# Attenuation

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In physics, attenuation or, in some contexts, extinction is the gradual loss of flux intensity through a medium. For instance, dark glasses attenuate sunlight, lead attenuates X-rays, and water and air attenuate both light and sound at variable attenuation rates.

Physics is the natural science that studies matter and its motion and behavior through space and time and that studies the related entities of energy and force. Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves.

Flux describes any effect that appears to pass or travel through a surface or substance. A flux is either a concept based in physics or used with applied mathematics. Both concepts have mathematical rigor, enabling comparison of the underlying mathematics when the terminology is unclear. For transport phenomena, flux is a vector quantity, describing the magnitude and direction of the flow of a substance or property. In electromagnetism, flux is a scalar quantity, defined as the surface integral of the component of a vector field perpendicular to the surface at each point.

A transmission medium is a material substance that can propagate energy waves. For example, the transmission medium for sounds is usually a gas, but solids and liquids may also act as a transmission medium for sound.

## Contents

Hearing protectors help reduce acoustic flux from flowing into the ears. This phenomenon is called acoustic attenuation and is measured in decibels (dBs).

Sound power or acoustic power is the rate at which sound energy is emitted, reflected, transmitted or received, per unit time. The SI unit of sound power is the watt (W). It is the power of the sound force on a surface of the medium of propagation of the sound wave. For a sound source, unlike sound pressure, sound power is neither room-dependent nor distance-dependent. Sound pressure is a property of the field at a point in space, while sound power is a property of a sound source, equal to the total power emitted by that source in all directions. Sound power passing through an area is sometimes called sound flux or acoustic flux through that area.

Acoustic attenuation is a measure of the energy loss of sound propagation in media. Most media have viscosity, and are therefore not ideal media. When sound propagates in such media, there is always thermal consumption of energy caused by viscosity. For inhomogeneous media, besides media viscosity, acoustic scattering is another main reason for removal of acoustic energy. Acoustic attenuation in a lossy medium plays an important role in many scientific researches and engineering fields, such as medical ultrasonography, vibration and noise reduction.

The decibel is a unit of measurement used to express the ratio of one value of a power or field quantity to another on a logarithmic scale, the logarithmic quantity being called the power level or field level, respectively. It can be used to express a change in value or an absolute value. In the latter case, it expresses the ratio of a value to a fixed reference value; when used in this way, a suffix that indicates the reference value is often appended to the decibel symbol. For example, if the reference value is 1 volt, then the suffix is "V", and if the reference value is one milliwatt, then the suffix is "m".

In electrical engineering and telecommunications, attenuation affects the propagation of waves and signals in electrical circuits, in optical fibers, and in air. Electrical attenuators and optical attenuators are commonly manufactured components in this field.

Electrical engineering is a professional engineering discipline that generally deals with the study and application of electricity, electronics, and electromagnetism. This field first became an identifiable occupation in the later half of the 19th century after commercialization of the electric telegraph, the telephone, and electric power distribution and use. Subsequently, broadcasting and recording media made electronics part of daily life. The invention of the transistor, and later the integrated circuit, brought down the cost of electronics to the point they can be used in almost any household object.

Telecommunication is the transmission of signs, signals, messages, words, writings, images and sounds or information of any nature by wire, radio, optical or other electromagnetic systems. Telecommunication occurs when the exchange of information between communication participants includes the use of technology. It is transmitted either electrically over physical media, such as cables, or via electromagnetic radiation. Such transmission paths are often divided into communication channels which afford the advantages of multiplexing. Since the Latin term communicatio is considered the social process of information exchange, the term telecommunications is often used in its plural form because it involves many different technologies.

Wave propagation is any of the ways in which waves travel.

## Background

In many cases, attenuation is an exponential function of the path length through the medium. In chemical spectroscopy, this is known as the Beer–Lambert law. In engineering, attenuation is usually measured in units of decibels per unit length of medium (dB/cm, dB/km, etc.) and is represented by the attenuation coefficient of the medium in question. [1] Attenuation also occurs in earthquakes; when the seismic waves move farther away from the hypocenter, they grow smaller as they are attenuated by the ground.

