Kirchhoff's law of thermal radiation
In heat transfer, Kirchhoff's law of thermal radiation refers to wavelength-specific radiative emission and absorption by a material body in thermodynamic equilibrium, including radiative exchange equilibrium. A body at temperature T radiates electromagnetic energy. A perfect black body in thermodynamic equilibrium absorbs all light that strikes it, radiates energy according to a unique law of radiative emissive power for temperature T, universal for all perfect black bodies. Kirchhoff's law states that: Here, the dimensionless coefficient of absorption is the fraction of incident light, absorbed by the body when it is radiating and absorbing in thermodynamic equilibrium. In different terms, the emissive power of an arbitrary opaque body of fixed size and shape at a definite temperature can be described by a dimensionless ratio, sometimes called the emissivity: the ratio of the emissive power of the body to the emissive power of a black body of the same size and shape at the same fixed temperature.
With this definition, Kirchhoff's law states, in simpler language: In some cases, emissive power and absorptivity may be defined to depend on angle, as described below. The condition of thermodynamic equilibrium is necessary in the statement, because the equality of emissivity and absorptivity does not hold when the material of the body is not in thermodynamic equilibrium. Kirchhoff's law has another corollary: the emissivity cannot exceed one, so it is not possible to thermally radiate more energy than a black body, at equilibrium. In negative luminescence the angle and wavelength integrated absorption exceeds the material's emission, such systems are powered by an external source and are therefore not in thermodynamic equilibrium. Before Kirchhoff's law was recognized, it had been experimentally established that a good absorber is a good emitter, a poor absorber is a poor emitter. A good reflector must be a poor absorber; this is why, for example, lightweight emergency thermal blankets are based on reflective metallic coatings: they lose little heat by radiation.
Kirchhoff's great insight was to recognize the universality and uniqueness of the function that describes the black body emissive power. But he did not know the precise character of that universal function. Attempts were made by Lord Rayleigh and Sir James Jeans 1900 - 1905 to describe it in classical terms, resulting in Rayleigh–Jeans law; this law turned out to be inconsistent yielding the ultraviolet catastrophe. The correct form of the law was found by Max Planck in 1900, assuming quantized emission of radiation, is termed Planck's law; this marks the advent of quantum mechanics. In a blackbody enclosure that contains electromagnetic radiation with a certain amount of energy at thermodynamic equilibrium, this "photon gas" will have a Planck distribution of energies. One may suppose a second system, a cavity with walls that are opaque and not reflective to any wavelength, to be brought into connection, through an optical filter, with the blackbody enclosure, both at the same temperature. Radiation can pass from one system to the other.
For example, suppose in the second system, the density of photons at narrow frequency band around wavelength λ were higher than that of the first system. If the optical filter passed only that frequency band there would be a net transfer of photons, their energy, from the second system to the first; this is in violation of the second law of thermodynamics, which requires that there can be no net transfer of heat between two bodies at the same temperature. In the second system, therefore, at each frequency, the walls must absorb and emit energy in such a way as to maintain the black body distribution. For the condition of thermal equilibrium, the absorptivity α λ is the ratio of the energy absorbed by the wall to the energy incident on the wall, for a particular wavelength, thus the absorbed energy is α λ E b λ where E b λ is the intensity of black body radiation at wavelength λ and temperature T. Independent of the condition of thermal equilibrium, the emissivity of the wall is defined as the ratio of emitted energy to the amount that would be radiated if the wall were a perfect black body.
The emitted energy is thus ϵ λ E b λ where ϵ λ is the emissivity at wavelength λ. For the maintenance of thermal equilibrium, these two quantities must be equal, or else the distribution of photon energies in the cavity will deviate from that of a black body; this yields Kirchhoff's law: α λ = ϵ λ By a similar, but more complicated argument, it can be shown that, since black body radiation is equal in every direction, the emissivity and the absorptivity, if they happen to be dependent on direction, must again be equal for any given direction. Average and overall absorptivity and emissivity data are given for materials with values which differ
Self-focusing is a non-linear optical process induced by the change in refractive index of materials exposed to intense electromagnetic radiation. A medium whose refractive index increases with the electric field intensity acts as a focusing lens for an electromagnetic wave characterized by an initial transverse intensity gradient, as in a laser beam; the peak intensity of the self-focused region keeps increasing as the wave travels through the medium, until defocusing effects or medium damage interrupt this process. Self-focusing of light was discovered by Gurgen Askaryan. Self-focusing is observed when radiation generated by femtosecond lasers propagates through many solids and gases. Depending on the type of material and on the intensity of the radiation, several mechanisms produce variations in the refractive index which result in self-focusing: the main cases are Kerr-induced self-focusing and plasma self-focusing. Kerr-induced self-focusing was first predicted in the 1960s and experimentally verified by studying the interaction of ruby lasers with glasses and liquids.
