INVERSION OF SYNTHETIC APERTUR,E R,ADAR (SAR) - MSpace ...

wheÌe
k':frf
a¡cl lc -_ uf us
antl rvhere i is a unit vector pointing flom a scattelel to tlle obselvation position,
and li; is the rvavenumber (Bleistein [10]). When Eq.(a.11) is substitutecl
into Eq.(4.9), the scattered fielcl in the {ar-field region beconìes
' exP(-ifrrì r
Us(r,ro;ø) = T;/
exp(ik'.r'') À''zô(r') exp(-lk.r'') r/r' (4.12)
rvhere k is the incidelt wave vector dilectecl frorr the soulce position to a
scatterer'. Thus the amplitucle of the scattered field is
?(k, k') : I
exp(ik'. r') ft2cv(r'') exp( -ik.
r') dr' (4.13)
If the ol¡servation point coincides rvith the source location, the observation
dilection k/is opposite to the clilection of the inciclent wave vector k (i.e.
k' : -k ). Tlien Eq. (4. t 3) l¡ecornes
?(k, -k) : [ .*p¡-ZtU' r') lcza(r'1dr'
J "
(4.14)
ancl a Fouliel tlansfolrn relationship gives
"ft) : & I r1t, -t¡eld?I' r) ¿¡
(4.15)
(Weglein [106]).
Eq.(4,15) thus allorvs the acoustic velocity configulation to be detelmined
rvithin the Born (first) approximation fi'orn backscattering infolrnation.
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