In mathematics, an exponential function is a function of the form

Spectroscopy is the study of the interaction between matter and electromagnetic radiation. Historically, spectroscopy originated through the study of visible light dispersed according to its wavelength, by a prism. Later the concept was expanded greatly to include any interaction with radiative energy as a function of its wavelength or frequency, predominantly in the electromagnetic spectrum, though matter waves and acoustic waves can also be considered forms of radiative energy; recently, with tremendous difficulty, even gravitational waves have been associated with a spectral signature in the context of LIGO and laser interferometry. Spectroscopic data are often represented by an emission spectrum, a plot of the response of interest as a function of wavelength or frequency.

The Beer–Lambert law, also known as Beer's law, the Lambert–Beer law, or the Beer–Lambert–Bouguer law relates the attenuation of light to the properties of the material through which the light is travelling. The law is commonly applied to chemical analysis measurements and used in understanding attenuation in physical optics, for photons, neutrons or rarefied gases. In mathematical physics, this law arises as a solution of the BGK equation.

## Ultrasound

One area of research in which attenuation plays a prominent role, is in ultrasound physics. Attenuation in ultrasound is the reduction in amplitude of the ultrasound beam as a function of distance through the imaging medium. Accounting for attenuation effects in ultrasound is important because a reduced signal amplitude can affect the quality of the image produced. By knowing the attenuation that an ultrasound beam experiences traveling through a medium, one can adjust the input signal amplitude to compensate for any loss of energy at the desired imaging depth. [2]

Ultrasound is sound waves with frequencies higher than the upper audible limit of human hearing. Ultrasound is not different from "normal" (audible) sound in its physical properties, except that humans cannot hear it. This limit varies from person to person and is approximately 20 kilohertz in healthy young adults. Ultrasound devices operate with frequencies from 20 kHz up to several gigahertz.

An emulsion is a mixture of two or more liquids that are normally immiscible. Emulsions are part of a more general class of two-phase systems of matter called colloids. Although the terms colloid and emulsion are sometimes used interchangeably, emulsion should be used when both phases, dispersed and continuous, are liquids. In an emulsion, one liquid is dispersed in the other. Examples of emulsions include vinaigrettes, homogenized milk, and some cutting fluids for metal working.

In chemistry, a colloid is a mixture in which one substance of microscopically dispersed insoluble particles is suspended throughout another substance. Sometimes the dispersed substance alone is called the colloid; the term colloidal suspension refers unambiguously to the overall mixture. Unlike a solution, whose solute and solvent constitute only one phase, a colloid has a dispersed phase and a continuous phase. To qualify as a colloid, the mixture must be one that does not settle or would take a very long time to settle appreciably.

An acoustic rheometer employs a piezo-electric crystal that can easily launch a successive wave of extensions and contractions into the fluid. It applies an oscillating extensional stress to the system. System response can be interpreted in terms of extensional rheology.

Wave equations which take acoustic attenuation into account can be written on a fractional derivative form, see the article on acoustic attenuation or e.g. the survey paper. [4]

### Attenuation coefficient

Attenuation coefficients are used to quantify different media according to how strongly the transmitted ultrasound amplitude decreases as a function of frequency. The attenuation coefficient (${\displaystyle \alpha }$) can be used to determine total attenuation in dB in the medium using the following formula:

${\displaystyle {\text{Attenuation}}=\alpha [{\text{dB}}/({\text{MHz}}\cdot {\text{cm}})]\cdot \ell [{\text{cm}}]\cdot {\text{f}}[{\text{MHz}}]}$

Attenuation is linearly dependent on the medium length and attenuation coefficient, and also –approximately– on the frequency of the incident ultrasound beam for biological tissue (while for simpler media, such as air, the relationship is quadratic). Attenuation coefficients vary widely for different media. In biomedical ultrasound imaging however, biological materials and water are the most commonly used media. The attenuation coefficients of common biological materials at a frequency of 1 MHz are listed below: [5]

Material${\displaystyle \alpha ({\text{dB}}/({\text{MHz}}\cdot {\text{cm}}))}$
Air 1.64 (20 °C) [6]
Blood 0.2
Bone, cortical6.9
Bone, trabecular9.94
Brain 0.6
Breast 0.75
Cardiac 0.52
Connective tissue 1.57
Dentin 80
Enamel 120
Fat 0.48
Liver 0.5
Marrow 0.5
Muscle 1.09
Tendon 4.7
Soft tissue (average) 0.54
Water 0.0022

