Page vii

Preface

This book deals with novel iterative methods and algorithms for calculating the transmission function of phase diffractive optical elements (DOEs). The development of DOEs is a topical problem of interest to those involved in computer optics.

The DOE is a phase-only element whose superficial microrelief has a height comparable with the light wavelength used. The DOE may be implemented in the form of a transparency or a reflecting mirror. DOEs can operate over a wide range of wavelengths from UV to IR radiation. The lens, the zone plate, the diffraction grating, the array illuminator, the kinoform, the axicon, and the phase spatial filter are examples of DOEs.

The technology of DOE manufacturing involves, as a rule, the use of image generators such as laser photoplotters or e-beam lithographers. The most critical stage of the technological process of DOE fabrication is generally the solving of an ill-defined inverse problem. Note that the robustness of the solutions arrived at is of fundamental importance here. Such problems can most efficiently be tackled through the use of iterative methods.

A distinctive feature of this book is that the methods covered realize a number of new approaches to the problem of synthesis of optical components:

• the design of DOEs is treated as an ill-defined inverse problem of the scalar theory of diffraction

• the formulation of a well-defined problem is related to the use of regularization techniques

• the development of parametric iterative algorithms allows one to control the rate of convergence