Radiant intensity in the context of Radiant exitance

In radiometry, photometry, and color science, a spectral power distribution (SPD) measurement describes the power per unit area per unit wavelength of an illumination (radiant exitance). More generally, the term spectral power distribution can refer to the concentration, as a function of wavelength, of any radiometric or photometric quantity (e.g. radiant energy, radiant flux, radiant intensity, radiance, irradiance, radiant exitance, radiosity, luminance, luminous flux, luminous intensity, illuminance, luminous emittance).

Knowledge of the SPD is crucial for optical-sensor system applications. Optical properties such as transmittance, reflectivity, and absorbance as well as the sensor response are typically dependent on the incident wavelength.

In radiometry, irradiance is the radiant flux received by a surface per unit area. The SI unit of irradiance is the watt per square metre (symbol W⋅m or W/m). The CGS unit erg per square centimetre per second (erg⋅cm⋅s) is often used in astronomy. Irradiance is often called intensity, but this term is avoided in radiometry where such usage leads to confusion with radiant intensity. In astrophysics, irradiance is called radiant flux.

Spectral irradiance is the irradiance of a surface per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. The two forms have different dimensions and units: spectral irradiance of a frequency spectrum is measured in watts per square metre per hertz (W⋅m⋅Hz), while spectral irradiance of a wavelength spectrum is measured in watts per square metre per metre (W⋅m), or more commonly watts per square metre per nanometre (W⋅m⋅nm).

Isotropic radiation is radiation that has the same intensity regardless of the direction of measurement, such as what would be found in a thermal cavity. This can be electromagnetic radiation, sound, or elementary particles.

In radiometry, radiant exitance or radiant emittance is the radiant flux emitted by a surface per unit area, whereas spectral exitance or spectral emittance is the radiant exitance of a surface per unit frequency or wavelength, depending on whether the spectrum is taken as a function of frequency or of wavelength. This is the emitted component of radiosity. The SI unit of radiant exitance is the watt per square metre (W/m), while that of spectral exitance in frequency is the watt per square metre per hertz (W·m·Hz) and that of spectral exitance in wavelength is the watt per square metre per metre (W·m)—commonly the watt per square metre per nanometre (W·m·nm). The CGS unit erg per square centimeter per second (erg·cm·s) is often used in astronomy. Radiant exitance is often called "intensity" in branches of physics other than radiometry, but in radiometry this usage leads to confusion with radiant intensity.

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, and is analogous to the radian, which quantifies planar angles. A solid angle in the form of a circular cone can be projected onto a sphere from its centre, delineating a spherical cap where the cone intersects the sphere. The magnitude of the solid angle expressed in steradians is defined as the quotient of the surface area of the spherical cap and the square of the sphere's radius. This is analogous to the way a plane angle projected onto a circle delineates a circular arc on the circumference, whose length is proportional to the angle. Steradians can be used to measure a solid angle of any projected shape. The solid angle subtended is the same as that of a cone with the same projected area. A solid angle of one steradian subtends a cone aperture of approximately 1.144 radians or 65.54 degrees.

In the SI, solid angle is considered to be a dimensionless quantity, the ratio of the area projected onto a surrounding sphere and the square of the sphere's radius. This is the number of square radians in the solid angle. This means that the SI steradian is the number of square radians in a solid angle equal to one square radian, which of course is the number one. It is useful to distinguish between dimensionless quantities of a different kind, such as the radian (in the SI, a ratio of quantities of dimension length), so the symbol sr is used. For example, radiant intensity can be measured in watts per steradian (W⋅sr). The steradian was formerly an SI supplementary unit, but this category was abolished in 1995 and the steradian is now considered an SI derived unit.

In optics, Lambert's cosine law says that the observed radiant intensity or luminous intensity from an ideal diffusely reflecting surface or ideal diffuse radiator is directly proportional to the cosine of the angle θ between the observer's line of sight and the surface normal; I = I₀ cos θ. The law is also known as the cosine emission law or Lambert's emission law. It is named after Johann Heinrich Lambert, from his Photometria, published in 1760.

A surface which obeys Lambert's law is said to be Lambertian, and exhibits Lambertian reflectance. Such a surface has a constant radiance/luminance, regardless of the angle from which it is observed; a single human eye perceives such a surface as having a constant brightness, regardless of the angle from which the eye observes the surface. It has the same radiance because, although the emitted power from a given area element is reduced by the cosine of the 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 is constant, radiance (power per unit solid angle per unit projected source area) stays the same.

Lambertian reflectance is the property that defines an ideal "matte" or diffusely reflecting surface. The apparent brightness of a Lambertian surface to an observer is the same regardless of the observer's angle of view. More precisely, the reflected radiant intensity obeys Lambert's cosine law, which makes the reflected radiance the same in all directions. Lambertian reflectance is named after Johann Heinrich Lambert, who introduced the concept of perfect diffusion in his 1760 book Photometria.