been able to incorporate these elements into their analyses, thus creating more sophisticated systems.

However, with appropriate formulations, efficient coding can also address some of these issues raised above. For example, some quantifiable degree of redundancies in neural representations of sensory inputs (manifested as correlations in neural responses) is predicted to occur when efficient coding is applied to noisy sensory inputs. Falsifiable theoretical predictions can also be made, and some of them subsequently tested.

Biomedical applications

Cochlear Implant

Possible applications of the efficient coding hypothesis include cochlear implant design. These neuroprosthetic devices stimulate the auditory nerve by an electrical impulses which allows some of the hearing to return to people who have hearing impairments or are even deaf. The implants are considered to be successful and efficient and the only ones in use currently. Using frequency-place mappings in the efficient coding algorithm may benefit in the use of cochlear implants in the future. Changes in design based on this hypothesis could increase speech intelligibility in hearing impaired patients. Research using vocoded speech processed by different filters showed that humans had greater accuracy in deciphering the speech when it was processed using an efficient-code filter as opposed to a cochleotropic filter or a linear filter. This shows that efficient coding of noise data offered perceptual benefits and provided the listeners with more information. More research is needed to apply current findings into medically relevant changes to cochlear implant design.