  Limited-diffraction beams are a class of waves that may be localized in space
and time. Theoretically, these beams are propagation invariant and can
propagate to an infinite distance without spreading. In practice, when these
beams are produced with wave sources of a finite aperture and energy, they have
a very large depth of field, meaning that they can keep a small beam width over
a large distance. Because of this property, limited-diffraction beams may have
applications in various areas such as medical imaging and tissue
characterization. In this paper, fundamentals of limited-diffraction beams are
reviewed and the studies of these beams are put into a unified theoretical
framework. Theory of limited-diffraction beams is further developed. New
limited-diffraction solutions to Klein-Gordon Equation and Schrodinger
Equation, as well as limited-diffraction solutions to these equations in
confined spaces are obtained. The relationship between the transformation that
converts any solutions to an (-1)-dimensional wave equation to
limited-diffraction solutions of an -dimensional equation and the Lorentz
transformation is clarified and extended. The transformation is also applied to
the Klein-Gordon Equation. In addition, applications of limited-diffraction
beams are summarized.

General Physics;Medical Physics