  All optical techniques used to probe the properties of Bose-Einstein
condensates have been based on dispersion and absorption that can be described
by a two-level atom. Both phenomena lead to spontaneous emission that is
destructive. Recently, both were shown to lead to the same limit to the signal
to noise ratio for a given destruction. We generalise this result to show that
no single-pass optical technique using classical light, based on any number of
lasers or coherences between any number of levels, can exceed the limit imposed
by the two-level atom. This puts significant restrictions on potential
non-destructive measurement schemes.
