In a method of spatial encoding in magnetic resonance experiments,
encoding kernels are imposed into the magnetization signal during the
excitation or re-focussing process using a transmit array coil. Separate
transmit array coil elements are provided so that in a particular phase
encode direction, z in this case, they can be driven to produce partially
orthogonal B1 fields, T.sub.t(r), that exhibit a Fourier phase
distribution given by
T.sub.t(r)=T.sub.0e.sup.i(k.sup..sub.t.sup..sup.T.sup.z)=T.sub.0e.sup.i(t.-
DELTA.k.sup..sub.z.sup.z).
The NMR signal, S.sub.m(k.sub.n), received by a coil array element m of
the M receive coils, during application of a pulse sequence for the n-th
phase encoding step in k-space is then given by
S.sub.m(k.sub.n)=.intg.dr.rho.'(r)e.sup.i(k.sup..sub.n.sup..multidot.r)C.s-
ub.m(r)
such that
.rho.'(r)=.rho.(r)T.sub.t(r)=.rho.(r)T.sub.0e.sup.i(t.DELTA.k.sup..sub.z.s-
up.z)
where k.sub.n is the n.sup.th spatial encoding k-space trajectory for the
spatial dimension r, C.sub.m(r) is the receive coil sensitivity, and
.rho.'(r) represents the magnetization spatial distribution arising from
the spin density spatial distribution .rho.(r), the pulse sequence and
the transmit array excitation/re-focussing phase profile. It is clear
that using an appropriately driven transmit array capable of producing
the t.sup.th phase encode term, gradient phase encode steps may be
eliminated.