There are two general ways of acoustic energy losses: absorption and scattering, for instance light scattering. [7] Ultrasound propagation through homogeneous media is associated only with absorption and can be characterized with absorption coefficient only. Propagation through heterogeneous media requires taking into account scattering. [8] Fractional derivative wave equations can be applied for modeling of lossy acoustical wave propagation, see also acoustic attenuation and Ref. [4]

## Light attenuation in water

Main article: Electromagnetic absorption by water

Shortwave radiation emitted from the sun have wavelengths in the visible spectrum of light that range from 360 nm (violet) to 750 nm (red). When the sun's radiation reaches the sea-surface, the shortwave radiation is attenuated by the water, and the intensity of light decreases exponentially with water depth. The intensity of light at depth can be calculated using the Beer-Lambert Law.

In clear open waters, visible light is absorbed at the longest wavelengths first. Thus, red, orange, and yellow wavelengths are absorbed at higher water depths, and blue and violet wavelengths reach the deepest in the water column. Because the blue and violet wavelengths are absorbed last compared to the other wavelengths, open ocean waters appear deep-blue to the eye.

In near-shore (coastal) waters, sea water contains more phytoplankton than the very clear central ocean waters. Chlorophyll-a pigments in the phytoplankton absorb light, and the plants themselves scatter light, making coastal waters less clear than open waters. Chlorophyll-a absorbs light most strongly in the shortest wavelengths (blue and violet) of the visible spectrum. In near-shore waters where there are high concentrations of phytoplankton, the green wavelength reaches the deepest in the water column and the color of water to an observer appears green-blue or green.

## Seismic waves

The energy with which an earthquake affects a location depends on the running distance. The attenuation in the signal of ground motion intensity plays an important role in the assessment of possible strong groundshaking. A seismic wave loses energy as it propagates through the earth (attenuation). This phenomenon is tied into the dispersion of the seismic energy with the distance. There are two types of dissipated energy:

• geometric dispersion caused by distribution of the seismic energy to greater volumes
• dispersion as heat, also called intrinsic attenuation or anelastic attenuation.

## Electromagnetic

Attenuation decreases the intensity of electromagnetic radiation due to absorption or scattering of photons. Attenuation does not include the decrease in intensity due to inverse-square law geometric spreading. Therefore, calculation of the total change in intensity involves both the inverse-square law and an estimation of attenuation over the path.

The primary causes of attenuation in matter are the photoelectric effect, compton scattering, and, for photon energies of above 1.022 MeV, pair production.

The beam of X-ray is attenuated when photons are absorbed when the x-ray beam passes through the tissue. Interaction with matter varies between high energy photons and low energy photons. Photons travelling at higher energy are more capable of travelling through a tissue specimen as they have less chances of interacting with matter. This is mainly due to the photoelectric effect which states that "the probability of photoelectric absorption is approximately proportional to (Z/E)3, where Z is the atomic number of the tissue atom and E is the photon energy. [9] In context of this, an increase in photon energy (E) will result in a rapid decrease in the interaction with matter.

### Optics

Attenuation in fiber optics, also known as transmission loss, is the reduction in intensity of the light beam (or signal) with respect to distance travelled through a transmission medium. Attenuation coefficients in fiber optics usually use units of dB/km through the medium due to the relatively high quality of transparency of modern optical transmission media. The medium is typically a fiber of silica glass that confines the incident light beam to the inside. Attenuation is an important factor limiting the transmission of a digital signal across large distances. Thus, much research has gone into both limiting the attenuation and maximizing the amplification of the optical signal. Empirical research has shown that attenuation in optical fiber is caused primarily by both scattering and absorption. [10]

Attenuation in fiber optics can be quantified using the following equation: [11]

${\displaystyle {\text{Attenuation (dB)}}=10\times \log _{10}\left({\frac {\text{Input intensity (W)}}{\text{Output intensity (W)}}}\right)}$

#### Light scattering

The propagation of light through the core of an optical fiber is based on total internal reflection of the lightwave. Rough and irregular surfaces, even at the molecular level of the glass, can cause light rays to be reflected in many random directions. This type of reflection is referred to as "diffuse reflection", and it is typically characterized by wide variety of reflection angles. Most objects that can be seen with the naked eye are visible due to diffuse reflection. Another term commonly used for this type of reflection is "light scattering". Light scattering from the surfaces of objects is our primary mechanism of physical observation. [12] [13] Light scattering from many common surfaces can be modelled by lambertian reflectance.

