In physics, attenuation (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.
Hearing protectors help reduce acoustic flux from flowing into the ears. This phenomenon is called acoustic attenuation and is measured in decibels (dBs).
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.
In many cases, attenuation is an exponential function of the path length through the medium. In optics and 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.
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]
Wave equations which take acoustic attenuation into account can be written on a fractional derivative form. [4]
In homogeneous media, the main physical properties contributing to sound attenuation are viscosity [5] and thermal conductivity. [6] [7]
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 () can be used to determine total attenuation in dB in the medium using the following formula:
Attenuation is linearly dependent on the medium length and attenuation coefficient, as well as – approximately – 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: [8]
Material | |
---|---|
Air, at 20 °C [9] | 1.64 |
Blood | 0.2 |
Bone, cortical | 6.9 |
Bone, trabecular | 9.94 |
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. [10] 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. [11]
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 mid-ocean waters, visible light is absorbed most strongly at the longest wavelengths. Thus, red, orange, and yellow wavelengths are totally absorbed at shallower depths, while blue and violet wavelengths reach deeper in the water column. Because the blue and violet wavelengths are absorbed least compared to the other wavelengths, open-ocean waters appear deep blue to the eye.
Near the shore, coastal water contains more phytoplankton than the very clear mid-ocean waters. Chlorophyll-a pigments in the phytoplankton absorb light, and the plants themselves scatter light, making coastal waters less clear than mid-ocean waters. Chlorophyll-a absorbs light most strongly in the shortest wavelengths (blue and violet) of the visible spectrum. In coastal waters where high concentrations of phytoplankton occur, the green wavelength reaches the deepest in the water column and the color of water appears blue-green or green.
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 (seismic attenuation). This phenomenon is tied into the dispersion of the seismic energy with the distance. There are two types of dissipated energy:
In porous fluid—saturated sedimentary rocks such as sandstones, intrinsic attenuation of seismic waves is primarily caused by the wave-induced flow of the pore fluid relative to the solid frame. [12] [13]
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 attenuation of RF cables is defined by:
where is the input power into a 100 m long cable terminated with the nominal value of its characteristic impedance, and is the output power at the far end of this cable. [14]
Attenuation in a coaxial cable is a function of the materials and the construction.
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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. [15] In context of this, an increase in photon energy (E) will result in a rapid decrease in the interaction with matter.
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. 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.
Attenuation in fiber optics can be quantified using the following equation:
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. [16] Light scattering from many common surfaces can be modelled by 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, 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. [17]
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:
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.
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.
In CT imaging, attenuation describes the density or darkness of the image.
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.
The Beer–Lambert law is commonly applied to chemical analysis measurements to determine the concentration of chemical species that absorb light. It is often referred to as Beer's law. In physics, the Bouguer–Lambert law is an empirical law which relates the extinction or attenuation of light to the properties of the material through which the light is travelling. It had its first use in astronomical extinction. The fundamental law of extinction is sometimes called the Beer–Bouguer–Lambert law or the Bouguer–Beer–Lambert law or merely the extinction law. The extinction law is also 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.
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 (when the electric field of the light is >108 V/m and thus comparable to the atomic electric field of ~1011 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 optics, the refractive index of an optical medium is a dimensionless number that gives the indication of the light bending ability of that medium.
In physics, optical depth or optical thickness is the natural logarithm of the ratio of incident to transmitted radiant power through a material. Thus, the larger the optical depth, the smaller the amount of transmitted radiant power through the material. 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.
In physics, scattering is a wide range of physical processes where moving particles or radiation of some form, such as light or sound, are forced to deviate from a straight trajectory by 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 of radiation that undergo scattering are often called diffuse reflections and unscattered reflections are called specular (mirror-like) reflections. Originally, the term was confined to light scattering. As more "ray"-like phenomena were discovered, the idea of scattering was extended to them, so that William Herschel could refer to the scattering of "heat rays" in 1800. John Tyndall, a pioneer in light scattering research, noted the connection between light scattering and acoustic scattering in the 1870s. Near the end of the 19th century, the scattering of cathode rays and X-rays was observed and discussed. With the discovery of subatomic particles and the development of quantum theory in the 20th century, the sense of the term became broader as it was recognized that the same mathematical frameworks used in light scattering could be applied to many other phenomena.
Mode locking is a technique in optics by which a laser can be made to produce pulses of light of extremely short duration, on the order of picoseconds (10−12 s) or femtoseconds (10−15 s). A laser operated in this way is sometimes referred to as a femtosecond laser, for example, in modern refractive surgery. The basis of the technique is to induce a fixed phase relationship between the longitudinal modes of the laser's resonant cavity. Constructive interference between these modes can cause the laser light to be produced as a train of pulses. The laser is then said to be "phase-locked" or "mode-locked".
In the field of optics, transparency is the physical property of allowing light to pass through the material without appreciable scattering of light. On a macroscopic scale, the photons can be said to follow Snell's law. Translucency 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 the index of refraction. In other words, a translucent material is made up of components with different indices of refraction. A transparent material is made up of components with a uniform index of refraction. 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. Other categories of visual appearance, related to the perception of regular or diffuse reflection and transmission of light, have been organized under the concept of cesia in an order system with three variables, including transparency, translucency and opacity among the involved aspects.
