Page 184 - Phase Space Optics Fundamentals and Applications

CHAPTER5

Imaging Systems:

Phase-Space

Representations

Jorge Ojeda-Casta˜neda
DICIS, University of Guanajuato, Salamanca, M´ exico

5.1 Introduction
For designing optical imaging systems, one is often faced with
an inevitable tradeoff between two figures of merit, which are ex-
pressed as two Fourier conjugate variables. For example, for image
acquisition there is a tradeoff between the size of the pupil aperture
and the depth of field of the optical system. Phase-space representa-
tions may be useful for suggesting novel solutions to these types of
tradeoffs.
The purpose of this chapter is to put the reader in touch with
the use of phase-space representation for analyzing and designing
novel imaging systems. To that end, we selected a group of imaging
devices that highlight key features on the use of phase-space repre-
sentations. We illustrate the use of the Wigner distribution function 1
2
(WDF) and the ambiguity function (AF) by considering equivalent
space-invariant, coherent optical processors, with unit magnification,
in a similar fashion to the approach discussed in Refs. 3 and 4 for other
applications. Our examples are invitations rather than endpoints. For
the sake of clarity, our discussions restrict mainly to one-dimensional
optical systems.

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