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Measure in 3-dimensional geometry
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
Solid_angle
Angle between a liquid–vapor interface and a solid surface
The contact angle (symbol θC) is the angle between a liquid surface and a solid surface where they meet. More specifically, it is the angle between the
Contact_angle
Any of the five regular polyhedra
analog of a plane angle is a solid angle. The solid angle, Ω, at the vertex of a Platonic solid is given in terms of the dihedral angle by Ω = q θ − ( q
Platonic_solid
List of constellations by area
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
IAU designated constellations by solid angle
IAU_designated_constellations_by_solid_angle
Figure formed by two rays meeting at a common point
Irrational angle Phase (waves) Protractor Solid angle Spherical angle Subtended angle Tangential angle Transcendent angle Trisection Zenith angle This approach
Angle
Concept in geometry
angle, formed by the two radii between the center of the sphere and each of the two arc endpoints. More generally, a surface subtends a solid angle if
Subtended_angle
Measure of the "spread" of light in an optical system
the solid angle the source subtends as seen from the pupil. These definitions must be applied for infinitesimally small "elements" of area and solid angle
Etendue
SI derived unit of illuminance
tilted at an angle to a source, the illumination provided on the surface is reduced because the tilted surface subtends a smaller solid angle from the source
Lux
SI derived unit of visible light emission
luminous intensity uniformly across a solid angle of one steradian, the total luminous flux emitted into that angle is one lumen (1 cd·1 sr = 1 lm). Alternatively
Lumen_(unit)
90° angle (π/2 radians)
is a right angle. Two application examples in which the right angle and the Thales' theorem are included (see animations). The solid angle subtended by
Right_angle
Photometric measure
from, or is reflected from a particular area, and falls within a given solid angle. The procedure for conversion from spectral radiance to luminance is
Luminance
Last letter of the Greek alphabet
refers to the multiplicity (number of microstates) in a system. The solid angle or the rate of precession in a gyroscope. In particle physics to represent
Omega
Optical Phenomenon
emission angle, the solid angle, subtended by surface visible to the viewer, is reduced by the very same amount. Because the ratio between power and solid angle
Lambert's_cosine_law
Physical quantity in radiometry
emitted, reflected, transmitted or received by a given surface, per unit solid angle per unit projected area. Radiance is used to characterize diffuse emission
Radiance
Measure of the steric bulk of a ligand in a coordination complex
ligand cone angle (θ) is a measure of the steric bulk of a ligand in a transition metal coordination complex. It is defined as the solid angle formed with
Ligand_cone_angle
SI unit of luminous intensity
unit of luminous intensity. It measures the luminous power per unit solid angle emitted in a particular direction. A common wax candle has a luminous
Candela
Coordinates comprising a distance and two angles
polar angle may be called inclination angle, zenith angle, normal angle, or the colatitude. The user may choose to replace the inclination angle by its
Spherical_coordinate_system
Intensity of electromagnetic radiation
the radiant flux emitted, reflected, transmitted or received, per unit solid angle, and spectral intensity is the radiant intensity per unit frequency or
Radiant_intensity
SI derived unit of solid angle
The steradian (symbol: sr) or square radian is the unit of solid angle in the International System of Units (SI). It is used in three-dimensional geometry
Steradian
Visible light per unit solid angle
wavelength-weighted power emitted by a light source in a particular direction per unit solid angle, based on the luminosity function, a standardized model of the sensitivity
Luminous_intensity
Field of mathematics dealing with three-dimensional Euclidean spaces
radius. Basic topics in solid geometry and stereometry include: incidence of planes and lines dihedral angle and solid angle the cube, cuboid, parallelepiped
Solid_geometry
Unit of solid angle
A square degree (deg2) is a non-SI unit measure of solid angle. Other denotations include sq. deg. and (°)2. Just as degrees are used to measure parts
