The effects of finite exposure time (used to record astronomical speckle data) on the speckle transfer function are shown to be highly dependent on the details of the atmospheric turbulence in the optical path as well as on the deterministic wavefront aberrations of the optical system. Both Taylor turbulence, where a frozen layer or layers are convected across the aperture, and Mintzer turbulence, where the turbulence is boiling and stationary, are taken into account. Computations have been made for some typical cases of the time integrated speckle transfer function for various combinations of Taylor and Mintzer turbulence with focused and defocused optical systems.