Fig. 9.

Phasor rotation by axial motion and signal penalty after complex averaging of axially displaced signals. (a) Example of a signal phasor trajectory of 1000 repeated measurements of a weak reflector (an attenuated glass surface). Over 1/70 second, the phasor (blue dots) is markedly moving around the origin. Corresponding noise signals are shown as red dots. The main source of displacement in this measurement was air flow from a nearby air condition outlet. (b) Relative signal intensity decrease caused by complex averaging of $N$ signals with relative displacements $W$ of 0.5 (solid line), 0.05 (dashed line), and 0.005 (dotted line). For reference, $1/N$ is plotted as well. While relative displacements of λ/200 (W = 0.005) between consecutive signals almost do not affect the intensity of the averaged signal, greater displacements such as $\lambda /20$ and $\lambda /2$ cause a periodic, significant signal reduction. In unlucky cases, $P(N,W)$ reaches zero such that the averaged signal is completely annihilated.