Square_degree
Perception of light level
coming from a source while luminance is the amount of light per unit solid angle per unit of area on the source's surface. The table below shows the standard
Brightness
Thermal electromagnetic radiation
{\displaystyle L} over the solid angle Ω {\displaystyle \Omega } for all azimuthal angle (0 to 2 π {\displaystyle 2\pi } ) and polar angle θ {\displaystyle \theta
Black-body_radiation
Spectral density of light emitted by a black body
body, Bν, describes the spectral emissive power per unit area, per unit solid angle and per unit frequency for particular radiation frequencies. The relationship
Planck's_law
Polyhedron with four faces
edges are equal. A solid angle of π {\displaystyle \pi } sr is one quarter of that subtended by all of space. When all the solid angles at the vertices of
Tetrahedron
SI derived unit of angle
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used
Radian
Measure of how much of an antenna's signal is transmitted in one direction
which simply calculates the ratio of the beam solid angle to the solid angle of a sphere. The beam solid angle can be approximated for antennas with one narrow
Directivity
Intersection of a sphere and cone emanating from its center
where Ω is the solid angle of the spherical sector in steradians, the SI unit of solid angle. One steradian is defined as the solid angle subtended by a
Spherical_sector
Extent of the observable world seen at any given moment
given moment. In the case of optical instruments or sensors, it is a solid angle through which a detector is sensitive to electromagnetic radiation. It
Field_of_view
3D rendering software developed by Autodesk
in Spain by Marcos Fajardo, it was later co-developed by his company Solid Angle SL (now owned by Autodesk) and Sony Pictures Imageworks. Arnold is one
Autodesk_Arnold
Perceived luminous power
by a light source that emits one candela of luminous intensity over a solid angle of one steradian. 1 lm = 1 cd × 1 sr {\displaystyle 1\ {\text{lm}}=1\
Luminous_flux
Convex polyhedron with regular faces
In geometry, a Johnson solid, sometimes also known as a Johnson–Zalgaller solid, is a convex polyhedron whose faces are regular polygons and that is not
Johnson_solid
Maximum energy available for use
solar radiation is contained in the solid angle subtended by the Sun, 10% is contained and isotropic in a solid angle 0.008 sr (this field of view includes
Exergy
Spherical triangle with three right angles
quartic Bézier triangle. The solid angle subtended by a spherical octant is π/2 steradian or one-eight of a spat, the solid angle of a full sphere. Hemisphere
Octant_of_a_sphere
Type of electron microscope
line-of-sight solid angle for direct geometric collection. Dedicated backscattered electron detectors are designed to greatly increase the solid angle of collection
Scanning_electron_microscope
Radiance of a surface
element of source area into a plane at right angles to the line of propagation, and to an element of solid angle subtended by the detector at the element
Spectral_radiance
following quantities are considered: length, area, volume, plane angle, solid angle, mass, density, time, frequency, velocity, volumetric flow rate, acceleration
List_of_conversion_factors
Approximation of a black body's spectral radiance
energy emitted per unit time per unit area of emitting surface, per unit solid angle, per unit wavelength, whereas B ν ( T ) {\displaystyle B_{\nu }(T)} has
Rayleigh–Jeans_law
Unit of spectral flux density
source is the integral of the spectral radiance, B, over the source solid angle: S = ∬ source B ( θ , ϕ ) d Ω . {\displaystyle S=\iint \limits _{\text{source}}B(\theta
Jansky
Function of four real variables that defines how light is reflected at an opaque surface
variables. The BRDF has units sr−1, with steradians (sr) being a unit of solid angle. The BRDF was first defined by Fred Nicodemus around 1965. The definition
Bidirectional reflectance distribution function
Bidirectional_reflectance_distribution_function
Angle between two planes in space
A dihedral angle is the angle between two intersecting planes or half-planes. It is a plane angle formed on a third plane, perpendicular to the line of
Dihedral_angle
Supplementary pair of angles at each vertex of a polygon
internal angle at that vertex, so each vertex of the rectangular solid is associated with an interior angle of 3 × 90° = 270° and an exterior angle of 360°
