Radiansi

Radiance, often called radiansi in some languages, is a fundamental radiometric quantity that describes how much light energy travels through or from a particular direction per unit area of the emitting or reflecting surface. It characterizes the brightness of a surface as seen along a specific line of sight, taking into account both the surface orientation and the direction of observation.

Formal definition: the radiance L is the radiant flux Φ crossing a differential area dA from directions within a differential solid angle dΩ, such that dΦ = L dA cos θ dΩ, where θ is the angle between the surface normal and the direction of observation. Thus L has units of watts per square meter per steradian (W·m^-2·sr^-1). Spectral radiance Lλ includes wavelength dependence: dΦ = Lλ dA cos θ dΩ dλ, with units W·m^-2·sr^-1·m^-1 or per nanometer for Lλ.

An important property is that radiance is invariant in a lossless optical system: the radiance of a beam remains the same after reflection, refraction, or passive imaging, although its distribution may change. This leads to the brightness (etendue) conservation principle: in passive optics, L is preserved and the product of L and the solid angle projected by the beam remains constant.

Projection onto a surface measures irradiance E = ∫ L cos θ dΩ over the hemisphere. Luminance, used in human vision, is related to radiance through photometric weighting; luminance units are candela per square meter.

Radiance concepts are central to remote sensing, computer graphics, lighting design, radiometric calibration, and imaging systems.