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. 2019 Aug 13;9:11748. doi: 10.1038/s41598-019-47979-8

Figure 1.

Figure 1

(a) In average, each speckle (schematically represented by the blue ellipses) carries valid phase information only for the correlation time of the speckle pattern. Assuming that all speckle in the averaged area are subject to a common phase change in addition to random uncorrelated phase changes, one can use the phase of speckle A as long as it is valid and then continue with the phase of speckle B. Using multiple speckle, phase information for times significantly exceeding the correlation time can be extracted. (b,e) Exemplary cross-spectrum magnitude and phase assuming infinite correlation time. Total phase changes can either be computed directly (blue arrow) or using the Knox-Thompson path (green arrows). (c,f) Magnitude and phase of the cross-spectrum without averaging; neither method can extract the phase beyond the correlation time. (d,g) Magnitude and phase of ensemble averaged cross-spectrum. Direct phase differences (blue) cannot be used for phase extraction, but Knox-Thompson (green) method can be applied since phase values for small Δt are valid.