Page 270 - Introduction to Information Optics

Chapter 5 Transformation with Optics

1 2
Yunlong Sheng and Yueh OuYang
'DEPARTMENT OF PHYSICS, LAVAL UNIVERSITY,
QUEBEC, CANADA
DEPARTMENT OF PHYSICS, CHINESE MILITARY ACADEMY,
KAOHSFUNG 830 TAIWAN

Lightwaves are one of the most important sources of information for human
beings, who acquire 85% of information by vision and 15% by audition. An
optical system, whether for imaging or nonimaging, performs mapping from
the input plane to the output plane with an extremely high information
throughput at the speed of light. In most cases, this mapping is a two-
dimensional (2D) transform.
Mathematical transforms are closely related to the history of the develop-
ment of optics. In the 1940s Duffieux introduced the Fourier transform to
optics [1]. This work and earlier works by Abbe and Rayleigh in the beginning
of the 20th century [2, 3], and many other later works by Marechal and
O'Neill in the 1950s [4, 5], and Leith and Van De Lugt in the 1960s constituted
the foundation of a new branch of optics science: Fourier optics [6, 7]. The
invention of the laser in 1960 created huge interest in coherent and incoherent
optical systems. Fourier optics with the concept of Fourier transform and
spatial-frequency spectrum analysis, is now a fundamental basis of optical
system analysis and design. Apart from imaging systems, many new optical
systems have been proposed and developed that perform a variety of trans-
formations for optical information processing, communication, and storage.
In this chapter, we discuss the relation between mathematical transfor-
mations and optics. All optical systems can be considered as systems which
perform mapping, or transformation, from the input plane to the output plane.
After a brief review of the Huygens-Fresnel diffraction, Fresnel transform, and

255