  In a microwave background polarization map that covers only part of the sky,
it is impossible to separate the E and B components perfectly. This difficulty
in general makes it more difficult to detect the B component in a data set. Any
polarization map can be separated in a unique way into "pure E," "pure B," and
"ambiguous" components. Power that resides in the pure E (B) component is
guaranteed to be produced by E (B) modes, but there is no way to tell whether
the ambiguous component comes from E or B modes. A polarization map can be
separated into the three components either by finding an orthonormal basis for
each component, or directly in real space by using Green functions or other
methods.
