Radiometer system designs specify the antenna in terms of beam efficiency.For a pencil beam antenna with the boresight at θ = 0, the beam efficiency is the ratio(or percent) of the pattern power within a specified cone centered on the boresight tothe total radiated power. In terms of the radiation intensity U,

 

where U includes both polarizations if necessary. Extended noise sources, such asradiometry targets, radiate noise into sidelobes of the antenna. Beam efficiency measuresthe probability of the detected target being located within the main beam (θ≤θ₁).

Sometimes we can calculate directivity more easily than the pattern everywhererequired by the denominator of Eq. (1): for example, a paraboloidal reflector. Weuse Eqs. (2) and (3) to calculate the denominator integral:

 

 

 

This reduces Eq. (1) to

 

Equation (4) greatly reduces the pattern calculation requirements to compute beamefficiency when the directivity can be found without pattern evaluation over the entireradiation sphere.