Steradian in the context of "Rayleigh–Jeans law"

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 (W·sr·m). 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.

In geometry, a solid angle (symbol: Ω) is a measure of the amount of the field of view from some particular point that a given object covers. That is, it is a measure of how large the object appears to an observer looking from that point.The point from which the object is viewed is called the apex of the solid angle, and the object is said to subtend its solid angle at that point.

In the International System of Units (SI), a solid angle is expressed in a dimensionless unit called a steradian (symbol: sr), which is equal to one square radian, sr = rad. One steradian corresponds to one unit of area (of any shape) on the unit sphere surrounding the apex, so an object that blocks all rays from the apex would cover a number of steradians equal to the total surface area of the unit sphere, ${\displaystyle 4\pi }$. Solid angles can also be measured in squares of angular measures such as degrees, minutes, and seconds.

In radiometry, radiant intensity is the radiant flux emitted, reflected, transmitted or received, per unit solid angle, and spectral intensity is the radiant intensity per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. These are directional quantities. The SI unit of radiant intensity is the watt per steradian (W/sr), while that of spectral intensity in frequency is the watt per steradian per hertz (W·sr·Hz) and that of spectral intensity in wavelength is the watt per steradian per metre (W·sr·m)—commonly the watt per steradian per nanometre (W·sr·nm). Radiant intensity is distinct from irradiance and radiant exitance, which are often called intensity in branches of physics other than radiometry. In radio-frequency engineering, radiant intensity is sometimes called radiation intensity.

The lumen (symbol: lm) is the SI unit of luminous flux, which quantifies the perceived power of visible light emitted by a source. Luminous flux differs from power (radiant flux), which encompasses all electromagnetic waves emitted, including non-visible ones such as thermal radiation (infrared). By contrast, luminous flux is weighted according to a model (a "luminosity function") of the human eye's sensitivity to various wavelengths; this weighting is standardized by the CIE and ISO.

The lumen is defined as equivalent to one candela-steradian (symbol cd·sr):

The bidirectional reflectance distribution function (BRDF), symbol ${\displaystyle f_{\text{r}}(\omega _{\text{i}},\,\omega _{\text{r}})}$, is a function of four real variables that defines how light from a source is reflected off an opaque surface. It is employed in the optics of real-world light, in computer graphics algorithms, and in computer vision algorithms. The function takes an incoming light direction, ${\displaystyle \omega _{\text{i}}}$, and outgoing direction, ${\displaystyle \omega _{\text{r}}}$ (taken in a coordinate system where the surface normal ${\displaystyle \mathbf {n} }$ lies along the z-axis), and returns the ratio of reflected radiance exiting along ${\displaystyle \omega _{\text{r}}}$ to the irradiance incident on the surface from direction ${\displaystyle \omega _{\text{i}}}$. Each direction ${\displaystyle \omega }$ is itself parameterized by azimuth angle ${\displaystyle \phi }$ and zenith angle ${\displaystyle \theta }$, therefore the BRDF as a whole is a function of 4 variables. The BRDF has units sr, with steradians (sr) being a unit of solid angle.

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 (W·sr·m·Hz) and that of spectral radiance in wavelength is the watt per steradian per square metre per metre (W·sr·m)—commonly the watt per steradian per square metre per nanometre (W·sr·m·nm). 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.

A square degree (deg) is a non-SI unit measure of solid angle. Other denotations include sq. deg. and (°). Just as degrees are used to measure parts of a circle, square degrees are used to measure parts of a sphere.

Analogous to one degree being equal to ⁠π/180⁠ radians, a square degree is equal to (⁠π/180⁠) steradians (sr), or about ⁠1/3283⁠ sr or about 3.046×10 sr.The whole sphere has a solid angle of 4πsr which is approximately 41253 deg:

The International Astronomical Union (IAU) designates 88 constellations of stars. In the table below, they are ranked by the solid angle that they subtend in the sky, measured in square degrees and millisteradians.

These solid angles depend on arbitrary boundaries between the constellations: the list below is based on constellation boundaries drawn up by Eugène Delporte in 1930 on behalf of the IAU and published in Délimitation scientifique des constellations (Cambridge University Press). Before Delporte's work, there was no standard list of the boundaries of each constellation.