How to derive the mathematical condition for the plane-wave approximation?

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Milo Hyde

Attached is the derivation for in-door-range RCS quiet zone. It is equivalent to the far-zone or plane-wave approximation in optics.

P. K. Karmakar

You are right, but in optics. I am, however, interested in the area of acoustics, where the required condition for plane-wave is given as, k.r>>1, where k is the wavenumber and r is the distance of the detector from the source. Could anybody provide books dealing with the derivation of this relation?

Ufimtsev discusses this in the first few pages of his Fundamentals of the Physical Theory of Diffraction.