Third, if clock CD controls the emission and reception of radar pulses to locate a scattering event in (filled circle in Figure 13), then upon being transferred to AB, these pulses can be used by AB to reconstruct an image of that event's location in (unfilled circle in Figure 13). By applying this reconstruction to scattering events lying on, say, a time-like hyperbola in , (dashed curve in Figure 13), one finds that its image in is a straight line in (dashed line in Figure 13). Similarly, a spacelike straight line of simultaneity gets reconstructed as a spacelike hyperbola of simultaneity in F.

Mathematically this reconstruction assumes its simples form when expressed in terms of the null coordinates

of Figure 1:

Physically this reconstruction is based entirely on , the
acceleration of radar unit C of clock CD, and Eq.(28), the common frequency shift factor, which is
best expressed in terms of the change in the boost coordinate ,

Let

be the integer-valued radar coordinate of a scattering event located by CD in . Then that event is related to its image in by

This is the relationship between the solid and the hollow circled events in Figure 13.