 
Advanced Radar Cross Section Signature Reduction
Short Courseby Marietta Scientific, Inc.
Course Description:
 Marietta Scientific is offering an Advanced Radar Cross Section Reduction short
course for new and experienced RCS engineers. The course emphasizes the importance
of physical understanding of scattering mechanisms through the use of electromagnetic
theory, analytical and measurement diagnostics. Several successful prediction codes are
reviewed. With base understanding, several methods are studied indepth to aid the
engineer in understanding what causes scattering and how it can be managed. Two
methodologies are discussed to aid in prediction and design of high performance scattering
geometries. Length and wavelength are tightly connected to give physical meaning for the
transitioning of energy. Additionally, an indepth review of far field imaging theory will
be discussed to establish the fundamentals of imaging in measurements and prediction
codes. 
Course Lecturers:
 John F. Shaeffer of Marietta Scientific, Inc. has over fifteen years experience
in low observable technologies and over thirty years in electromagnetics. John is the
primary lecturer of RCSR short course by Marietta Scientific, Inc. and Georgia Tech
Research Institute. He is a coauthor of RADAR
CROSSSECTION. 
 Brett A. Cooper of Marietta Scientific, Inc. has over thirteen years experience
in hardware and software radar design and design of high performance RCS systems. Brett
has developed several short course lectures, which has been given thought industry for
several years. 
Course Availability:
 The Advanced Radar Cross Section short course is available to any United States
organization. The course attendance can vary with a typical load of less than 40 attendees
being optimal. Contact John Shaeffer
or Brett Cooper for more details. 
Course Outline:



Introduction 
Fresnel Scattering 
Design Topics 
EM Theory 
RCS (back of the envelope)
Solutions 
Scaling Issues 
Scattering Phenomena 
Aperture Theory 
Fixture Design 
EM Prediction Codes &
Their Uses 
Geometrical Shaping 
Radar Imaging Theory 
Analytical Diagnostics 
Planform Shaping 
Bistatic KSpace Imaging
Theory 
Advanced Codes 
Shaping / Material
Synthesis 
bistatic KSpace Imaging II 
 Introduction – Radar Cross Section Reduction
methodology and phenomenology will be reviewed. This overview will discuss the approaches
to be examined in the forthcoming lectures. A general methodology will be reviewed on how
to better understand complex scattering bodies. Scattering phenomena, though better
understanding of the physical mechanisms will be discussed. Along with becoming a
"Phenomenologist" the concepts and methods of energy management will be
discussed to achieve RCSR. Other topics will include an overview of typical threats
sectors.

 EM Theory – Electromagnetic theory as it
applies to scattering bodies will be reviewed. This lecture will prepare the attendee with
a better physical feel for the underlying theory and the practical applications of the
theory. Topics include Maxwell’s equations; EM wave characteristics; boundary
conditions; and near & far field scattering.

 Scattering Phenomena – Electromagnetic
scattering mechanisms will be reviewed. Emphasis will be on the physical understanding of
how scattering occurs. This will enable the attendee to identify scattering phenomena on
more complex scattering bodies. Simple geometries will first be used to demonstrate
scattering phenomena. Then, progressively more complex bodies will be used to illustrate
how to decompose these complex bodies into their simpler form. Included are: specular;
side lobes; diffraction; traveling waves (surface, creeping and edge); and multiple
bounce. Several illustrations and animations will be used to enhance the physical
understanding of each phenomenon.

 EM Prediction Codes & Their Uses – An
indepth discussion of the several types of EM modeling codes that are available
throughout industry will be reviewed. Each prediction code will be discussed the general
approximations used in their formulation. A better link between scattering phenomena and
what type of codes will predict them will be among the major topics. Additional topics
include: modeling issues such as rendering and tessellation; solution fidelity; several
code implementations (including GO; PO; GTD; PTD; MOM; and FTD); resources needed; and
utilization of codes (what code when).

 Analytical Diagnostics –The utilization of
several types of analytical diagnostic tools will be discussed to demonstrate the power in
interrogating their results for more information. Discussed will be the different ways
that useful information can be ascertained from commonly used codes to help in quickly
understanding complex scattering solutions with limited resources. The attendee will be
shown the utility of such exploits to help in an overall better understanding of the
problem along with an accelerated design process. Topics include: near & far field
mapping; current and power flow mapping; Imaging; optimization techniques; and an
introduction to the utilization of these tools for design.

