Orthogonality of crossing plane waves

Normally, waves do not contain zero frequency. Thus the time integral of a waveform normally vanishes. Likewise, for a dipping plane wave, the time integral vanishes. Likewise, a line integral across the (t,x)-plane along a straight line that crosses a plane wave or a dipping plane wave vanishes. Likewise, two plane waves with different slopes should be orthogonal if one of them has zero mean.

I suggest that spatial aliasing may be defined and analyzed with reference to plane waves rather than with reference to frequencies. Aliasing is when two planes that should be orthogonal, are not. This is like two different frequency sinusoids. They are orthogonal except perhaps if there is aliasing.