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

The Hehnholtz equation in the fi equelcy-domain is given by
(r' * !)u(r, ro; c,r) : -/(r - 16)
(4. 16)
rvhele
U(r, ro;ar) : l*
U1r,r";t) e-ì-t rlt
arrd wlrere U(r,r";u) is the total electromagnetic wavefield, /(r -
r'") is the
source, c is the velocity of light, ancl ro is the source coordinate. The first
algument of U(r,ro;ø) replesents the receivel location, ancl the second is
the soulce location. Comparecl rvitli Eq.(4.4), the subsulface velocity perturbation
a(r) is norv not necessary to be included in the SAR case. The
source function /(" - ".)
of a SAR system is a point source with respect
to the azimuth dimension. But this source functiol is a tirne-dependent
function in the range climension because the tlansmitted signal is lineally
fi'equeucy-nodulated. The source function il the range dilnension is a silrple
convolution of a clelta function with a fi'equercy rnoclulation function,
and consequently the ternpolal terr¡ cloes not play an important role aftel
the range complession. The lange cornpression is straightfolwald, and is not
main interest of the discussion in this section. Our analysis can continue rvitlt
the assurnption that the rânge coù1pÌession has already been cornpleted.
The total rvavefielcl U(r, r'o;ø) can be clecornposecl ilto the incident rvavefielcl
U¡ genelated by the soulce, and the scattered rvavefielcl Us clue to scattering
on the sul'face; Tlius U(r, ro;c,r) can be rervritten as
U(r, ro; ø) : Ut(r,ro; o) * Us(r, ro; i,:)
(4.r7)