Its origin lies in the optical Kerr effect, a non-linear process which arises in media exposed to intense electromagnetic radiation, which produces a variation of the refractive index n as described by the formula n = n 0 + n 2 I, where n0 and n2 are the linear and non-linear components of the refractive index, I is the intensity of the radiation. Since n2 is positive in most materials, the refractive index becomes larger in the areas where the intensity is higher at the centre of a beam, creating a focusing density profile which leads to the collapse of a beam on itself. Self-focusing beams have been found to evolve into a Townes profile regardless of their initial shape. Self-focusing occurs if the radiation power is greater than the critical power P c r = α λ 2 4 π n 0 n 2,where λ is the radiation wavelength in vacuum and α is a constant which depends on the initial spatial distribution of the beam. Although there is no general analytical expression for α, its value has been derived numerically for many beam profiles.
The lower limit is α ≈ 1.86225, which corresponds to Townes beams, whereas for a Gaussian beam α ≈ 1.8962. For air, n0 ≈ 1, n2 ≈ 4×10−23 m2/W for λ = 800 nm, the critical power is Pcr ≈ 2.4 GW, corresponding to an energy of about 0.3 mJ for a pulse duration of 100 fs. For silica, n0 ≈ 1.453, n2 ≈ 2.4×10−20 m2/W, the critical power is Pcr ≈ 2.8 MW. Kerr induced self-focusing is crucial for many applications in laser physics, both as a key ingredient and as a limiting factor. For example, the technique of chirped pulse amplification was developed to overcome the nonlinearities and damage of optical components that self-focusing would produce in the amplification of femtosecond laser pulses. On the other hand, self-focusing is a major mechanism behind Kerr-lens modelocking, laser filamentation in transparent media, self-compression of ultrashort laser pulses, parametric generation, many areas of laser-matter interaction in general. Kelley predicted that homogeneously broadened two-level atoms may focus or defocus light when carrier frequency ω is detuned downward or upward the center of gain line ω 0.
Laser pulse propagation with varying envelope E is governed in gain medium by Nonlinear Schrodinger-Frantz-Nodvik equation. When ω is detuned downward or upward the ω 0. Noteworthy the red detuning leads to increase of index during saturation of resonant transition, i.e. to self-focusing, while for blue detuning the radiation is defocused during saturation: ∂ E ∂ z + 1 c ∂ E ∂ t + i 2 k ∇ ⊥ 2 E = + i k n 2 | E | 2 E + σ N 2 E ( r
In electrodynamics, linear polarization or plane polarization of electromagnetic radiation is a confinement of the electric field vector or magnetic field vector to a given plane along the direction of propagation. See polarization and plane of polarization for more information; the orientation of a linearly polarized electromagnetic wave is defined by the direction of the electric field vector. For example, if the electric field vector is vertical the radiation is said to be vertically polarized; the classical sinusoidal plane wave solution of the electromagnetic wave equation for the electric and magnetic fields is E =∣ E ∣ R e B = z ^ × E / c for the magnetic field, where k is the wavenumber, ω = c k is the angular frequency of the wave, c is the speed of light. Here ∣ E ∣ is the amplitude of the field and | ψ ⟩ = d e f = is the Jones vector in the x-y plane; the wave is linearly polarized when the phase angles α x, α y are equal, α x = α y = d e f α. This represents. In that case, the Jones vector can be written | ψ ⟩ = exp .