Light scattering depends on the wavelength of the light being scattered. Thus, limits to spatial scales of visibility arise, depending on the frequency of the incident lightwave and the physical dimension (or spatial scale) of the scattering center, which is typically in the form of some specific microstructural feature. For example, since visible light has a wavelength scale on the order of one micrometer (one millionth of a meter), scattering centers will have dimensions on a similar spatial scale.

Thus, attenuation results from the incoherent scattering of light at internal surfaces and interfaces. In (poly)crystalline materials such as metals and ceramics, in addition to pores, most of the internal surfaces or interfaces are in the form of grain boundaries that separate tiny regions of crystalline order. It has recently been shown that, when the size of the scattering center (or grain boundary) is reduced below the size of the wavelength of the light being scattered, the scattering no longer occurs to any significant extent. This phenomenon has given rise to the production of transparent ceramic materials.

Likewise, the scattering of light in optical quality glass fiber is caused by molecular-level irregularities (compositional fluctuations) in the glass structure. Indeed, one emerging school of thought is that a glass is simply the limiting case of a polycrystalline solid. Within this framework, "domains" exhibiting various degrees of short-range order become the building-blocks of both metals and alloys, as well as glasses and ceramics. Distributed both between and within these domains are microstructural defects that will provide the most ideal locations for the occurrence of light scattering. This same phenomenon is seen as one of the limiting factors in the transparency of IR missile domes. [14]

#### UV-Vis-IR absorption

In addition to light scattering, attenuation or signal loss can also occur due to selective absorption of specific wavelengths, in a manner similar to that responsible for the appearance of color. Primary material considerations include both electrons and molecules as follows:

• At the electronic level, it depends on whether the electron orbitals are spaced (or "quantized") such that they can absorb a quantum of light (or photon) of a specific wavelength or frequency in the ultraviolet (UV) or visible ranges. This is what gives rise to color.
• At the atomic or molecular level, it depends on the frequencies of atomic or molecular vibrations or chemical bonds, how close-packed its atoms or molecules are, and whether or not the atoms or molecules exhibit long-range order. These factors will determine the capacity of the material transmitting longer wavelengths in the infrared (IR), far IR, radio and microwave ranges.

The selective absorption of infrared (IR) light by a particular material occurs because the selected frequency of the light wave matches the frequency (or an integral multiple of the frequency) at which the particles of that material vibrate. Since different atoms and molecules have different natural frequencies of vibration, they will selectively absorb different frequencies (or portions of the spectrum) of infrared (IR) light.

### Applications

In optical fibers, attenuation is the rate at which the signal light decreases in intensity. For this reason, glass fiber (which has a low attenuation) is used for long-distance fiber optic cables; plastic fiber has a higher attenuation and, hence, shorter range. There also exist optical attenuators that decrease the signal in a fiber optic cable intentionally.

Attenuation of light is also important in physical oceanography. This same effect is an important consideration in weather radar, as raindrops absorb a part of the emitted beam that is more or less significant, depending on the wavelength used.

Due to the damaging effects of high-energy photons, it is necessary to know how much energy is deposited in tissue during diagnostic treatments involving such radiation. In addition, gamma radiation is used in cancer treatments where it is important to know how much energy will be deposited in healthy and in tumorous tissue.

In Computer Graphics attenuation defines the local or global influence of light sources and force fields.

Attenuation is an important consideration in the modern world of wireless telecommunication. Attenuation limits the range of radio signals and is affected by the materials a signal must travel through (e.g., air, wood, concrete, rain). See the article on path loss for more information on signal loss in wireless communication.

## Related Research Articles

Nonlinear optics (NLO) is the branch of optics that describes the behaviour of light in nonlinear media, that is, media in which the polarization density P responds non-linearly to the electric field E of the light. The non-linearity is typically observed only at very high light intensities (values of atomic electric fields, typically 108 V/m) such as those provided by lasers. Above the Schwinger limit, the vacuum itself is expected to become nonlinear. In nonlinear optics, the superposition principle no longer holds.

