The φ angle is the angle from the positive *y*-axis
toward the positive *z*-axis, to the vector's
orthogonal projection onto the *yz* plane. The φ
angle is between 0 and 360 degrees. The θ angle is the angle
from the *x*-axis toward the *yz* plane,
to the vector itself. The θ angle is between 0 and 180 degrees.

The figure illustrates φ and θ for a vector that
appears as a green solid line. The coordinate system is relative to
the center of a uniform linear array, whose elements appear as blue
circles.

The coordinate transformations between φ/θ and *az/el* are
described by the following equations

$$\begin{array}{l}\mathrm{sin}(\text{el})=\mathrm{sin}\varphi \mathrm{sin}\theta \hfill \\ \mathrm{tan}(\text{az})=\mathrm{cos}\varphi \mathrm{tan}\theta \hfill \\ \hfill \\ \mathrm{cos}\theta =\mathrm{cos}(\text{el})\mathrm{cos}(\text{az})\hfill \\ \mathrm{tan}\varphi =\mathrm{tan}(\text{el})/\mathrm{sin}(\text{az})\hfill \end{array}$$