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

4.4 The Inversion
The equation Eq.(a.23), clelived in the previous section, inclicates that the
inverse scattering problem associated s'ith the SAR theory leduces to a problem
of estirnating the cornplex backscatteling coefficient oi(r) fr:orn the backscatteled
wavefielcl Ue(.r¡,y¡,261c.l) as observecl along the line y6 : so : 6.
Inversion of Eq.(a.23) can utilize a spatial Fourier tlansfolmation to clerive a
sirnple relation between the obselvecl clata and the backscattering coefÊcient
in the /-fr clomail.
As rlentioned in the plevious section, the forwalcl founula, Eq.(4.23), is
sinilar to the conventional expression of the range-compressecl SAR siglal
except for the spreading fa ctot lf R2 tenn. Most conventional SAR processor-s
use exp{-i 2a,,,8/c} as the azimuth inpulse-response function. It has l¡een
known that it is clifÊcult to find an explicit Fouliel transfolm forr¡ula for this
frrnctiorr.
If, horvever', olly a 1/,R terrn is ilcluded, it becomes to obtain an explicit
Fourier transforur relationship with respect to ¿0. T1ìe Fouliel tt'ansfortl
of tlre function exp\*i2uRlcj f R is a Hankel function of the seconcl kincl
(Magnus ancl Obelhettinger' [71], p.ll8). Moreovei', the fir'st-olcler asymptotic
approxirnation of the Hankel function recluces the result to the kelnel of
the Foulier t¡:ansform as shown by Eq.(4..3) in Appendix A. The integland
in Eq. (4.24), ltowever', is a squale of the Green's function. To ovelcome
this problem, a modified function can be introducecl il an analogous rnanner
to tlie seismic Born inversioli scheme ({ol instance, trq.(10) of Bleistein
78