Two signals recorded at different spatial locations during the rebroadcast of the TR signal from a single channel. Left: signal located at the position of the original virtual source pulse. Right: signal recorded at an arbitrary position away from the original virtual source. For the calculation of [Eq. (4)], each waveform is split at the time of focus (here , denoted by the vertical black dashed line and the change in color of the waveform from blue to red). The blue portion of the waveform illustrates while the red portion represents . Figure 2 shows the same two signals expanded around the focal time .
Same signals presented in Fig. 1. The -axis has been expanded around the focal time, , to show the fine structure of the waveforms.
Spatial focusing image resulting from the TRP. Left: maximum-in-time amplitude squared , right: symmetry . Both images are normalized to the maximum values and the colormap floor is restricted to 0.25, to easily extract the resolution. Note the unfortunate additional noise introduced in the symmetry image; though this spatial noise does not inhibit the ability of the symmetry metric to more accurately reconstructs the original source shape. For the single pointlike source scenario, the symmetry of the focused signal adds little information, however, the added value of the symmetry measurement is apparent for more complex, or multiple sources (see Figs. 4 and 5).
Spatial focusing image resulting from the TRP for two closely spaced sources (distance between the centers ). Left: maximum-in-time amplitude squared , right: symmetry . Both images are normalized to the maximum values and the colormap floor is restricted to 0.25, to easily extract the resolution. Note the ability of the symmetry measurement to discern the two sources while the amplitude metric illuminates only one oblong source.
Spatial focusing image resulting from the TRP for two closely spaced sources (distance between the centers ). Left: maximum-in-time amplitude squared , right: symmetry . Both images are normalized to the maximum values and the colormap floor is restricted to 0.25, to easily extract the resolution. Here the symmetry metric is not able to resolve the two sources completely, however, it does indicate an oblong source shape, as opposed to the circular source shape shown for a single source in Fig. 3. In both Figs. 3 and 5, the amplitude metric alone does not allow this same level of source shape/extent discrimination.
Spatial focusing comparison of maximum-in-time amplitude squared (, solid blue line), the symmetry measure (, solid red line), the energy metric (, dark yellow line) and the spatial variation in the Green function (, dashed green line). The variation in the Green function is calculated by the Green function from the source transducer to the virtual source location cross-correlated with the Green function from the same source location to each scanning position with zero-lag (or shift) in the correlation. Note that all metrics define approximately the same focal extent for a single source, as indicated by the vertical black dotted lines.
Spatial time reversal focusing in the case of two close-by point-like sources. Comparison between the maximum-in-time squared amplitude image (, solid blue line) and the temporal symmetry image (, solid red line). The images are calculated along the vertical line at in the plane where both sources lay (see Fig. 4). The variation of the Green functions (, or 2) away from the two source locations are shown by the dashed lines (green and yellow represent source 1 and 2, respectively) as well as the linear superposition of these variations (i.e., ) shown in the black dotted line. Additionally the original source locations are indicated by the two open circles at 10 and .
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