Page 328 - Phase Space Optics Fundamentals and Applications

CHAPTER10

Sampling and Phase

Space

Bryan M. Hennelly

National University of Ireland, Maynooth, Ireland
John J. Healy and John T. Sheridan

University College Dublin, Ireland

10.1 Introduction
Sampling a continuous signal in order to represent or approximate
it with a discrete one is of enormous importance in today’s digital
world. In the optical sciences we are often interested in recording opti-
cal signals with discrete photosensitive devices such as CCD or CMOS
cameras. Such devices are sensitive to the intensity of an incident op-
tical wave field and bring about the spatial sampling of this intensity
pattern. By using interferometry it is possible to recover phase infor-
mation from the recorded intensity pattern, and so we may say that
we are effectively sampling the complex wavefront with our digital
camera. The operation of discrete display devices, such as liquid crys-
tal displays (LCDs) and electrically addressed spatial light modulators
(SLMs), are also governed by sampling theory and are of increasing
interest in diffractive optics. Thus, the discrete signal processing of
digitally captured data plays a central role in modern optoelectronics,
and this science is anchored in sampling theory. In the past decade
the Wigner distribution function (WDF) and, moreover, its simplified
version, the phase-space diagram (PSD), have been shown to be effec-
tive tools in gaining considerable insight into the discrete sampling of
signals. Not only does the PSD elegantly account for known sampling

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