Absorbance is defined as "the logarithm of the ratio of incident to transmitted radiant power through a sample ". Alternatively, for samples which scatter light, absorbance may be defined as "the negative logarithm of one minus absorptance, as measured on a uniform sample". The term is used in many technical areas to quantify the results of an experimental measurement. While the term has its origin in quantifying the absorption of light, it is often entangled with quantification of light which is “lost” to a detector system through other mechanisms. What these uses of the term tend to have in common is that they refer to a logarithm of the ratio of a quantity of light incident on a sample or material to that which is detected after the light has interacted with the sample.
In electromagnetism, Brillouin scattering, named after Léon Brillouin, refers to the interaction of light with the material waves in 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.
In physics, Raman scattering or the Raman effect is the inelastic scattering of photons by matter, meaning that there is both an exchange of energy and a change in the light's direction. Typically this effect involves vibrational energy being gained by a molecule as incident photons from a visible laser are shifted to lower energy. This is called normal Stokes-Raman scattering.
In physics, absorption of electromagnetic radiation is how matter takes up a photon's energy — and so transforms electromagnetic energy into internal energy of the absorber.
An optical fiber, or optical fibre, is a flexible glass or plastic fiber that can transmit light from one end to the other. Such fibers find wide usage in fiber-optic communications, where they permit transmission over longer distances and at higher bandwidths than electrical cables. Fibers are used instead of metal wires because signals travel along them with less loss and are immune to electromagnetic interference. Fibers are also used for illumination and imaging, and are often wrapped in bundles so they may be used to carry light into, or images out of confined spaces, as in the case of a fiberscope. Specially designed fibers are also used for a variety of other applications, such as fiber optic sensors and fiber lasers.
In atomic physics, two-photon absorption (TPA or 2PA), also called two-photon excitation or non-linear absorption, is the simultaneous absorption of two photons of identical or different frequencies in order to excite an atom or a molecule from one state (usually the ground state), via a virtual energy level, to a higher energy, most commonly an excited electronic state. Absorption of two photons with different frequencies is called non-degenerate two-photon absorption. Since TPA depends on the simultaneous absorption of two photons, the probability of TPA is proportional to the photon dose (D), which is proportional to the square of the light intensity (D ∝ I2); thus it is a nonlinear optical process. The energy difference between the involved lower and upper states of the molecule is equal or smaller than the sum of the photon energies of the two photons absorbed. Two-photon absorption is a third-order process, with absorption cross section typically several orders of magnitude smaller than one-photon absorption cross section.
The linear attenuation coefficient, 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 coefficient value that is large represents a beam becoming 'attenuated' as it passes through a given medium, while a small value represents that the medium had little effect on loss. The (derived) SI unit of attenuation coefficient is the reciprocal metre (m−1). Extinction coefficient is another term for this quantity, often used in meteorology and climatology. Most commonly, the quantity measures the exponential decay of intensity, that is, the value of downward e-folding distance of the original intensity as the energy of the intensity 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 broad-beam attenuation coefficient counts forward-scattered radiation as transmitted rather than attenuated, and is more applicable to radiation shielding. The mass attenuation coefficient is the attenuation coefficient normalized by the density of the material.
The mass attenuation coefficient, or mass narrow beam attenuation coefficient of a material is the attenuation coefficient normalized by the density of the material; that is, the attenuation per unit mass. Thus, it characterizes how easily a mass of material can be penetrated by a beam of light, sound, particles, or other energy or matter. In addition to visible light, mass attenuation coefficients can be defined for other electromagnetic radiation, sound, or any other beam that can be attenuated. The SI unit of mass attenuation coefficient is the square metre per kilogram. Other common units include cm2/g and L⋅g−1⋅cm−1. Mass extinction coefficient is an old term for this quantity.
The photoacoustic Doppler effect is a type of Doppler effect that occurs when an intensity 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 X-ray filter is a device placed in front of an X-ray source in order to reduce the intensity of particular wavelengths from its spectrum and selectively alter the distribution of X-ray wavelengths within a given beam before reaching the image receptor. Adding a filtration device to certain x-ray examinations attenuates the x-ray beam by eliminating lower energy x-ray photons to produce a clearer image with greater anatomic detail to better visualize differences in tissue densities. While a compensating filter provides a better radiographic image by removing lower energy photons, it also reduces radiation dose to the patient.
Ultrasound-modulated optical tomography (UOT), also known as Acousto-Optic Tomography (AOT), is a hybrid imaging modality that combines light and sound; it is a form of tomography involving ultrasound. It is used in imaging of biological soft tissues and has potential applications for early cancer detection. As a hybrid modality which uses both light and sound, UOT provides some of the best features of both: the use of light provides strong contrast and sensitivity ; these two features are derived from the optical component of UOT. The use of ultrasound allows for high resolution, as well as a high imaging depth. However, the difficulty of tackling the two fundamental problems with UOT have caused UOT to evolve relatively slowly; most work in the field is limited to theoretical simulations or phantom / sample studies.
Photoacoustic microscopy 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.