irradian

Irradian is a term used in radiometry to describe a scalar measure of how directionally concentrated a source’s radiant emission is. The word blends irradiation concepts with the idea of a radian, reflecting a focus on angular distribution. It is not a standard quantity in international radiometric practice, and there is no official symbol or unit for irradian.

Definition and calculation: In its common formulation, irradian is defined as the ratio of radiant power emitted within a specified angular cone around a chosen principal emission axis to the total radiant power emitted over the full sphere. Expressed as Ir = (∫Ωcone I(Ω) dΩ) / (∫Ωsphere I(Ω) dΩ), where I(Ω) is the radiant intensity in direction Ω and Ωcone represents the measurement cone with half-angle α. The result is dimensionless and lies between 0 and 1. The concept assumes a well-defined main emission axis; for isotropic sources the axis is not defined, which limits practical interpretation.

Interpretation and use: Irradian provides a compact descriptor of directional concentration, useful for comparing LEDs, laser diodes, and other light sources in design and testing contexts. A highly collimated source yields irradian values near 1 for a small cone, while broad or diffuse sources produce lower values. Because irradian depends on the chosen cone angle and axis, comparisons should specify the geometry and measurement conditions.

Limitations and status: As a non-standardized quantity, irradian appears mostly in niche discussions and exploratory literature. It is not part of formal lighting measurement standards, and its adoption varies. Users should document the reference cone and axis when reporting irradian to avoid ambiguity.