The state vectors for linear polarization in x or y are special cases of this state vector. If unit vectors are defined such that | x ⟩ = d e f and | y ⟩ = d e f the polarization state can be written in the "x-y basis" as | ψ ⟩ = cos θ exp | x ⟩ + sin θ exp | y ⟩ = ψ x | x ⟩ + ψ y | y ⟩. Sinusoidal plane-wave solutions of the electromagnetic wave equation Polarization Circular polarization Elliptical polarization Plane of polarization Photon polarization Jackson, John D.. Classical Electrodynamics. Wiley. ISBN 0-471-30932-X. Animation of Linear Polarization Comparison of Linear Polarization with Circular and Elliptical Polarizations This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C"
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 an absolute value. In the latter case, it expresses the ratio of a value to a fixed reference value. For example, if the reference value is 1 volt the suffix is "V", if the reference value is one milliwatt the suffix is "m". Two different scales are used when expressing a ratio in decibels, depending on the nature of the quantities: power and field; when expressing a power ratio, the number of decibels is ten times its logarithm to base 10. That is, a change in power by a factor of 10 corresponds to a 10 dB change in level; when expressing field quantities, a change in amplitude by a factor of 10 corresponds to a 20 dB change in level. The decibel scales differ by a factor of two so that the related power and field levels change by the same number of decibels in, for example, resistive loads.
The definition of the decibel is based on the measurement of power in telephony of the early 20th century in the Bell System in the United States. One decibel is one tenth of one bel, named in honor of Alexander Graham Bell. Today, the decibel is used for a wide variety of measurements in science and engineering, most prominently in acoustics and control theory. In electronics, the gains of amplifiers, attenuation of signals, signal-to-noise ratios are expressed in decibels. In the International System of Quantities, the decibel is defined as a unit of measurement for quantities of type level or level difference, which are defined as the logarithm of the ratio of power- or field-type quantities; the decibel originates from methods used to quantify signal loss in telegraph and telephone circuits. The unit for loss was Miles of Standard Cable. 1 MSC corresponded to the loss of power over a 1 mile length of standard telephone cable at a frequency of 5000 radians per second, matched the smallest attenuation detectable to the average listener.
The standard telephone cable implied was "a cable having uniformly distributed resistance of 88 Ohms per loop-mile and uniformly distributed shunt capacitance of 0.054 microfarads per mile". In 1924, Bell Telephone Laboratories received favorable response to a new unit definition among members of the International Advisory Committee on Long Distance Telephony in Europe and replaced the MSC with the Transmission Unit. 1 TU was defined such that the number of TUs was ten times the base-10 logarithm of the ratio of measured power to a reference power. The definition was conveniently chosen such that 1 TU approximated 1 MSC. In 1928, the Bell system renamed the TU into the decibel, being one tenth of a newly defined unit for the base-10 logarithm of the power ratio, it was named the bel, in honor of the telecommunications pioneer Alexander Graham Bell. The bel is used, as the decibel was the proposed working unit; the naming and early definition of the decibel is described in the NBS Standard's Yearbook of 1931: Since the earliest days of the telephone, the need for a unit in which to measure the transmission efficiency of telephone facilities has been recognized.
The introduction of cable in 1896 afforded a stable basis for a convenient unit and the "mile of standard" cable came into general use shortly thereafter. This unit was employed up to 1923 when a new unit was adopted as being more suitable for modern telephone work; the new transmission unit is used among the foreign telephone organizations and it was termed the "decibel" at the suggestion of the International Advisory Committee on Long Distance Telephony. The decibel may be defined by the statement that two amounts of power differ by 1 decibel when they are in the ratio of 100.1 and any two amounts of power differ by N decibels when they are in the ratio of 10N. The number of transmission units expressing the ratio of any two powers is therefore ten times the common logarithm of that ratio; this method of designating the gain or loss of power in telephone circuits permits direct addition or subtraction of the units expressing the efficiency of different parts of the circuit... In 1954, J. W. Horton argued that the use of the decibel as a unit for quantities other than transmission loss led to confusion, suggested the name'logit' for "standard magnitudes which combine by addition".
