# Attenuation

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In physics, attenuation (in some contexts also called extinction) is the gradual loss in intensity of any kind of flux through a medium. For instance, sunlight is attenuated by dark glasses, and X-rays are attenuated by lead.

In electrical engineering and telecommunications, attenuation affects the propagation of waves and signals in electrical circuits, in optical fibres, as well as in air (radio waves).

## Background Edit

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 grow smaller and smaller farther away from the epicenter.

## UltrasoundEdit

One area of research in which attenuation figures strongly 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]

### Attenuation coefficientEdit

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 ($\alpha$) can be used to determine total attenuation in dB in the medium using the following formula:

$\mathrm{Attenuation[dB]} = \alpha\mathrm{[dB/(MHz*cm)]}\cdot\mathit{l}\mathrm{[cm]}\cdot\mathrm{f[MHz]}$

As this equation shows, besides the medium length and attenuation coefficient, attenuation is also linearly dependent on the frequency of the incident ultrasound beam. 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:[2]

Material $\alpha\mathrm{(dB/(MHz*cm))}$
Lung 41
Bone 20
Kidney 1.0
Liver 0.94
Brain 0.85
Fat 0.63
Blood 0.18
Water 0.23222

There are two general ways of acoustic energy losses: absorption and scattering, for instance light scattering.[4] 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.[5]

## EarthquakeEdit

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 ground shaking. A seismic wave loses energy as it propagates through the earth (attenuation). This phenomenon is tied in to the dispersion of the seismic energy with the distance. There are two types of dissipated energy:

1. geometric dispersion caused by distribution of the seismic energy to greater volumes
2. dispersion as heat

## ElectromagneticEdit

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 1.022MeV, pair production.

See Attenuation coefficient article.

### OpticsEdit

Main article: Transparent materials

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.

[6] Attenuation in fiber optics can be quantified using the following equation:[7]

$\mathrm{Attenuation(dB)} = 10\times\log_{10}\left(\frac{\mathrm{Input\ intensity(W)}}{\mathrm{Output\ intensity(W)}}\right)$

#### Light scattering Edit

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. We refer to this type of reflection as "diffuse reflection", and it is typically characterized by wide variety of reflection angles. Most of the objects that you see 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. [8] [9]

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. E.G. Since visible light has a wavelength scale on the order of one micron (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 which 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.

Similarly, 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 which 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.[10]

#### UV-Vis-IR absorption Edit

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:

1) 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.

2) 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 design of any optically transparent device requires the selection of materials based upon knowledge of its properties and limitations. The lattice absorption characteristics observed at the lower frequency regions (mid IR to far-infrared wavelength range) define the long-wavelength transparency limit of the material. They are the result of the interactive coupling between the motions of thermally induced vibrations of the constituent atoms and molecules of the solid lattice and the incident light wave radiation. Hence, all materials are bounded by limiting regions of absorption caused by atomic and molecular vibrations (bond-stretching)in the far-infrared (>10 µm).

Thus, multi-phonon absorption occurs when two or more phonons simultaneously interact to produce electric dipole moments with which the incident radiation may couple. These dipoles can absorb energy from the incident radiation, reaching a maximum coupling with the radiation when the frequency is equal to the fundamental vibrational mode of the molecular dipole (e.g. Si-O bond) in the far-infrared, or one of its harmonics.

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.

Reflection and transmission of light waves occur because the frequencies of the light waves do not match the natural resonant frequencies of vibration of the objects. When IR light of these frequencies strike an object, the energy is either reflected or transmitted.

### ApplicationsEdit

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 which decrease the signal in a fiber optic cable intentionally.

Attenuation of light is also important in physical oceanography. Here, attenuation is the decrease in light intensity with depth due to absorption by water molecules and scattering by suspended particulates. This same effect is an important consideration in weather radar as rain drops absorb a part of the emitted beam that is more or less significant depending on the wavelength used.

The attenuation of photons, particularly of those in the x-ray spectrum, is important in the field of medical physics. 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. Additionally 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.

Main article: Path loss

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.

### Power vs AmplitudeEdit

Attenuation of a signal's power by n decibels is equivalent to attenuating its amplitude by 2*n decibels.