Internal_and_external_angles
Measurable property of a material or system
the CGS and MKS systems of units). The angular quantities, plane angle and solid angle, are defined as derived dimensionless quantities in the SI. For
Physical_quantity
to n for P itself), its interior (higher-dimensional) solid angle ∠ ( F ) {\displaystyle \angle (F)} is defined by choosing a small enough ( n − 1 ) {\displaystyle
Gram–Euler_theorem
Method of drawing geometric objects
could (only) trisect an arbitrary angle? Such constructions are solid constructions, but there exist numbers with solid constructions that cannot be constructed
Straightedge and compass construction
Straightedge_and_compass_construction
Deliberate use of light to achieve practical or aesthetic effects
through or is emitted from a particular area, and falls within a given solid angle. The SI unit for luminance is candela per square metre (cd/m2). The CGS
Lighting
Topics referred to by the same term
Radiant intensity, power per unit solid angle (W/sr) Luminous intensity, luminous flux per unit solid angle (lm/sr or cd) Irradiance, power per unit
Intensity
Mathematical concept applicable to physics
uniquely be determined anyway. If the flux j passes through the area at an angle θ to the area normal n ^ {\displaystyle \mathbf {\hat {n}} } , then the
Flux
Symbols for constants, special functions
Retrieved 2025-02-06. Weisstein, Eric W. "Solid Angle". mathworld.wolfram.com. Retrieved 2025-02-07. The solid angle Ω subtended by a surface S is defined
Greek letters used in mathematics, science, and engineering
Greek_letters_used_in_mathematics,_science,_and_engineering
American software company
May 7, 2016, at the Wayback Machine SolidSmack January 8, 2013 0.6.376 - Arnold for 3DS Max User Guide 5 - Solid Angle, Autodesk, September 28, 2016 Autodesk
Autodesk
Electromagnetic radiation due to deceleration of charged particles
towards the observer, and d Ω {\displaystyle d\Omega } is an infinitesimal solid angle. In the case where velocity is parallel to acceleration (for example
Bremsstrahlung
Proportion in thermal radiation
covered by this projection. The projection onto the hemisphere, giving the solid angle subtended by Aj, takes care of the factors cos θ2 and 1/r2; the projection
View_factor
Concept in physics
gauge-dependent while the Berry curvature is not. The Berry curvature per solid angle is given by Ω ¯ θ ϕ = Ω θ ϕ / sin θ = 1 / 2 {\displaystyle {\overline
Berry connection and curvature
Berry_connection_and_curvature
Computer graphics shading and rendering technique
over the hemisphere Ω {\displaystyle \Omega } with respect to projected solid angle: A p ¯ = 1 π ∫ Ω V p ¯ , ω ^ ( n ^ ⋅ ω ^ ) d ω {\displaystyle A_{\bar
Ambient_occlusion
Specific probability distribution function, important in physics
{\displaystyle d\Omega =\sin {\theta }~d\phi ~d\theta } is an element of solid angle and v 2 = | v | 2 = v x 2 + v y 2 + v z 2 {\textstyle v^{2}=|\mathbf
Maxwell–Boltzmann distribution
Maxwell–Boltzmann_distribution
Energy transfer in the form of electromagnetic radiation
per unit time, per unit area of surface of sourcing passage, per unit solid angle of reception at a distance, per unit wavelength interval being considered
Radiative_transfer
Surface on an antenna in electromagnetics
the integral over solid angle can be generalized for an antenna that is not isotropic (that is, any real antenna). Since the angle of arriving electromagnetic
Aperture_(antenna)
Phase of a cycle
the angles where the segments of the geodesics meet; the total precession is equal to the net deficit angle which in turn equals the solid angle enclosed
Geometric_phase
Low energy photon scattering off charged particles
dΩ dλ is the energy scattered by a volume element dV in time dt into solid angle dΩ between wavelengths λ and λ + dλ. From the point of view of an observer
Thomson_scattering
Quantities describing probability of absorption or emission of light
volume × solid angle). ε dt dV dΩ is then the energy emitted by a volume element d V {\displaystyle dV} in time d t {\displaystyle dt} into solid angle d Ω
Einstein_coefficients
Electromagnetic energy transfer rate
extends over the full range of solid angles of a sphere. Mathematically, defined as an unweighted integral over the solid angle of a full sphere, the flux
Spectral_flux_density
Physical law on the emissive power of black body
{\displaystyle I(\nu ,T)} is the amount of power per unit surface area per unit solid angle per unit frequency emitted at a frequency ν {\displaystyle \nu } by a
