  Estimators of outer scales of atmospheric turbulence usually fit the phase
screen snapshots derived from local wave front sensors to a Zernike basis, and
then compare the spectrum of expansion coefficients in this basis with a
narrowing associated with decreasing outer scales.
  This manuscript discusses aspects that arise if the Zernike basis is
exchanged for a Karhunen-Loeve basis of statistically independent modes. Data
acquisition turns out to be more demanding because sensing the tip-tilt mode is
required. The data reduction methodology is replaced by fitting of variance
ratios of an entire (long exposure) data set. Statistical testing of hypotheses
on outer scale models can be applied to a set of modes - supposing other noise
originating from detector readout and the optical train can be disentangled.
