Physical optics inverse diffraction

A general method for solving the inverse diffraction problem is presented. It is based on an identity of Bojarski which states that
\gamma(x)
and
\Gamma(p)
are a Fourier transform pair. Here
\gamma(x)
is the characteristic function of the target (
\gamma=1
inside the target,
\gamma = 0
outside),
p = (2\omega/c)J,\omega
is the frequency,
J
is a unit vector specifying the aspect, and
\Gamma(P)
can be obtained by measurement of the backscattered electromagnetic far field at frequency
\omega = (c/2)|P|
and aspect
J=|p|^{-1}p
. If data is obtained in any subset
D
of
p
space, the method yields partial or complete information about the target geometry. It is used to rederive earlier results very simply and to obtain a significant new solution, in which the target geometry is completely determined using frequencies only in a practical frequency band and aspects in a narrow cone.