The spectral maps of dynamic speckle patterns: A new perspective to look at the motion-induced spatiotemporal cross-correlation

We introduce the spectral map method as a means to visualize the spatiotemporal correlation in dynamic speckles. Dynamic speckle patterns of moving diffuse objects are Fourier transformed to construct spectral maps in spatial domain (r-space) and spatial-frequency domain (k-space). The periodic patterns in r-space spectral maps demonstrate the spatiotemporal cross-correlation induced by the directional motions. To resolve the spectral bands in k-space spectral maps, and to observe the concomitant appearance of the periodic pattern in r-space spectral maps, the frequency must exceed the minimum values given by the speckle size and the speed. A bigger speckle size helps to reveal fast dynamics, and to ease the requirement on the minimum frequency. The transition from ordered translational speckles to chaotic boiling speckles at different speeds and speckle sizes is elucidated in connection with the change observed in spectral maps.