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Brightness Temperature
Brightness temperature or radiance temperature is the temperature at which a black body in thermal equilibrium with its surroundings would have to be in order to duplicate the observed intensity of a grey body object at a frequency \nu. This concept is used in radio astronomy, planetary science and materials science. The brightness temperature of a surface is typically determined by an optical measurement, for example using a pyrometer, with the intention of determining the real temperature. As detailed below, the real temperature of a surface can in some cases be calculated by dividing the brightness temperature by the emissivity of the surface. Since the emissivity is a value between 0 and 1, the real temperature will be greater than or equal to the brightness temperature. At high frequencies (short wavelengths) and low temperatures, the conversion must proceed through Planck's law. The brightness temperature is not a temperature as ordinarily understood. It characterizes ...
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Black Body
A black body or blackbody is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. The name "black body" is given because it absorbs all colors of light. A black body also emits black-body radiation. In contrast, a white body is one with a "rough surface that reflects all incident rays completely and uniformly in all directions." A black body in thermal equilibrium (that is, at a constant temperature) emits electromagnetic black-body radiation. The radiation is emitted according to Planck's law, meaning that it has a spectrum that is determined by the temperature alone (see figure at right), not by the body's shape or composition. An ideal black body in thermal equilibrium has two main properties: #It is an ideal emitter: at every frequency, it emits as much or more thermal radiative energy as any other body at the same temperature. #It is a diffuse emitter: measured per unit area perpendicular to ...
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Temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temperature scales that historically have relied on various reference points and thermometric substances for definition. The most common scales are the Celsius scale with the unit symbol °C (formerly called ''centigrade''), the Fahrenheit scale (°F), and the Kelvin scale (K), the latter being used predominantly for scientific purposes. The kelvin is one of the seven base units in the International System of Units (SI). Absolute zero, i.e., zero kelvin or −273.15 °C, is the lowest point in the thermodynamic temperature scale. Experimentally, it can be approached very closely but not actually reached, as recognized in the third law of thermodynamics. It would be impossible to extract energy as heat from a body at that temperature. Tem ...
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Temperature
Temperature is a physical quantity that expresses quantitatively the perceptions of hotness and coldness. Temperature is measurement, measured with a thermometer. Thermometers are calibrated in various Conversion of units of temperature, temperature scales that historically have relied on various reference points and thermometric substances for definition. The most common scales are the Celsius scale with the unit symbol °C (formerly called ''centigrade''), the Fahrenheit scale (°F), and the Kelvin scale (K), the latter being used predominantly for scientific purposes. The kelvin is one of the seven base units in the International System of Units (SI). Absolute zero, i.e., zero kelvin or −273.15 °C, is the lowest point in the thermodynamic temperature scale. Experimentally, it can be approached very closely but not actually reached, as recognized in the third law of thermodynamics. It would be impossible to extract energy as heat from a body at that temperature. Tem ...
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Coherence Length
In physics, coherence length is the propagation distance over which a coherent wave (e.g. an electromagnetic wave) maintains a specified degree of coherence. Wave interference is strong when the paths taken by all of the interfering waves differ by less than the coherence length. A wave with a longer coherence length is closer to a perfect sinusoidal wave. Coherence length is important in holography and telecommunications engineering. This article focuses on the coherence of classical electromagnetic fields. In quantum mechanics, there is a mathematically analogous concept of the quantum coherence length of a wave function. Formulas In radio-band systems, the coherence length is approximated by :L = \frac \approx \frac ~, where \, c \, is the speed of light in a vacuum, \, n \, is the refractive index of the medium, and \, \mathrm f \, is the bandwidth of the source or \, \lambda \, is the signal wavelength and \, \Delta \lambda \, is the width of the range of wavelengt ...
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Radiance
In radiometry, radiance is the radiant flux emitted, reflected, transmitted or received by a given surface, per unit solid angle per unit projected area. Radiance is used to characterize diffuse emission and reflection of electromagnetic radiation, and to quantify emission of neutrinos and other particles. The SI unit of radiance is the watt per steradian per square metre (). It is a ''directional'' quantity: the radiance of a surface depends on the direction from which it is being observed. The related quantity spectral radiance is the radiance of a surface per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. Historically, radiance was called "intensity" and spectral radiance was called "specific intensity". Many fields still use this nomenclature. It is especially dominant in heat transfer, astrophysics and astronomy. "Intensity" has many other meanings in physics, with the most common being power per unit ...
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Spectral Linewidth
A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to identify atoms and molecules. These "fingerprints" can be compared to the previously collected ones of atoms and molecules, and are thus used to identify the atomic and molecular components of stars and planets, which would otherwise be impossible. Types of line spectra Spectral lines are the result of interaction between a quantum system (usually atoms, but sometimes molecules or atomic nuclei) and a single photon. When a photon has about the right amount of energy (which is connected to its frequency) to allow a change in the energy state of the system (in the case of an atom this is usually an electron changing orbitals), the photon is absorbed. Then the energy will be spontaneously re-emitted, either as one photon at the same frequenc ...
