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. The results of recent analytical work performed to characterize the short-exposure blurring effects of path integrated optical turbulence for annular aperture systems is described using the modulation transfer function. Results presented here extend the circular case to the annular aperture problem involving a circularly symmetric central obscuration associated with telescope optics secondary mirrors. To enable this extension, adjustments to procedures that compute the tilt-variance and phase-tilt correlation effects are described, and the results are illustrated. A four-dimensionally parameterized function of turbulence strength, diffraction influence, angular frequency, and fractional central obscuration is given.

Short-exposure turbulence effects on the modulation transfer function of annular aperture optical systems