In physics, optical depth or optical thickness, is the natural logarithm of the ratio of incident to transmitted radiant power through a material, and spectral optical depth or spectral optical thickness is the natural logarithm of the ratio of incident to transmitted spectral radiant power through a material. Optical depth is dimensionless, and in particular is not a length, though it is a monotonically increasing function of optical path length, and approaches zero as the path length approaches zero. The use of the term "optical density" for optical depth is discouraged.

Scattering is a general physical process where some forms of radiation, such as light, sound, or moving particles, are forced to deviate from a straight trajectory by one or more paths due to localized non-uniformities in the medium through which they pass. In conventional use, this also includes deviation of reflected radiation from the angle predicted by the law of reflection. Reflections that undergo scattering are often called diffuse reflections and unscattered reflections are called specular (mirror-like) reflections.

In the field of optics, transparency is the physical property of allowing light to pass through the material without being scattered. On a macroscopic scale, the photons can be said to follow Snell's Law. Translucency is a superset of transparency: it allows light to pass through, but does not necessarily follow Snell's law; the photons can be scattered at either of the two interfaces, or internally, where there is a change in index of refraction. In other words, a translucent medium allows the transport of light while a transparent medium not only allows the transport of light but allows for image formation. Transparent materials appear clear, with the overall appearance of one color, or any combination leading up to a brilliant spectrum of every color. The opposite property of translucency is opacity.

Brillouin scattering, named after Léon Brillouin, refers to the interaction of light and material waves within a medium. It is mediated by the refractive index dependence on the material properties of the medium; as described in optics, the index of refraction of a transparent material changes under deformation.

Raman scattering or the Raman effect {{IPAc-en|ˈ|raman| is the inelastic scattering of a photon by molecules which are excited to higher energy levels. The effect was discovered in 1928 by C. V. Raman and his student K. S. Krishnan in liquids, and independently by Grigory Landsberg and Leonid Mandelstam in crystals. The effect had been predicted theoretically by Adolf Smekal in 1923.

Resonance Raman spectroscopy is a Raman spectroscopy technique in which the incident photon energy is close in energy to an electronic transition of a compound or material under examination. The frequency coincidence can lead to greatly enhanced intensity of the Raman scattering, which facilitates the study of chemical compounds present at low concentrations.

In physics, absorption of electromagnetic radiation is the way in which the energy of a photon is taken up by matter, typically the electrons of an atom. Thus, the electromagnetic energy is transformed into internal energy of the absorber, for example thermal energy. The reduction in intensity of a light wave propagating through a medium by absorption of a part of its photons is often called attenuation. Usually, the absorption of waves does not depend on their intensity, although in certain conditions, the medium changes its transparency dependently on the intensity of waves going through, and saturable absorption occurs.

Functional Near-Infrared Spectroscopy (fNIRS), is the use of near-infrared spectroscopy (NIRS) for the purpose of functional neuroimaging. Using fNIRS, brain activity is measured through hemodynamic responses associated with neuron behaviour.

Ultrafast laser spectroscopy is a spectroscopic technique that uses ultrashort pulse lasers for the study of dynamics on extremely short time scales. Different methods are used to examine dynamics of charge carriers, atoms and molecules. Many different procedures have been developed spanning different time scales and photon energy ranges; some common methods are listed below.

Two-photon absorption (TPA) is the absorption of two photons of identical or different frequencies in order to excite a molecule from one state to a higher energy, most commonly an excited electronic state. The energy difference between the involved lower and upper states of the molecule is equal to the sum of the photon energies of the two photons absorbed. Two-photon absorption is a third-order process, typically several orders of magnitude weaker than linear absorption at low light intensities. It differs from linear absorption in that the optical transition rate due to TPA depends on the square of the light intensity, thus it is a nonlinear optical process, and can dominate over linear absorption at high intensities.

The attenuation coefficient or narrow-beam attenuation coefficient characterizes how easily a volume of material can be penetrated by a beam of light, sound, particles, or other energy or matter. A large attenuation coefficient means that the beam is quickly "attenuated" (weakened) as it passes through the medium, and a small attenuation coefficient means that the medium is relatively transparent to the beam. The SI unit of attenuation coefficient is the reciprocal metre (m−1). Extinction coefficient is an old term for this quantity but is still used in meteorology and climatology. Most commonly, the quantity measures the number of downward e-foldings of the original intensity that will be had as the energy passes through a unit thickness of material, so that an attenuation coefficient of 1 m-1 means that after passing through 1 metre, the radiation will be reduced by a factor of e, and for material with a coefficient of 2 m-1, it will be reduced twice by e, or e2. Other measures may use a different factor than e, such as the decadic attenuation coefficient below.