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Narrowband
Narrowband signals are signals that occupy a narrow range of frequencies or that have a small fractional bandwidth. In the audio spectrum, narrowband sounds are sounds that occupy a narrow range of frequencies. In telephony, narrowband is usually considered to cover frequencies 300–3400 Hz, i.e. the voiceband. In radio communications, a narrowband channel is a channel in which the bandwidth of the message does not significantly exceed the channel's coherence bandwidth. In the study of wired channels, ''narrowband'' implies that the channel under consideration is sufficiently narrow that its frequency response can be considered flat. The message bandwidth will therefore be less than the coherence bandwidth of the channel. That is, no channel has perfectly flat fading, but the analysis of many aspects of wireless systems is greatly simplified if flat fading can be assumed. Two-way radio narrowband Two-Way Radio Narrowbanding refers to a U.S. Federal Communications Com ...
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Spectral Index
In astronomy, the spectral index of a source is a measure of the dependence of radiative flux density (that is, radiative flux per unit of frequency) on frequency. Given frequency \nu and radiative flux density S_\nu, the spectral index \alpha is given implicitly by :S_\nu\propto\nu^\alpha. Note that if flux does not follow a power law in frequency, the spectral index itself is a function of frequency. Rearranging the above, we see that the spectral index is given by :\alpha \! \left( \nu \right) = \frac. Clearly the power law can only apply over a certain range of frequency because otherwise the integral over all frequencies would be infinite. Spectral index is also sometimes defined in terms of wavelength \lambda. In this case, the spectral index \alpha is given implicitly by :S_\lambda\propto\lambda^\alpha, and at a given frequency, spectral index may be calculated by taking the derivative :\alpha \! \left( \lambda \right) =\frac. The spectral index using the S_\nu, which we ma ...
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Black-body Radiation
Black-body radiation is the thermal electromagnetic radiation within, or surrounding, a body in thermodynamic equilibrium with its environment, emitted by a black body (an idealized opaque, non-reflective body). It has a specific, continuous spectrum of wavelengths, inversely related to intensity, that depend only on the body's temperature, which is assumed, for the sake of calculations and theory, to be uniform and constant., Chapter 13. A perfectly insulated enclosure which is in thermal equilibrium internally contains black-body radiation, and will emit it through a hole made in its wall, provided the hole is small enough to have a negligible effect upon the equilibrium. The thermal radiation spontaneously emitted by many ordinary objects can be approximated as black-body radiation. Of particular importance, although planets and stars (including the Earth and Sun) are neither in thermal equilibrium with their surroundings nor perfect black bodies, black-body radiation is ...
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Rayleigh–Jeans Law
In physics, the Rayleigh–Jeans law is an approximation to the spectral radiance of electromagnetic radiation as a function of wavelength from a black body at a given temperature through classical arguments. For wavelength λ, it is: B_ (T) = \frac, where B_ is the spectral radiance, the power emitted per unit emitting area, per steradian, per unit wavelength; c is the speed of light; k_ is the Boltzmann constant; and T is the temperature in kelvin. For frequency \nu, the expression is instead B_(T) = \frac. The Rayleigh–Jeans law agrees with experimental results at large wavelengths (low frequencies) but strongly disagrees at short wavelengths (high frequencies). This inconsistency between observations and the predictions of classical physics is commonly known as the ultraviolet catastrophe. Its resolution in 1900 with the derivation by Max Planck of Planck's law, which gives the correct radiation at all frequencies, was a foundational aspect of the development of quantum ...
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Spectral Radiance
In radiometry, spectral radiance or specific intensity is the radiance of a surface per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. The SI unit of spectral radiance in frequency is the watt per steradian per square metre per hertz () and that of spectral radiance in wavelength is the watt per steradian per square metre per metre ()—commonly the watt per steradian per square metre per nanometre (). The microflick is also used to measure spectral radiance in some fields. Spectral radiance gives a full radiometric description of the field of classical electromagnetic radiation of any kind, including thermal radiation and light. It is conceptually distinct from the descriptions in explicit terms of Maxwellian electromagnetic fields or of photon distribution. It refers to material physics as distinct from psychophysics. For the concept of specific intensity, the line of propagation of radiation lies in a semi ...
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Boltzmann Constant
The Boltzmann constant ( or ) is the proportionality factor that relates the average relative kinetic energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, and in Planck's law of black-body radiation and Boltzmann's entropy formula, and is used in calculating thermal noise in resistors. The Boltzmann constant has dimensions of energy divided by temperature, the same as entropy. It is named after the Austrian scientist Ludwig Boltzmann. As part of the 2019 redefinition of SI base units, the Boltzmann constant is one of the seven " defining constants" that have been given exact definitions. They are used in various combinations to define the seven SI base units. The Boltzmann constant is defined to be exactly . Roles of the Boltzmann constant Macroscopically, the ideal gas law states that, for an ideal gas, the product of pressure and volume is proportional to the product of amount ...
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