Page 15 - Phase Space Optics Fundamentals and Applications

xiv Preface

are well explored, as are their relationships with one another. How-
ever, it is, without question, desirable to have a simple, common plat-
form with which to unify these models, while preserving their unique
features.
Fromourviewpoint,suchaplatformcanprovideapowerfultoolfor
understanding and applying the physics of light propagation through
optical systems. Ideally, this common platform should be a superior
model, with all other models reducing to different facets of a common
framework. The contributions collected in this book emphasize the
fact that this model may be best implemented by what we term phase-
space optics.
Phase-space optics refers to a representation of optical signals in
an artificial configuration space simultaneously providing informa-
tion about spatial properties of the signal and its angular spectrum,
or equivalently in terms of its temporal and time-frequency charac-
teristics. In coherent optics, this concept has also been popularized
as “Wigner optics” since the properties of the Wigner distribution
function are often used to motivate the use of a joint signal represen-
tation. In the signal processing community, the Wigner-Ville distri-
bution is recognized as a relevant member of a larger class of joint
time-frequency transforms. Closely connected with the Wigner dis-
tribution function through a double Fourier transform, the ambiguity
function is used by the radar community for representing signals si-
multaneously carrying information about the down range of the target
and its velocity.
In contrast, the term phase space, while being based on the same con-
ceptual and formal mathematical tools, rather emphasizes the dynam-
ics of the physical system. Phase space, and in particular the Wigner
distribution, can be recognized as one common platform for under-
standing and applying the physics of more traditional models for de-
scribingelectromagneticsignalsastheyevolveandpropagatethrough
an optical system.
By compiling this book, it was our desire to create a mosaic of phase-
space optics. Each contribution constitutes a self-consistent perspec-
tive on one particular aspect of optical signals in phase space, while
revealing its full beauty and importance only as part of this entire
collection. We owe it to the authors who contributed to this effort that
the result has far exceeded our expectations.
Each of the chapters illustrates original ways to gain physical in-
sight and to develop novel engineering applications. All chapters are
written by authors who are pioneers in using phase-space optics in
their fields of expertise. As a consequence, the topics are discussed
with unique depth, without losing sight of the necessity to embed
phase-space optics in a broader context.