 Advanced Codes – A present look at the state
of the art in code implementations and packages will be discussed. Topics will include FTD
codes; MOM codes; hybrid mom codes; and fast iterative solver solutions.

 Fresnel Scattering – An indepth study of specular and
nonspecular scattering concepts will be conducted to lay the foundation for high
performance scattering control. Fresnel scattering (stationary phase) will be reviewed to
understand its significance in prediction utilization of why scattering bodies scatter the
way they do. A better physical understanding of how energy scatters to the far field will
result. Topics include: far field integral review; specular scattering; curved surface
scattering; edge scattering. 
 RCS (back of the envelope) Solutions Discussed will be the
utilization of several scattering concepts to derive approximate solutions for complex
scatters. In demonstrating these derivations, the attendee will gain a better
understanding of what controls scattering energy to the far field. Physical optics and
diffraction scattering along with the concept of stationary phase will be utilized to
derive several useful back of the envelope formulas. 
 Aperture Theory – Signalprocessing theory as it applies to
scattering bodies for advanced side lobe envelope control will be discussed. An outline of
aperture theory will be presented to set the foundation for understanding how side lobe
scattering is controlled. Implementation of standard signal processing windowing
techniques for high performance sidelobe control will be introduced. Other topics
included are the concepts of energy scattering envelopes for off specular scattering; the
relationship between aperture length and wavelength (l/l); the
implementation of performance windowing; and trade off analysis. 
 Geometrical Shaping  Geometrical shaping using aperture theory
will be discussed indepth. The implementation of signalprocessing windowing to
synthesize high performance geometrical shapes will include: faceting; Scurve design;
blended aperture tapering (BAT); body of revolution aperture tapering (BORAT); serration
designing; and several other examples which will provide the necessary methodology to
design high performance geometries by controlling side lobe scattering. 
 Planform Shaping – Planform designing using aperture theory
will be introduced. An indepth discussion of how to optimally draw planforms given threat
sectors. Line lengths and the number of lines along with curved edge planform lines will
be reviewed. In addition, linestacking and serrations, limited material treatment and
traveling wave attenuation will be discussed. 
 Shaping / Material Synthesis – Introduction to shaping and
material synthesis using aperture theory for high performance scattering. The combination
of attenuating materials with geometrical shaping to produce high performance scattering
bodies will be reviewed. Other topics include: resistive card tapering synthesis;
balancing geometrical and material implementations; and aperture analysis techniques to
evaluate material shaped geometries. 
 Design Topics – A review of the design process for several DOD
systems will be examined. Existing DOD systems like the F117, Sea Shadow and the Darkstar
will be reviewed. 
 Scaling Issues – An indepth review of scaling issues for
frequency and/or size. The theory and problems of scaling will be discussed with an
emphasis on subscale modeling. Other topics include: geometry considerations such as
smoothness and gaps and cracks; material scaling and difficulties. 
 Fixture design – The implementation of the design techniques
reviewed above will be used to design commonly used RCS range fixtures. Planform shaping
and high performance shaping will be demonstrated in the design. Several predictions along
with the approximations will be reviewed. 
 Radar Imaging Theory – Far field imaging theory will be
discussed indepth. A physical understanding of how imaging works and the parameters that
affect images will be reviewed. Topics included: SAR and ISAR imaging processing; noise
effects; processing gain; imaging units; focusing techniques for typical ISAR data
acquisition; and high resolution imaging. 
 Bistatic KSpace Imaging Theory – New imaging theory for
prediction codes will be discussed in detail. Kspace bistatic imaging theory will be
introduced. The implementations for several EM prediction codes will be reviewed.
Additional topics include Kspace bandwidth; geometrical sampling and the significance of
only needing one frequency to obtain an image. 
 Bistatic KSpace Imaging II – Kspace imaging results will be
examined in detail to quantify the differences and advantages of this new imaging
technique from traditional experimental imaging theory. Limitations and advantages will be
discussed with several examples to illustrate this technique. 
