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High-contrast imaging observations are fundamentally limited by the spatiallyand temporally correlated noise source called speckles. Suppression of specklenoise is the key goal of wavefront control and adaptive optics (AO),coronagraphy, and a host of post-processing techniques. Speckles average at arate set by the statistical speckle lifetime, and speckle-limited integrationtime in long exposures is directly proportional to this lifetime. As progresscontinues in post-coronagraph wavefront control, residual atmospheric speckleswill become the limiting noise source in high-contrast imaging, so a completeunderstanding of their statistical behavior is crucial to optimizinghigh-contrast imaging instruments. Here we present a novel power spectraldensity (PSD) method for calculating the lifetime, and develop a semi-analyticmethod for predicting intensity PSDs behind a coronagraph. Considering afrozen-flow turbulence model, we analyze the residual atmosphere specklelifetimes in a MagAO-X-like AO system as well as 25--39 m giant segmentedmirror telescope (GSMT) scale systems. We find that standard AO controlshortens atmospheric speckle lifetime from ~130 ms to ~50 ms, and predictivecontrol will further shorten the lifetime to ~20 ms on 6.5 m MagAO-X. We findthat speckle lifetimes vary with diameter, wind speed, seeing, and locationwithin the AO control region. On bright stars lifetimes remain within a roughrange of ~20 ms to ~100 ms. Due to control system dynamics there are no simplescaling laws which apply across a wide range of system characteristics.Finally, we use these results to argue that telemetry-based post-processingshould enable ground-based telescopes to achieve the photon-noise limit inhigh-contrast imaging.

The Mysterious Lives Of Speckles. I. Residual atmospheric speckle lifetimes in ground-based coronagraphs