  An approach to diffraction tomography is investigated for two-dimensional
image reconstruction of objects surrounded by an arbitrarily-shaped curve of
sources and receivers. Based on the integral theorem of Helmholtz and
Kirchhoff, the approach relies upon a valid choice of the Green's functions for
selected conditions along the (possibly-irregular) boundary. This allows field
projections from the receivers to an arbitrary external location. When
performed over all source locations, it will be shown that the field caused by
a hypothetical source at this external location is also known along the
boundary. This field can then be projected to new external points that may
serve as a virtual receiver. Under such a reformation, data may be put in a
form suitable for image construction by synthetic aperture methods. Foundations
of the approach are shown, followed by a mapping technique optimized for the
approach. Examples formed from synthetic data are provided.