Stefan–Boltzmann_law
Geometric shape
[0,2\pi )} is the angle "around" the cone, and h ∈ R {\displaystyle h\in \mathbb {R} } is the "height" along the cone. A right solid circular cone with
Cone
Model for light scattering
relative to its original trajectory. The standard form, normalized over the solid angle sphere 4 π {\displaystyle 4\pi } , is given by: p ( θ ) = 1 4 π 1 − g
Henyey–Greenstein phase function
Henyey–Greenstein_phase_function
How large a sphere or circle appears
diameter ratio of 105, so Sirius is roughly 6 times as bright per unit solid angle.) The angular diameter of the Sun is also about 250,000 times that of
Angular_diameter
Unit of plane angle where a full circle equals 1
or Cycle per second (older) Angle of rotation Revolutions per minute Repeating circle Spat (angular unit) – the solid angle counterpart of the turn, equivalent
Turn_(angle)
Optical effect seen in stars
the integral of the intensity over the disk of the star divided by the solid angle subtended by the disk: I m = ∫ I ( ψ ) d ω ∫ d ω , {\displaystyle I_{m}={\frac
Limb_darkening
Theorem in physics
'} of scattering and d Ω {\displaystyle d\Omega } is the differential solid angle. When n = n ′ {\displaystyle \mathbf {n} =\mathbf {n} '} , the above
Optical_theorem
Topics referred to by the same term
Sustained release, in medicine Steradian (symbol: sr), the SI unit of solid angle Strontium (symbol: Sr), a chemical element .sr, the Internet top-level
SR
Probability of a given process occurring in a particle collision
The differential angular range of the scattered particle at angle θ is the solid angle element dΩ = sin θ dθ dφ. The differential cross section is the
Cross_section_(physics)
Unit of angle in solid geometry
("space"), is a unit of solid angle. One spat is equal to 4π steradians or approximately 41253 square degrees of solid angle (sequence A125560 in the
Spat_(angular_unit)
Measure of radiant energy over surface area
,} where ⟨ • ⟩ is the time-average; S is the Poynting vector; α is the angle between a unit vector normal to the surface and S. For a propagating sinusoidal
Irradiance
Hypothetical wave source which radiates equally in all directions
cavity; the power of black-body radiation per unit area (m2) per unit solid angle (steradian) per unit frequency (hertz) at frequency ν {\displaystyle
Isotropic_radiator
Directional variation in strength of radio waves
(large) radius (an amplitude pattern or field pattern), the power per unit solid angle (power pattern), and the directive gain (gain pattern). Very often, only
Radiation_pattern
Law of physics
is the amount of energy per unit surface area per unit time per unit solid angle per unit frequency emitted at a frequency ν, the so called spectral radiance
Wien_approximation
Frequencies of light emitted by atoms or chemical compounds
applications. If X dV dΩ dλ is the energy scattered by a volume element dV into solid angle dΩ between wavelengths λ and λ + dλ per unit time then the emission coefficient
Emission_spectrum
Mechanics analogue of the geometric phase
In classical mechanics, the Hannay angle is a mechanics analogue of the geometric phase (or Berry phase). It was named after John Hannay of the University
Hannay_angle
} . Radiance is defined as energy flow per unit normal area per unit solid angle per unit time. Here, r → {\displaystyle {\vec {r}}} denotes position
Radiative transfer equation and diffusion theory for photon transport in biological tissue
Radiative_transfer_equation_and_diffusion_theory_for_photon_transport_in_biological_tissue
Angle between diagonal and edge of a cube
polynomial vanishes at the magic angle. This property makes the magic angle of particular importance in magic angle spinning solid-state NMR spectroscopy. In
Magic_angle
Set of points equidistant from a center
Sphere Napkin ring problem Orb (optics) Pseudosphere Riemann sphere Solid angle Sphere packing Spherical coordinates Spherical cow Spherical helix, tangent
Sphere
File format
"Pixar's RenderMan Products". Renderman.pixar.com. Retrieved 27 May 2016. "Solid Angle - Arnold Renderer". Solidangle.com. Archived from the original on 8 February
Alembic_(computer_graphics)
Luminous flux incident on a surface per area
}\cos(\theta )}{D^{2}}}} where Iv is the luminous intensity of the source θ is the angle of incidence, and D is the distance between the source and the surface.
