Contribution to the space–time study of stellar speckle patterns

The temporal behavior of stellar speckle patterns is statistically analyzed. The time-only power spectrum is shown to be the sum of two exponentially decreasing functions defining two characteristic time constants. The corresponding correlation is the sum of two Lorentzian functions. This is consistent with the first-order expansion of the power spectrum deduced from the multiple-layer model for atmospheric turbulence. However, this model fails to account for the experimental data that show a strong correlation between the spatial structure of a speckle pattern and its temporal behavior. This leads to the introduction of a new empirical model, called the randomly jittered speckle pattern model, which gives a preponderant place to image motion. The speckle lifetime then appears to be substantially longer than the corresponding measured time constant. As a consequence, a preliminary compensation of the image motion appears to be particularly interesting in speckle interferometry or active optics experiments.