In April 2003, the International Committee for Weights and Measures considered a recommendation for the inclusion of the decibel in the International System of Units, but decided against the proposal. However, the decibel is recognized by other international bodies such as the International Electrotechnical Commission and International Organization for Standardization; the IEC permits the use of the decibel with field quantities as well as power and this recommendation is followed by many national standards bodies, such as NIST, which justifies the use of the decibel for voltage ratios. The term field quantity is deprecated by ISO 80000-1. In spite of their widespread use, suffixes are not recognized by the IEC or ISO. ISO 80000-3 describes definitions for units of space and time; the decibel for use in acoustics is defined in ISO 80000-8. The major difference from the article below is that for acoustics the decibel has no
A collimator is a device that narrows a beam of particles or waves. To narrow can mean either to cause the directions of motion to become more aligned in a specific direction, or to cause the spatial cross section of the beam to become smaller. An English physicist Henry Kater was the inventor of the floating collimator, which rendered a great service to practical astronomy, he reported about his invention in January 1825. In his report, Kater mentioned previous work in this area by Carl Friedrich Gauss and Friedrich Bessel. In optics, a collimator may consist of a curved mirror or lens with some type of light source and/or an image at its focus; this can be used to replicate a target focused at infinity with no parallax. In lighting, collimators are designed using the principles of nonimaging optics. Optical collimators can be used to calibrate other optical devices, to check if all elements are aligned on the optical axis, to set elements at proper focus, or to align two or more devices such as binoculars or gun barrels and gunsights.
A surveying camera may be collimated by setting its fiduciary markers so that they define the principal point, as in photogrammetry. Optical collimators are used as gun sights in the collimator sight, a simple optical collimator with a cross hair or some other reticle at its focus; the viewer only sees an image of the reticle. They have to use it either with both eyes open and one eye looking into the collimator sight, with one eye open and moving the head to alternately see the sight and the target, or with one eye to see the sight and target at the same time. Adding a beam splitter allows the viewer to see the reticle and the field of view, making a reflector sight. Collimators may be used with laser diodes and CO2 cutting lasers. Proper collimation of a laser source with long enough coherence length can be verified with a shearing interferometer. In X-ray optics, gamma ray optics, neutron optics, a collimator is a device that filters a stream of rays so that only those traveling parallel to a specified direction are allowed through.
Collimators are used for X-ray, gamma-ray, neutron imaging because it is not yet possible to focus these types of radiation into an image using lenses, as is routine with electromagnetic radiation at optical or near-optical wavelengths. Collimators are used in radiation detectors in nuclear power stations to make directional sensitivity; the figure to the right illustrates how a Söller collimator is used in X-ray machines. The upper panel shows a situation where a collimator is not used, while the lower panel introduces a collimator. In both panels the source of radiation is to the right, the image is recorded on the gray plate at the left of the panels. Without a collimator, rays from all directions will be recorded; the resultant image will be so indistinct as to be useless. In the lower panel of the figure, a collimator has been added; this may be a sheet of lead or other material opaque to the incoming radiation with many tiny holes bored through it or in the case of neutrons it can be a sandwich arrangement with many layers alternating between neutron absorbing material with neutron transmitting material.
This can be something simple e.g. air. Or if mechanical strength is needed aluminium may be used. If this forms part of a rotating assembly, the sandwich may be curved; this allows energy selection in addition to collimation - the curvature of the collimator and its rotation will present a straight path only to one energy of neutrons. Only rays that are travelling nearly parallel to the holes will pass through them—any others will be absorbed by hitting the plate surface or the side of a hole; this ensures. For industrial radiography using gamma radiation sources such as iridium-192 or cobalt-60, a collimator allows the radiographer to control the exposure of radiation to expose a film and create a radiograph, to inspect materials for defects. A collimator in this instance is most made of tungsten, is rated according to how many half value layers it contains, i.e. how many times it reduces undesirable radiation by half. For instance, the thinnest walls on the sides of a 4 HVL tungsten collimator 13 mm thick will reduce the intensity of radiation passing through them by 88.5%.
The shape of these collimators allows emitted radiation to travel toward the specimen and the x-ray film, while blocking most of the radiation, emitted in undesirable directions such as toward workers. Although collimators improve resolution, they reduce intensity by blocking incoming radiation, undesirable for remote sensing instruments that require high sensitivity. For this reason, the gamma ray spectrometer on the Mars Odyssey is a non-collimated instrument. Most lead collimators let less than 1% of incident photons through. Attempts have been made to replace collimators with electronic analysis. Collimators are used in linear accelerators used for radiotherapy treatments, they help to shape the beam of radiation emerging from the machine and can limit the maximum field size of a beam. The treatment head of a linear accelerator consists of both a secondary collimator; the primary collimator is positioned. When using photons, it is placed after the beam has passed th
In optics, the refractive index or index of refraction of a material is a dimensionless number that describes how fast light propagates through the material. It is defined as n = c v, where c is the speed of light in vacuum and v is the phase velocity of light in the medium. For example, the refractive index of water is 1.333, meaning that light travels 1.333 times as fast in vacuum as in water. The refractive index determines how much the path of light is bent, or refracted, when entering a material; this is described by Snell's law of refraction, n1 sinθ1 = n2 sinθ2, where θ1 and θ2 are the angles of incidence and refraction of a ray crossing the interface between two media with refractive indices n1 and n2. The refractive indices determine the amount of light, reflected when reaching the interface, as well as the critical angle for total internal reflection and Brewster's angle; the refractive index can be seen as the factor by which the speed and the wavelength of the radiation are reduced with respect to their vacuum values: the speed of light in a medium is v = c/n, the wavelength in that medium is λ = λ0/n, where λ0 is the wavelength of that light in vacuum.