Illuminance
Bright light which impairs vision
numbered n {\displaystyle n} , ω n {\displaystyle \omega _{n}} is the solid angle of the light source seen from the observer and p n {\displaystyle p_{n}}
Glare_(vision)
Experiments proving existence of atomic nuclei
scattered into solid angle }}\mathrm {d} \Omega {\text{ per unit time}}}{\text{incident intensity}}}} In classical mechanics, the scattering angle θ {\displaystyle
Rutherford scattering experiments
Rutherford_scattering_experiments
Ability of a liquid to maintain contact with a solid surface
flat, solid surface increases, the contact angle decreases. Thus, the contact angle is used as an inverse measure of wettability. A contact angle less
Wetting
Power transferred per unit area
has a different meaning: it is the luminous or radiant power per unit solid angle. This can cause confusion in optics, where intensity can mean any of
Intensity_(physics)
Technique in solid-state NMR spectroscopy
In solid-state NMR spectroscopy, magic-angle spinning (MAS) is a technique routinely used to produce better resolution NMR spectra. MAS NMR consists in
Magic_angle_spinning
Technique of illustration
truncated cone in either first-angle or third-angle projection, as shown by the diagram on the right. The 3D interpretation is a solid truncated cone, with the
Multiview orthographic projection
Multiview_orthographic_projection
Solid with four equal triangular faces
segments, one of which is twice as long as the other (see proof). Its solid angle at a vertex subtended by a face is arccos ( 23 27 ) = π 2 − 3 arcsin
Regular_tetrahedron
Excess energy at the surface of a material relative to its interior
experimentally determine wetting is to look at the contact angle (θ), which is the angle connecting the solid–liquid interface and the liquid–gas interface (as
Surface_energy
Measure of radiant energy over time
|\rangle \cos \alpha \ dA,} where ⟨-⟩ is the time average, and α is the angle between n and S. Spectral flux in frequency, denoted Φe,ν, is defined as
Radiant_flux
Measure of electromagnetic energy
amount of energy emitted per unit surface area per unit time per unit solid angle and in the frequency range between ν {\displaystyle \nu } and ν + d ν
Brightness_temperature
Parameter in coordination chemistry
catalysis include the pocket angle, solid angle, repulsive energy, and accessible molecular surface. Also of importance is the cone angle, which in diphosphines
Bite_angle
Technique in spectroscopy
Multiple quantum magic angle spinning (MQMAS) NMR was developed in 1995 and has become a routine method for obtaining high resolution solid-state NMR spectra
Solid-state nuclear magnetic resonance
Solid-state_nuclear_magnetic_resonance
coherent superposition of emitted light on the detector is possible. The solid angle Ω {\displaystyle \Omega } that is used for illumination and detection
4Pi_microscope
Counting photons using a single-photon detector
considered. The flux per unit solid angle is the photon intensity. The flux per unit source area per unit solid angle is photon radiance. SI units for
Photon_counting
energy reaching the pixel comes from the integral of radiance from the solid angle by which the sensor pixel sees the scene through the pinhole at the focal
Cone_tracing
Constellation in the southern celestial hemisphere
"atmosphere". It is the eighth-smallest constellation, and subtends a solid angle of around 0.038 steradians, just less than that of Corona Australis.
