Haldun Ozaktas has made contributions to several areas of optical
information processing and in particular to the development of the
fractional Fourier transform and its applications.
With the development of the fractional Fourier transform, the common
frequency domain is seen to be merely a special case of a continuum
of so-called fractional domains, a concept that is elegantly related to
the notion of space-frequency distributions.
Every property and application of the common Fourier transform becomes a
special case of that for the fractional transform. In every area in which
Fourier transforms and frequency-domain concepts are used, there exists the
potential for generalization and improvement by using the fractional
transform. In particular, the fractional Fourier transform has been
found to have several applications in analog optical information
processing, allowing a reformulation of Fourier optics in a much more
general way. Its applications in digital signal
and image processing are growing steadily and it is expected to have
an impact in the form of deeper understanding, new applications, or
improved algorithms in every area in which the Fourier transform plays
a significant role.
Ozaktas has made fundamental contributions to both analog
optical information processing and Fourier optics, and to
optics in digital computing and optical interconnections.
In the former category, apart from the development of the fractional
Fourier transform and its applications, he has made several other
contributions to general optics, information optics and optical signal
processing, as well as digital signal and image processing.
In the latter category, his major contribution is his study of the
physical limits to communication in digital computing systems.
At the heart of this work lies abstract yet physically accurate models
of optical, normally conducting, and superconducting interconnections
which fully characterize their capabilities and limitations as
information transfer media, and a physically accurate characterization of
the scaling behavior imposed by heat removal considerations in
three-dimensional systems.
In addition to concentrating on the fundamental limitations of optical
communication within computing systems (as opposed to long-distance
communications), Ozaktas also focused on the development of
optimal optical interconnection architectures and their limitations,
and how to best use optics and electronics together in
high-performance computing systems.
By defining the limits of what is achievable, and how it can be
achieved, this body of work aims to provide a framework and a vision
for the development of optoelectronic and optically interconnected
computing systems which can provide flexible and effective platforms
for high-performance applications.
Taken as a whole, Ozaktas's work is characterized by the combined emphasis on physical principles, and concepts from information and signal theory, and computer science.