** Master's thesis (March 1997)**

**
Application of Genetic Algorithms in Diffractive Optics Design**

ABSTRACT
The scalar diffraction theory is used to derive a 2D
mathematical model for light propagating through a phase mask. The
Green's function approach is used to compute the intensity of the light
in the
near field of the phase mask.
An overview of optimization methods and an introduction to Genetic
Algorithms is given. Genetic Algorithms use
analogies to natural evolution and heredity to optimize an objective
function.
The Micro-genetic algorithm which operates on a small population of
solutions with an adaptive mutation scheme is used
to obtain a phase mask profile
that approximates a desired intensity image.
Numerical results for a
problem with a known exact solution are shown. Suggestions for future
research in this direction are also discussed.

CONTENTS
1. Introduction

2. Diffraction theory

2.1. Scalar diffraction theory

2.2. Green's formula

3. Mathematical model

3.1. Forward problem

3.2. Inverse problem

4. Optimization by genetic algorithms

4.1. Overview of search methods

4.2. Simple genetic algorithm

4.3. Further development of genetic algorithms

4.4. Micro-genetic algorithm

5. Numerical results

6. Conclusions

Bibliography

Last modified: August 11, 1999.

*Send questions to Svetlana Rudnaya:
rudnaya@math.umn.edu *