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Detection and inference about remote objects using transmitted radio waves and their returned electromagnetic radiation. A received signal depends on propagation, directional antenna gain, target scattering and receiver sensitivity.

Radiant energy is the amount of energy emitted, transferred or received as electromagnetic radiation. It is measured in joules. For the specified beam or collection of rays crossing a boundary,where radiant flux ${\Phi }_{\mathrm{e}}$ is radiation power. The receiving geometry and time interval are part of the statement; dividing by a receiving area produces radiant exposure, rather than another total energy.^[ref]

For an original passive-optic example, stipulate $5.0\mathrm{mJ}$ incident during an interval, with no remaining change of stored energy afterward. Suppose $3.0\mathrm{mJ}$ is transmitted, $1.25\mathrm{mJ}$ reflected and $0.75\mathrm{mJ}$ absorbed. Their sum is the incoming $5.0\mathrm{mJ}$. A detector collecting only the transmitted path receives $3.0\mathrm{mJ}$, even though the source supplied more. This radiometric energy balance specifies the collection boundary instead of equating every energy readout in the apparatus.

A thermal detector converts absorbed radiation into an observable temperature response; a calibrated model relates that response to received energy. A documented NIST arrangement uses a slow thermal reference and calibrated beam splitting to establish pulse-energy measurements.^[ref] Absorbed energy, incident radiant energy and energy in an uncollected branch must remain distinct in that calibration.

Two sources can deliver the same radiant energy with different radiant flux histories or spectra. Their total energies agree only for the specified integration and collection; this alone does not determine peak power, radiant exposure at a point or detector response.

Radiant flux is the power carried by electromagnetic radiation: radiation energy transferred per unit time, measured in watts, $\mathrm{W}=\mathrm{J}{\mathrm{s}}^{-1}$. Specify what is counted: all radiation emitted by a source, radiation within one beam, or radiation intercepted by a photodetector. Writing $Q(t)$ for the cumulative energy crossing the specified boundary givesThe first expression is an instantaneous derivative; the second is an average over the stated time interval. If $0.020\mathrm{J}$ arrives during $0.010\mathrm{s}$, the mean radiant flux is $2\mathrm{W}$. The photodetector's absorbed power equals this incident radiant flux only if it absorbs all of the incident radiation.

Keeping radiant flux fixed while widening a beam reduces its irradiance, the incident power per receiving area. Radiance additionally resolves the propagation direction and has units $\mathrm{W}{\mathrm{m}}^{-2}\mathrm{s}{\mathrm{r}}^{-1}$; an optical camera can collect different radiant fluxes from sources with the same radiance but different apparent solid angles. Luminous flux, measured in lumens, weights the optical spectrum by the human eye's standardized response instead of counting energy equally at every wavelength. Equal radiant fluxes need not give equal luminous fluxes.^[ref]

Radiant power also differs from the optical power of an optical lens, which is reciprocal focal length in dioptres. Likewise, astronomical radiative flux is power per area. Stating the units prevents these shared words from hiding different physical quantities.

Radiation transports energy away from a source through propagating fields or emitted particles. Electromagnetic radiation includes radio waves, visible light, X-rays and gamma rays; alpha particles, beta particles and neutrons provide particle-radiation examples. The word alone does not specify an energy, a hazard, or a detection method.

An experiment must distinguish the incident field from its interaction with the detector. A photodetector measures a light-induced response, while an ionization chamber collects charge created in a gas. Neither instrument responds equally to every kind of radiation. Ionizing radiation is classified by its ability to remove bound electrons under the relevant interaction conditions, rather than simply by whether the source is radioactive.

The energy entering and leaving a system through electromagnetic radiation. A top-of-atmosphere radiation budget compares absorbed sunlight with outgoing thermal radiation. A latitude-dependent imbalance can be balanced by atmospheric and ocean heat fluxes even when the global mean is zero.

Radiation pressure is the normal momentum flux transferred by electromagnetic radiation to a surface. A photon travelling in vacuum carries momentum $p_{\gamma }=E_{\gamma }/c=h\nu /c$, where $E_{\gamma }$ is its energy, $\nu$ its frequency, $h$ the Planck constant and $c$ the speed of light. Photon absorption transfers that momentum; specular reflection reverses its normal component. This lets light exert a force even when almost no energy becomes heat in the receiver.

Two useful formulas describe different preparations. A directed beam normally incident on a stationary perfect absorber gives pressure $I/c$, and on a stationary perfect mirror gives $2I/c$. Here $I$ is light intensity, the incident power per beam cross-sectional area perpendicular to propagation, in $\mathrm{W}{\mathrm{m}}^{-2}$. An isotropic photon gas has pressure $u/3$, where $u=U/V$ is its radiation internal energy per volume, in $\mathrm{J}{\mathrm{m}}^{-3}$. Stored energy density and travelling energy flux must be distinguished: an isotropic field can have zero net energy flux and positive radiation pressure.

The physical appeal is that the same momentum conservation connects a single photon collision, a mirror's measurable force, and a radiation-filled cavity's equation of state. The directional calculation below complements radiation pressure on a perfectly absorbing surface; the equilibrium spectrum and its temperature dependence belong to blackbody radiation and the photon gas.