This implies that vacuum has a refractive index of 1, that the frequency of the wave is not affected by the refractive index. As a result, the energy of the photon, therefore the perceived color of the refracted light to a human eye which depends on photon energy, is not affected by the refraction or the refractive index of the medium. While the refractive index affects wavelength, it depends on photon frequency and energy so the resulting difference in the bending angle causes white light to split into its constituent colors; this is called dispersion. It can be observed in prisms and rainbows, chromatic aberration in lenses. Light propagation in absorbing materials can be described using a complex-valued refractive index; the imaginary part handles the attenuation, while the real part accounts for refraction. The concept of refractive index applies within the full electromagnetic spectrum, from X-rays to radio waves, it can be applied to wave phenomena such as sound. In this case the speed of sound is used instead of that of light, a reference medium other than vacuum must be chosen.
The refractive index n of an optical medium is defined as the ratio of the speed of light in vacuum, c = 299792458 m/s, the phase velocity v of light in the medium, n = c v. The phase velocity is the speed at which the crests or the phase of the wave moves, which may be different from the group velocity, the speed at which the pulse of light or the envelope of the wave moves; the definition above is sometimes referred to as the absolute refractive index or the absolute index of refraction to distinguish it from definitions where the speed of light in other reference media than vacuum is used. Air at a standardized pressure and temperature has been common as a reference medium. Thomas Young was the person who first used, invented, the name "index of refraction", in 1807. At the same time he changed this value of refractive power into a single number, instead of the traditional ratio of two numbers; the ratio had the disadvantage of different appearances. Newton, who called it the "proportion of the sines of incidence and refraction", wrote it as a ratio of two numbers, like "529 to 396".
Hauksbee, who called it the "ratio of refraction", wrote it as a ratio with a fixed numerator, like "10000 to 7451.9". Hutton wrote it as a ratio with a fixed denominator, like 1.3358 to 1. Young did not use a symbol for the index of refraction, in 1807. In the next years, others started using different symbols: n, m, µ; the symbol n prevailed. For visible light most transparent media have refractive indices between 1 and 2. A few examples are given in the adjacent table; these values are measured at the yellow doublet D-line of sodium, with a wavelength of 589 nanometers, as is conventionally done. Gases at atmospheric pressure have refractive indices close to 1 because of their low density. All solids and liquids have refractive indices above 1.3, with aerogel as the clear exception. Aerogel is a low density solid that can be produced with refractive index in the range from 1.002 to 1.265. Moissanite lies at the other end of the range with a refractive index as high as 2.65. Most plastics have refractive indices in the range from 1.3 to 1.7, but some high-refractive-index polymers can have values as high as 1.76.
