  The concept of time reversal (TR) of scalar wave is reexamined from basic
principles. Five different time reversal mirrors (TRM) are introduced and their
relations are analyzed. For the boundary behavior, it is shown that for
paraxial wave only the monopole TR scheme satisfies the exact boundary
condition while for spherical wave only one of the mixed mode TR scheme, after
multiplication by two, satisfies the exact boundary condition. The asymptotic
analysis of the near-field focusing property is presented. It is shown that to
have a subwavelength focal spot the TRM should involve dipole fields. The
monopole TR is extremely ineffective to focus below wavelength as the focal
spot size decreases logarithmically with the distance between the source and
TRM. Contrary to the matched field processing and the phase processor, both of
which resemble TR, TR in a weak- or non-scattering medium is usually biased in
the longitudinal direction, especially when TR is carried out on a {\em single}
plane with a {finite} aperture. This is true for all five TR schemes. On the
other hand, the TR focal spot has been shown repeatedly in the literature, both
theoretically and experimentally, to be centered at the source point when the
medium is multiply scattering. A reconciliation of the two seemingly
conflicting results is found in the random fluctuations in the intensity of the
Green function for a multiply scattering medium and the notion of
scattering-enlarged effective aperture.
