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## Retardation (frequency domain)

It is often convenient to arrange the calculation of a wave to remove the effect of overall translation, thereby making the wave appear to stand still.'' It is easy enough to introduce the time shift t0 of a vertically propagating wave in a hypothetical medium of velocity , namely,
 (67)
Instead of solving equations in coordinates (t,x,z) we could solve them in the so-called retarded coordinates (t',x',z') where t'=t-t0(z), x'=x and z'=z. (For more details, see IEI sections 2.5-2.7.) A time delay t0 in the time domain corresponds to multiplication by in the -domain. Thus, the wave pressure P is related to the time-shifted mathematical variable Q by
 (68)
which is a generalization of equation (55) to depth-variable velocity. (Equations () and () apply in both x- and kx-space). Differentiating with respect to z gives
 (69) (70)
Next, substitute () and () into Table .4 to obtain the retarded equations in Table .5.

 zero general diffraction + thin lens

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12/26/2000