To be relativistically precise, we must add that these equations are correct only if the observers at both A and B are at rest with respect to A, but since the corrections for moving observers is of order [] , they are negligible compared to doppler errors which are always of order v/c. Doppler errors arise in two ways: first, from the radial velocity, v , of the reference element with respect to the pilot source, and second, from the difference, [] , between the radial velocities of the kth and reference elements, In Appendix A we have derived an expression for <5, the difference in phase between the contributions to the field at the pilot source, as a function []. and [], for j, k = 1, ..., n. Perfect retrodirection is, of course, equivalent to [] for all pairs of elements, j and k. Considering first the error due only to the radial motion of the reference element (i.e. setting [] in the expression for [] in Appendix A), we get where is the phase delay time for the signal from the i-th element arriving at the pilot source (r = o) at time t. For a planar array,
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