= Outgoing angular spectrum
{title2=$\mathcal E g=(2\pi)^{-1}\int\widehat g(q)e^{iqx+i\beta(q)z}dq$}
The <outgoing angular spectrum> propagates prescribed scalar boundary data into a half-space. For $e^{-i\omega t}$ time dependence, $\beta(q)=\sqrt{k^2-q^2}$ has nonnegative real part on propagating modes and nonnegative imaginary part on evanescent modes. Its trace at the boundary is $g$, and each mode solves the <Helmholtz equation>. The spectral representation can be interpreted through distributions for nondecaying plane-wave data.
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