We present the electron density map of the asymmetric ripple phase of dilau
roylphosphatidylcholine. We find that the primary feature characterizing th
e "asymmetry" of the rippled bilayers is the difference in the bilayer thic
kness in the two arms, and not the asymmetry of the bilayer height profile
as is generally assumed. This difference in the bilayer thickness can be at
tributed to a mean tilt of the hydrocarbon chains of the lipid molecules al
ong the direction of the ripple wave vector. We propose a Landau theory for
this phase which takes into account the anisotropic elastic properties of
a bilayer with tilt order.