If the intergalactic medium were suddenly reionized at a redshift z, then the optical depth to electron scattering would be ~ 0.02 h-1 ((1 + z) / 10)3/2 (b h2 / 0.02) (generalisation to more realistic scenarios of gradual reionization is straightforward). Even when this optical depth is far below unity, the ionized gas constitutes a `fog' - a partially opaque `screen' - that attenuates the fluctuations imprinted at the recombination era; the fraction of photons that are scattered at zi then manifest a different pattern of fluctuations, characteristically on larger angular scales. This optical depth is consequently one of the parameters that can in principle be determined from CMB anisotropy measurements (Zaldarriaga, Spergel and Seljak 1997). It is feasible to detect a value as small as 0.1 - polarization measurements may allow even greater precision, since the scattered component would imprint polarization on angular scales of a few degrees, which would be absent from the Sachs-Wolfe fluctuations on that angular scale originating at trec.
here are two effects that could introduce secondary fluctuations on small angular scales. First, the ionization may be patchy on a large enough scale for irregularities in the `screen' to imprint extra angular structure on the radiation shining through from the `last scattering surface at the recombination epoch'. Second, the fluctuations may have large enough amplitudes for second-order effects to induce perturbations. (Hu, 1999)