simply as the results of various integrations and
simulation of two-dimensionally rough surfaces
manipulations of the underlying electromagnetic
is still to come, awaiting the completion of more
wave equations. The integrands contain (usually)
tractable numerical treatments of fully vectorial
unknown tangential field or equivalent current
electromagnetic scattering.
values, which serve as sources of the general field
In contrast to the PO-based approaches, the
to be calculated. Use of the tangent-plane KA
small perturbation method (SPM) proceeds by
approximations to obtain these surface sources
applying a correction factor to the field that would
implies a large radius of curvature on the scatter-
be present on a flat surface located at the mean of
ing surface relative to the incident wavelength.
the actual surface. This factor is expanded in a
This statement does not supply a very precise
perturbation series. Small rms surface heights and
criterion for range of validity, and investigations
slopes are required. Relative at least to the more
have shown the importance of having a relatively
basic KA formulations, SPM has the advantage of
large correlation length, even for rms heights that
being fully polarimetric in principle, although
one might suppose corresponded to mild radii of
cumbersome higher-order calculations may be re-
curvature (Thorsos 1988). Except in some deter-
quired for reasonably accurate and complete po-
ministic cases, additional assumptions must typi-
larimetry. Recently the phase perturbation method
cally be made (including small slopes and con-
(PPM) was introduced as an enhancement of SPM
stant Fresnel reflection coefficients), otherwise
(Winebrenner and Ishimaru 1985). Exploration of
evaluation of the integrals cannot in general be
the method by workers at the University of Wash-
carried out. With the stationary phase approxi-
ington and elsewhere has established a consider-
mation applied in the high frequency limit, one
ably wider range of application of PPM relative
obtains the geometrical optics approximation
to the more traditional SPM formulations (see
(GO). This implies essentially that only parts of
figure in Ishimaru and Chen 1990).
the surface with local specular scatter toward the
Fung et al. (1992) have extended earlier work
observer contribute to the integral. The Fresnel
for perfectly conducting surfaces (Fung and Pan
coefficients applied within conventional KA for-
1987) so that computations for dielectric surfaces
mulations have polarimetric content in the sense
can be carried out in the same manner. The re-
that they are different for horizontal and vertical
sulting integral equation method reduces to KA
polarizations. This inclusion of polarization ef-
and SPM terms at the appropriate limits for both
fects is approximate at best, however, and one
like and cross-polarized results. Good results are
should not expect complete and accurate pola-
shown with the new method for rms surface
rimetry based on classical KA formulations.
heights on the order of the wavelength and slopes
Without the addition of special measures, such
(i.e., correlation length divided by rms height)
formulations also do not conserve energy in
approaching 0.4.
general, hence they do not provide reciprocal
The unified perturbation method (UPM) has
information, i.e., the use of active to infer passive
been introduced and tested by Rodriguez, Kim,
behavior.
and their co-workers (Kim et al. 1992, Rodriguez
Over recent years the shortcomings of these
and Kim 1992, Rodriguez et al. 1992a). A pertur-
approximations in terms of shadowing and mul-
bation expansion is used that converges over a
tiple reflection have been attacked, and higher-
wider domain than SPM, and that converges in
order versions have been constructed (Chen and
the appropriate limits to the KA, SPM, and two-
Ishimaru 1990, Ishimaru and Chen 1990). Suc-
scale results. In the last case, this is accomplished
cessful application of these enhanced KA treat-
without the introduction of an artificial adjust-
ments is seen even at slopes on the order of unity,
able parameter for the spectral split. Recent 1-D
with rms heights and correlation lengths some-
roughness tests show success in addressing sur-
what greater than one wavelength. Thus, these
faces with rms height approaching one wave-
formulations may be capable of addressing the
length with rms slopes less than or equal to about
roughest surfaces without handling the smallest
0.8, for both horizontal and vertical polarizations.
correlation length range. We note as an important
In addition to the obvious merits of the UPM
advance that energy is conserved in these calcu-
system on the basis of this reported performance,
lations. At the same time, the introduction of the
we pause to take note of a particular application
shadowing and tapering functions is cumbersome
of the method to ocean backscatter simulation.
and requires further study. For the most part,
Little or no work has been done on ocean simula-
5
Previous Page