For infrared light refractive indices can be higher. Germanium is transparent in the wavelength region from 2 to 14 µm and has a refractive index of about 4. A type of new materials, called topological insulator, was found holding higher refractive index of up to 6 in near to mid infrared frequency range. Moreover, topological insulator material are transparent; these excellent properties make them a type of significant materials for infrared optics. According to the theory of relativity, no information can travel faster than the speed of light in vacuum, but this does not mean that the refractive index cannot be lower than 1; the refractive index measures the phase velocity of light. The phase velocity is the speed at which the crests of the wave move and can be faster than the speed of light in vacuum, thereby give a refractive index below 1; this can occur close to resonance frequencies, for absorbing media, in plasmas, for X-rays. In the X-ray regime the refractive indices are
An opto-isolator is an electronic component that transfers electrical signals between two isolated circuits by using light. Opto-isolators prevent high voltages from affecting the system receiving the signal. Commercially available opto-isolators withstand input-to-output voltages up to 10 kV and voltage transients with speeds up to 25 kV/μs. A common type of opto-isolator consists of a phototransistor in the same opaque package. Other types of source-sensor combinations include LED-photodiode, LED-LASCR, lamp-photoresistor pairs. Opto-isolators transfer digital signals, but some techniques allow them to be used with analog signals; the value of optically coupling a solid state light emitter to a semiconductor detector for the purpose of electrical isolation was recognized in 1963 by Akmenkalns, et al.. Photoresistor-based opto-isolators were introduced in 1968, they are the slowest, but the most linear isolators and still retain a niche market in the audio and music industries. Commercialization of LED technology in 1968–1970 caused a boom in optoelectronics, by the end of the 1970s the industry developed all principal types of opto-isolators.
The majority of opto-isolators on the market use bipolar silicon phototransistor sensors. They attain medium data transfer speed, sufficient for applications like electroencephalography; the fastest opto-isolators use PIN diodes in photoconductive mode. An opto-isolator contains a source of light always a near infrared light-emitting diode, that converts electrical input signal into light, a closed optical channel, a photosensor, which detects incoming light and either generates electric energy directly, or modulates electric current flowing from an external power supply; the sensor can be a photoresistor, a photodiode, a phototransistor, a silicon-controlled rectifier or a triac. Because LEDs can sense light in addition to emitting it, construction of symmetrical, bidirectional opto-isolators is possible. An optocoupled solid-state relay contains a photodiode opto-isolator which drives a power switch a complementary pair of MOSFETs. A slotted optical switch contains a source of light and a sensor, but its optical channel is open, allowing modulation of light by external objects obstructing the path of light or reflecting light into the sensor.
Electronic equipment and signal and power transmission lines can be subjected to voltage surges induced by lightning, electrostatic discharge, radio frequency transmissions, switching pulses and perturbations in power supply. Remote lightning strikes can induce surges up to 10 kV, one thousand times more than the voltage limits of many electronic components. A circuit can incorporate high voltages by design, in which case it needs safe, reliable means of interfacing its high-voltage components with low-voltage ones; the main function of an opto-isolator is to block such high voltages and voltage transients, so that a surge in one part of the system will not disrupt or destroy the other parts. This function was delegated to isolation transformers, which use inductive coupling between galvanically isolated input and output sides. Transformers and opto-isolators are the only two classes of electronic devices that offer reinforced protection — they protect both the equipment and the human user operating this equipment.
They contain a single physical isolation barrier, but provide protection equivalent to double isolation. Safety and approval of opto-couplers are regulated by national and international standards: IEC 60747-5-2, EN 60747-5-2, UL 1577, CSA Component Acceptance Notice #5, etc. Opto-isolator specifications published by manufacturers always follow at least one of these regulatory frameworks. An opto-isolator connects output sides with a beam of light modulated by input current, it transforms useful input signal into light, sends it across the dielectric channel, captures light on the output side and transforms it back into electric signal. Unlike transformers, which pass energy in both directions with low losses, opto-isolators are unidirectional and they cannot transmit power. Typical opto-isolators can only modulate the flow of energy present on the output side. Unlike transformers, opto-isolators can pass DC or slow-moving signals and do not require matching impedances between input and output sides.
Both transformers and opto-isolators are effective in breaking ground loops, common in industrial and stage equipment, caused by high or noisy return currents in ground wires. The physical layout of an opto-isolator depends on the desired isolation voltage. Devices rated for less than a few kV have planar construction; the sensor die. The sensor is covered with a sheet of glass or clear plastic, topped with the LED die; the LED beam fires downward. To minimize losses of light, the useful absorption spectrum of the sensor must match the output spectrum of the LED, which invariably lies in the near infrared; the optical channel is made as thin as possible for a desired breakdown voltage. For example, to be rated for short-term voltages of 3.75 kV and transients of 1 kV/μs, the clear polyimide sheet in the Avago ASSR-300 series is only 0.08 mm thick. Breakdown voltages of planar assemblies depend on the thickness of the transparent sheet and the configuration of bonding wires that connect the dies with external pins.
Real in-circuit isolation voltage is further reduced by creepage over the PCB and the surface of the package. Safe design rules require a minimal clearance of