Caelum
1998 video game
Metal Gear Solid is a 1998 action-adventure stealth game developed and published by Konami for the PlayStation. Directed, produced, and written by Hideo
Metal_Gear_Solid_(video_game)
SOLID ANGLE
SOLID ANGLE
Boy/Male
Indian
Solid
Boy/Male
Muslim
Firm, Solid
Boy/Male
Muslim/Islamic
Solid
Boy/Male
Indian, Sanskrit
Strong; Solid
Boy/Male
Indian
Firm, Solid
Girl/Female
Arabic, British, Danish, English, Muslim
Solid; Strong
Boy/Male
Muslim
Solid
Boy/Male
Arabic, Muslim
Solid
Girl/Female
Indian
Firm, Solid, Determined
Surname or Lastname
Spanish and Asturian-Leonese (SolÃs)
Spanish and Asturian-Leonese (SolÃs) : habitational name from SolÃs in Asturies or a similarly named place elsewhere.English : from a medieval personal name bestowed on a child born after the death of a sibling, from Middle English solace ‘comfort’, ‘consolation’. The word also came to have the sense ‘delight’, ‘amusement’, and in some cases the surname may have arisen from a nickname for a playful or entertaining person.
Girl/Female
Biblical
Nativity, generation.
Boy/Male
Muslim
Solid structure
Boy/Male
Indian
Solid structure
Boy/Male
Arabic, Muslim, Parsi
Firm; Solid
Girl/Female
Indian
Strong, Solid
Biblical
nativity; generation;begetter;
Boy/Male
Tamil
Solid redemption
Boy/Male
Hindu, Indian
Solid Redemption
Girl/Female
Muslim
Strong, Solid
Boy/Male
Muslim/Islamic
Firm Solid
SOLID ANGLE
SOLID ANGLE
Boy/Male
Arabic, German, Hindu, Indian, Malayalam, Muslim, Parsi
Silver Flame; Black Haired Man; Greek Emperor
Girl/Female
Hindu
Who protect
Girl/Female
Hebrew, Hindu, Indian, Marathi
To Take
Girl/Female
Tamil
Prakrthi | பà¯à®°à®•à¯à®°à®¤à¯€
Nature, Goddess Lakshmi
Surname or Lastname
English (Shropshire)
English (Shropshire) : variant of Farrington.
Boy/Male
Arabic
Variant of Shafa'at; Mediation; Advocacy
Boy/Male
Hindu
The best
Boy/Male
Native American
accomplished.
Biblical
walking; going
Girl/Female
Tamil
God has blessed
SOLID ANGLE
SOLID ANGLE
SOLID ANGLE
SOLID ANGLE
SOLID ANGLE
a.
Having the constituent parts so compact, or so firmly adhering, as to resist the impression or penetration of other bodies; having a fixed form; hard; firm; compact; -- opposed to fluid and liquid or to plastic, like clay, or to incompact, like sand.
a.
Applied to a compound word whose parts are closely united and form an unbroken word; -- opposed to hyphened.
a.
Not hollow; full of matter; as, a solid globe or cone, as distinguished from a hollow one; not spongy; dense; hence, sometimes, heavy.
a.
Not having the lines separated by leads; not open.
n.
Solid coal on the side of a gallery; solid ore in a vein.
a.
Impenetrable; resisting or excluding any other material particle or atom from any given portion of space; -- applied to the supposed ultimate particles of matter.
superl.
Solid; nourishing; as, strong meat.
a.
Of a fleshy, uniform, undivided substance, as a bulb or root; not spongy or hollow within, as a stem.
a.
Fig.: Worthy of credit, trust, or esteem; substantial, as opposed to frivolous or fallacious; weighty; firm; strong; valid; just; genuine.
a.
Having all the geometrical dimensions; cubic; as, a solid foot contains 1,728 solid inches.
n.
The art of delineating the forms of solid bodies on a plane; a branch of solid geometry which shows the construction of all solids which are regularly defined.
n.
A magnitude which has length, breadth, and thickness; a part of space bounded on all sides.
a.
Partially solid.
v. i.
To become solid; to harden.
a.
Sound; not weakly; as, a solid constitution of body.
a.
Solid; gross; opaque.
a.
Firm; compact; strong; stable; unyielding; as, a solid pier; a solid pile; a solid wall.
n.
A substance that is held in a fixed form by cohesion among its particles; a substance not fluid.
a.
Enduring; solid; firm; substantial.
a.
United; without division; unanimous; as, the delegation is solid for a candidate.