Luminance

Luminance measures how much luminous intensity, per unit area, travels in a specific direction. It quantifies the light passing through, emitted from, or reflected off a given area, within a defined solid angle. Its SI unit is the candela per square metre (cd/m²), also called the nit. The conversion from spectral radiance to luminance follows standards set by the CIE and ISO. The term "brightness" refers to the subjective impression of this objective measurement.

Luminance is commonly used to describe emission or reflection from flat, diffuse surfaces. The levels indicate how much luminous power the human eye would detect when viewing a surface from a particular angle, making luminance a predictor of how bright that surface will appear. In this context, the relevant solid angle is the one subtended by the eye's pupil. In the video industry, luminance characterizes display brightness; a typical computer display emits between 50 and 300 cd/m², while the sun at noon has a luminance of about 1.6×10⁹ cd/m².

In geometric optics, luminance is invariant: for an ideal optical system, output luminance equals input luminance. For real, passive systems, output luminance is at most equal to the input. For instance, using a lens to form a smaller image concentrates luminous power into a smaller area, raising illuminance, but the light fills a larger solid angle, so luminance remains the same if the lens has no loss. The image can never be "brighter" than the source.

High luminance can damage the retina through local heating or photochemical effects, especially at short wavelengths. The IEC 60825 series provides safety guidance for laser exposure, while the IEC 62471 series evaluates photobiological safety of lamps and lamp systems (including LEDs, excluding lasers) from 200 nm to 3000 nm. This standard originated as CIE S 009:2002.

A luminance meter measures luminance in a specific direction and solid angle. Simple devices measure a single direction, while imaging luminance meters work similarly to a digital camera recording color images.

Mathematically, the luminance at a point on a light source in a given direction is defined by the mixed partial derivative \( L_{\mathrm{v}} = \frac{\mathrm{d}^{2}\Phi_{\mathrm{v}}}{\mathrm{d}\Sigma \, \mathrm{d}\Omega_{\Sigma} \cos \theta_{\Sigma}} \), where \( L_{\mathrm{v}} \) is luminance (cd/m²), \( \mathrm{d}^{2}\Phi_{\mathrm{v}} \) is luminous flux (lm) leaving area \( \mathrm{d}\Sigma \) within solid angle \( \mathrm{d}\Omega_{\Sigma} \), and \( \theta_{\Sigma} \) is the angle between the surface normal and the specified direction. In a lossless medium, luminance remains constant along a light ray. When the ray crosses an arbitrary surface S, luminance is given by \( L_{\mathrm{v}} = \frac{\mathrm{d}^{2}\Phi_{\mathrm{v}}}{\mathrm{d}S \, \mathrm{d}\Omega_{S} \cos \theta_{S}} \).