Illumination efficiency

Antenna [aperture] illumination efficiency is a measure of the extent to which an antenna or array is uniformly excited or illuminated. It is typical for an antenna [aperture] or array to be intentionally under-illuminated or under-excited in order to mitigate sidelobes and reduce antenna temperature. It is not to be confused with radiation efficiency or antenna efficiency.

Definition

Antenna [aperture] illumination efficiency is defined as "The ratio, usually expressed in percent, of the maximum directivity of an antenna [aperture] to its standard directivity." It is synonymous with normalized directivity. Standard [reference] directivity is defined as "The maximum directivity from a planar aperture of area A, or from a line source of length L, when excited with a uniform-amplitude, equiphase distribution.". Key to understanding these definitions is that "maximum" directivity refers to the direction of maximum radiation intensity, i.e., the main lobe. Therefore, illumination efficiency is not a function of angle with respect to the antenna [aperture], but rather is a constant of the aperture for all aspect angles.

Standard directivity

The distinction between maximum directivity and standard directivity is subtle. However, one can infer that, if an antenna [aperture] were excited [illuminated] uniformly with no phase difference (equiphase) over the entire aperture, then the illumination efficiency would be equal to unity. It is very typical for an antenna [aperture] to be intentionally under-excited [illuminated] with a "taper" in order to reduce radiation pattern sidelobes and antenna temperature. In such a design, the maximum directivity is reduced because the full aperture is not being used to the full extent possible, and the illumination efficiency will be less than unity. IEEE's choice of words is somewhat confusing, because "maximum" directivity is always less than or equal to "standard" directivity. The word maximum, in this case, is used to mean the maximum radiation intensity of the overall directivity pattern, which is otherwise defined for all aspect angles.

Relationship to antenna efficiency

There is a very nuanced relationship between illumination efficiency and antenna efficiency, but essentially it is that the former is a constant over all aspect angles, while the latter is a function of aspect angle.

The relationship of the directivity of an antenna to its effective area is a universal constant:

${\frac {D}{A_{e}}}={\frac {4\pi }{\lambda ^{2}}}$

Effective area, $A_{e}$ is less than or equal to the physical aperture area, $A$, by its antenna efficiency, $\eta _{a}$:

$A_{e}=A\eta _{a}$

Therefore, the standard directivity cannot exceed:

$D_{std}\leq A{\frac {4\pi }{\lambda ^{2}}}$

since $\eta _{a}\leq 1$.

Per the IEEE definition:

$D_{max}=\eta _{i}D_{std}\leq {\frac {\eta _{i}}{\eta _{a}}}A_{e}{\frac {4\pi }{\lambda ^{2}}}={\frac {\eta _{i}}{\eta _{a}}}D$

where $\eta _{i}$ is the illumination efficiency.

Therefore:

$D_{max}\leq {\frac {\eta _{i}}{\eta _{a}}}D$

Since $D_{max}\geq D$ this can only be true if $\eta _{i}\geq \eta _{a}$

This conundrum is explained by the fact that effective area is reduced as one changes aspect angle away from broadside. To understand this, imagine viewing an aperture or array from the side, and one realizes that the effective area is zero. Therefore, both effective area and antenna efficiency are functions of aspect angle, since the area is a constant, and therefore:

$0\leq \eta _{a}\leq \eta _{i}$