A radiometer measures electromagnetic radiation through its received power. A radio radiometer can express that power as a noise temperature, allowing an unknown source to be compared with calibrated reference temperatures.

Radiometry measures the energy and power carried by electromagnetic radiation, including light. It asks how much radiation a source supplies, where it travels, and how much reaches a receiving surface. The measurements are physical rather than weighted by the sensitivity of the human eye: equal radiant fluxes at different wavelengths need not look equally bright. ^[ref].

The five quantities below answer different questions about the same radiation. The International System of Units makes the distinctions visible: a watt is a joule per second, while a steradian measures solid angle. ^[ref].

Resolving wavelength or frequency adds a further “per unit interval”, as in spectral radiance. The notation is consistent with NIST's table of spectral quantities. In particular, radiant flux is power, whereas the existing astronomical radiative flux is power per area. ^[ref].

This bookkeeping makes an optical camera's collected signal calculable from a source's radiance and the geometry of the receiving aperture. It also lets radiation measurements from different instruments be compared. For example, NIST describes separate calibrations of spectral radiance and spectral irradiance for instruments used to observe Earth. ^[ref].

A radio wave is electromagnetic radiation in the radio portion of the frequency spectrum. In vacuum its frequency and wavelength obey the vacuum frequency-wavelength relation.

Rayleigh scattering is elastic scattering of electromagnetic radiation by particles much smaller than the incident wavelength. In the stationary particle approximation, the scattered electromagnetic radiation keeps the incident frequency: its direction changes, rather than its color. The incident electric field induces an oscillating electric dipole moment, which produces electric dipole radiation. This is a useful example of how a microscopic response can explain a familiar large-scale sight, why the sky is blue. ^[ref].

The smallness condition for Rayleigh scattering by a small sphere of radius $a$ is $ka\ll 1$, where the wavenumber is $k=2\pi /\lambda$ and $\lambda$ is the surrounding medium's wavelength. For ordinary materials with modest refractive index, the incident electric field then varies little across the particle, making the electric-dipole approximation for radiation useful. For very large refractive index, also check the internal size $|m|ka\ll 1$ before applying the simple electric dipole model. Once these conditions fail, use Mie scattering for a sphere instead of extrapolating the Rayleigh scattering wavelength dependence.

Historically, the 1871 paper ^[ref] connected the color and polarization of an electromagnetic wave of scattered skylight with particles smaller than the wavelength. Its dimensional analysis anticipates scattered light intensity proportional to particle volume squared and to ${\lambda }^{-4}$. The original mechanical picture is historical; the modern explanation uses induced electric dipole radiation.

Consider a fixed, homogeneous, nonabsorbing, nonmagnetic sphere of radius $a$ in vacuum. Let $m$ be its relative refractive index, a fixed real number; in vacuum this equals the sphere's refractive index. Treat $m$ as independent of wavelength over the range being compared, neglecting optical dispersion. Air can be approximated by vacuum here because its refractive index is close to one. These assumptions describe a toy particle, rather than a literal model of an individual air molecule.

The Rayleigh scattering cross-section $\sigma$ is an effective area: the total scattered power is $P_{\mathrm{sca}}=I_{\mathrm{inc}}\sigma$, where $I_{\mathrm{inc}}$ is the incident light intensity. For $ka\ll 1$ its leading approximation isThe units are area, since $k^4{a}^6$ has units ${\mathrm{m}}^{-4}{\mathrm{m}}^6={\mathrm{m}}^2$. This Rayleigh scattering cross-section measures scattering, not conversion of the incident electromagnetic radiation into heat. The definition follows ^[ref].

To see the mechanism, the nearly uniform applied electric field produces an electric dipole moment with peak magnitudewhere $E_0$ is the incident electric field peak wave amplitude and ${ϵ}_0$ is vacuum permittivity. This is the sphere's response in electrostatics, with its permittivity divided by vacuum permittivity equal to $m^2$ under the nonmagnetic assumption. ^[ref]. The averaged electric dipole radiation power is $P_{\mathrm{sca}}={\omega }^4{p}_0^2/(12\pi {ϵ}_0{c}^3)$, with angular frequency $\omega =ck$ and speed of light $c$. Dividing by $I_{\mathrm{inc}}={ϵ}_{0}c{E}_0^2/2$ gives the displayed Rayleigh scattering cross-section. Thus doubling radius multiplies the electric dipole moment by eight and the scattered power by $64$, provided the larger sphere still satisfies $ka\ll 1$. ^[ref].

Inferring properties of a distant object from measured signals, often electromagnetic radiation. Spatial sampling, spectral information and observation cadence must jointly resolve the physical process of interest. Received radiance alone need not uniquely separate temperature, emissivity and atmospheric attenuation.

A scientific instrument converts a physical interaction into an observable indication under a stated measurement model. An ionization chamber converts deposited energy into collected electric charge; a telescope collects incoming electromagnetic radiation; a force probe converts a mechanical load into a calibrated response.

