Halvevermogenstraal

Halvevermogenstraal, in Dutch, is the radial distance from the center of a radially symmetric source or beam within which half of the total power or energy is contained. It is used as a measure of how concentrated the power distribution is around the center and is defined for a given intensity profile I(r) by the condition that the cumulative power P(r) equals half of the total power Ptotal. Here P(r) = 2π ∫0^r I(r') r' dr' and Ptotal = P(∞) for the chosen profile.

Calculation and interpretation depend on the specific radial profile. The general idea is to find r such that P(r) = Ptotal/2. In practice, many common profiles yield simple results. For a Gaussian beam I(r) = I0 exp(-2 r^2 / w^2) with w as the 1/e^2 radius, the half-power radius is r_hp = w sqrt(ln 2 / 2) ≈ 0.589 w. For a uniform disk, where I(r) = I0 for r ≤ R and 0 beyond, the half-power radius is r_hp = R / √2 ≈ 0.707 R.

Applications and context vary. The halvevermogenstraal is used in optics and photonics to characterize beam concentration and focusing quality, in astronomy to describe how starlight or galaxy light is distributed, and in antenna theory or imaging to compare radial energy concentration. It is related to, but distinct from, concepts such as the full width at half maximum and the half-light or effective radius, depending on the profile and field of application.