Inverse Source Problem

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Inverse Source Problem
A.J. Devaney Department of Electrical and
Computer Engineering Northeastern
University Boston, MA 02115 tonydev2_at_aol.com ,
devaney_at_ece.neu.edu
Research supported by Delaware MURI
A.J. Devaney and Mei-Li, The inverse source
problem in non-homogeneous background media,
accepted to JOSA A
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Inverse Source Problem
E (r,?), H (r,?)
Determine charge current distribution
that radiates a prescribed field
j(r,?), ?(r,?)
Non-unique due to N.R. charge-current
distributions
Radome
Determine charge current distribution
that radiates a prescribed field in presence
of known background structure and subject to
energy constraints
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Radiation Problem
Background potential
Radiation Condition
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Inverse Source Problem
Determine the source that generates a prescribed
field everywhere outside the source region
Determine the source that generates a prescribed
radiation pattern
Radiation pattern multipole expansion
Determine the source that generates a prescribed
set of multipole moments
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Non-uniqueness-N.R. Sources
Pseudo-inverse Minimize source energy
Minimum energy source
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Free-space Case
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Multipole Expansion
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Free-space I.S.P.
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Source Energy
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I.S.P. In a Non-Homogeneous Background

• Motivation
• Most antennas include passive structures that
• can be modeled this way
• The radiation patterns generated by such
  composite
• sources may have interesting properties

Field dependent effective source
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Scattering Wave States
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Spherically Symmetrical Backgrounds
Same as free space case with spherical Bessel
functions replaced with the radial wave functions
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Inverse Problem
Same as free space case with spherical Bessel
functions replaced with the radial wave functions
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Minimum Energy Source
Same as free space case with spherical Bessel
functions replaced with the radial wave functions
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Piece-wise Constant Backgrounds
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Eigenvalues
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Source Energy
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Source Energy
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Future Work

• Include source-field interaction constraints
• Full EM case
• Other examples
• Planar backgrounds