An indication is not yet the desired measurand. The instrument's response, measurement resolution, measurement calibration and measurement uncertainty determine what can be inferred. Changing a controlled input and comparing with a reference is often more revealing than reading the same display repeatedly: it tests whether the instrument is responding to the intended quantity or to an unwanted influence.

The second, symbol $\mathrm{s}$, is the SI base unit of time. Its definition fixes the unperturbed frequency of the ground-state atomic transition between levels split by hyperfine structure in caesium with mass number $133$ to exactly $9192631770\mathrm{Hz}$. One second therefore corresponds to that many cycles of the specified electromagnetic radiation.^[ref]

A practical atomic clock realizes the reference by interrogating atoms and controlling a reference oscillation. Magnetic fields, motion and environmental effects require corrections: an exact unit definition does not make every physical realization free of measurement uncertainty.

For an illustrative $n=2\to 1s$ emission calculation, retain only the first-order shifts above and neglect the quadratic shift of the hydrogen atom ground state. The unperturbed Lyman-alpha line frequency is ${\nu }_0=(E_2-E_1)/h$. The possible offsets areThe outer pair originates in the $p_0$ parts of $|{\psi }_{\pm }⟩$ and has transition electric dipole moments along the applied electric field, conventionally called $\pi$ components. The central pair originates in $p_{\pm 1}$ and has transverse rotating transition electric dipole moments, conventionally called ${\sigma }^{\pm }$ components. Because electromagnetic radiation is transverse, the $\pi$ components disappear when viewed along the electric field. Viewed from the side, the $\pi$ and $\sigma$ components have polarization of an electromagnetic wave respectively parallel and perpendicular to the applied electric field. Line intensities additionally require the initial quantum state populations and the collection geometry.

A spectroscopic wavenumber commonly means the reciprocal of the vacuum wavelength ${\lambda }_0$ of electromagnetic radiation, often in $\mathrm{c}{\mathrm{m}}^{-1}$. It is an ordinary spatial frequency, so the vacuum angular wavenumber is $K_0=2\pi \tilde{\nu }$. Specify vacuum or in-medium wavelength: the same frequency can have different wavelengths in different media. IUPAC's “wavenumber in medium” entry defines the in-medium reciprocal $1/\lambda$ and notes that unqualified spectroscopic usage often means the vacuum reciprocal.^[ref]

For example, a vacuum wavelength of $500\mathrm{nm}=5\times 10^{-5}\mathrm{cm}$ corresponds to $\tilde{\nu }=20000\mathrm{c}{\mathrm{m}}^{-1}=2\times 10^6{\mathrm{m}}^{-1}$. Multiplication by $2\pi$ gives $K_0=4\pi \times 10^6\mathrm{rad}{\mathrm{m}}^{-1}$. Converting centimetres to metres and converting cycles to radians are separate operations.

Synchrotron radiation is electromagnetic radiation emitted by relativistic charged particles undergoing transverse acceleration, typically when a magnetic field bends their paths. For ultrarelativistic particles, emission is concentrated near the instantaneous direction of motion rather than distributed isotropically.

A circulating electron beam therefore loses energy even when the bending magnet itself does no work. Radiofrequency accelerating fields replenish that loss in a storage ring. The extracted radiation is useful as an intense source for spectroscopy and imaging; its angular distribution, polarization and optical spectrum depend on particle energy and magnetic geometry. In synchrotron cooling, those same radiation losses reshape a particle population.

A telescope collects electromagnetic radiation from distant objects and forms an image or supplies a signal to a detector. An optical telescope can use lenses or mirrors; instruments for other wavelengths can require different collecting structures. Collection increases the detectable signal, while the aperture and wavelength constrain the angular resolution.

For an ideal unobscured circular aperture of diameter $D$, the Rayleigh criterion gives an angular scale $\theta \simeq 1.22\lambda /D$. Increasing the magnification of an already blurred image cannot recover angular detail lost through diffraction, optical aberrations or atmospheric seeing. This makes a double star a useful observing test: a larger apparent image is different from two genuinely resolved intensity peaks.^[ref]

Thermal radiation is electromagnetic radiation emitted by matter because of its temperature. Matter in thermal equilibrium emits a spectrum governed by its absorptivity, approaching the Planck law for a blackbody.

A thermopile connects multiple thermocouples in series to turn a temperature difference into a larger electrical signal. Absorbed thermal radiation can heat its sensing junctions while reference junctions remain cooler; the signal depends on the thermal and optical design.

A thermopile is an array of thermocouples connected as a series circuit with their electromotive forces adding in the chosen terminal order. It measures a collective temperature difference through the Seebeck effect. An open-circuit electric potential difference requires no externally supplied electric current through the array: a high-input-electrical resistance voltmeter reads the signal. The heat that maintains the junction temperature difference still comes from somewhere, such as absorbed electromagnetic radiation.

In a membrane detector, an absorbing film heats the measuring junctions while reference junctions lie on the surrounding support. Actual junction temperatures can differ across the membrane.^[ref] This converts difficult-to-observe heat transfer into an accessible electrical signal; the series connection combines many small contributions without requiring every thermocouple to have a separate meter.