The photoacoustic Doppler effect, as its name implies, is one specific kind of Doppler effect, which occurs when an intensely modulated light wave induces a photoacoustic wave on moving particles with a specific frequency. The observed frequency shift is a good indicator of the velocity of the illuminated moving particles. A potential biomedical application is measuring blood flow.

An optical modulator is an optical device which is used to modulate a beam of light with a perturbation device. It is a kind of transmitter to convert information to optical binary signal through optical fiber or transmission medium of optical frequency in fiber optic communication. There are several methods to manipulate this device depending on the parameter of a light beam like amplitude modulator (majority), phase modulator, polarization modulator etc. The easiest way to obtain modulation is modulation of intensity of a light by the current driving the light source. This sort of modulation is called direct modulation, as opposed to the external modulation performed by a light modulator. For this reason, light modulators are called external light modulators. According to manipulation of the properties of material modulators are divided into two groups, absorptive modulators and refractive modulators. Absorption coefficient can be manipulated by Franz-Keldysh effect, Quantum-Confined Stark Effect, excitonic absorption, or changes of free carrier concentration. Usually, if several such effects appear together, the modulator is called electro-absorptive modulator. Refractive modulators most often make use of electro-optic effect, other modulators are made with acousto-optic effect, magneto-optic effect such as Faraday and Cotton-Mouton effects. The other case of modulators is spatial light modulator (SLM) which is modified two dimensional distribution of amplitude & phase of an optical wave.

Photoelectrochemical processes are processes in photoelectrochemistry; they usually involve transforming light into other forms of energy. These processes apply to photochemistry, optically pumped lasers, sensitized solar cells, luminescence, and photochromism.

Multi-spectral optoacoustic tomography (MSOT), also known as functional photoacoustic tomography (fPAT), is an imaging technology that generates high-resolution optical images in scattering media, including biological tissues. MSOT illuminates tissue with light of transient energy, typically light pulses lasting 1-100 nanoseconds. The tissue absorbs the light pulses, and as a result undergoes thermo-elastic expansion, a phenomenon known as the optoacoustic or photoacoustic effect. This expansion gives rise to ultrasound waves (photoechoes) that are detected and formed into an image. Image formation can be done by means of hardware or computed tomography. Unlike other types of optoacoustic imaging, MSOT involves illuminating the sample with multiple wavelengths, allowing it to detect ultrasound waves emitted by different photoabsorbing molecules in the tissue, whether endogenous or exogenous. Computational techniques such as spectral unmixing deconvolute the ultrasound waves emitted by these different absorbers, allowing each emitter to be visualized separately in the target tissue. In this way, MSOT can allow visualization of hemoglobin concentration and tissue oxygenation or hypoxia. Unlike other optical imaging methods, MSOT is unaffected by photon scattering and thus can provide high-resolution optical images deep inside biological tissues.

Photoacoustic microscropy is an imaging method based on the photoacoustic effect and is a subset of photoacoustic tomography. Photoacoustic microscopy takes advantage of the local temperature rise that occurs as a result of light absorption in tissue. Using a nanosecond pulsed laser beam, tissues undergo thermoelastic expansion, resulting in the release of a wide-band acoustic wave that can be detected using a high-frequency ultrasound transducer. Since ultrasonic scattering in tissue is weaker than optical scattering, photoacoustic microscopy is capable of achieving high-resolution images at greater depths than conventional microscopy methods. Furthermore, photoacoustic microscopy is especially useful in the field of biomedical imaging due to its scalability. By adjusting the optical and acoustic foci, lateral resolution may be optimized for the desired imaging depth.

The collimated transmission method is a direct way of measuring the optical properties of materials. It is especially useful for sensing the optical properties of tissues to guide developments of both diagnostic and therapeutic techniques. These optical properties are described by the absorption coefficient μa, scattering coefficient μs, and anisotropy factor g.

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