## Date of Award

7-1995

## Document Type

Dissertation

## Degree Name

Doctor of Philosophy (PhD)

## Department

Department of Electrical and Computer Engineering

## First Advisor

Vittal Pyati, PhD

## Abstract

Two formulations for the far field statistical average power pattern of a strip grating with errors in strip and slit width are presented. The first formulation utilizes the Born approximation in which the unknown aperture fields are replaced by the incident fields. The second formulation utilizes an approximation which satisfies the edge condition. Approximations for the scattered fields are first derived using PEC surface equivalence for a TEz polarized plane wave incident upon a strip grating consisting of an infinite PEC screen cut by a number of infinitely long slits. Babinet's principle is then used to obtain approximations for the fields obtained when a TMz polarized plane wave is incident upon the complementary grating formed by interchanging the slits and strips of the original grating. Expressions for the average power pattern are developed in terms of the following variables: number of slits or strips, desired width and spacing to wavelength ratios, and the characteristic functions of the probability density functions of the width and spacing errors. Examples are presented for different combinations of the above variables for both uniform and cosine distributed errors. Results are compared to the patterns obtained from gratings with actual random errors.

## AFIT Designator

AFIT-DSG-ENG-95S-02

## DTIC Accession Number

ADA297540

## Recommended Citation

Godsey, James A., "Tolerance Theory of Periodic Surfaces" (1995). *Theses and Dissertations*. 6309.

https://scholar.afit.edu/etd/6309