  Aberration-corrected microscopes with sub-atomic resolution will impact broad
areas of science and technology. However, the experimentally observed lifetime
of the corrected state is just a few minutes. Here we show that the corrected
state is intrinsically unstable; the higher its quality, the more unstable it
is. Analyzing the Contrast Transfer Function near optimum correction, we define
an 'instability budget' which allows a rational trade-off between resolution
and stability. Unless control systems are developed to overcome these
challenges, intrinsic instability poses a fundamental limit to the resolution
practically achievable in the electron microscope.
