Mapping diamond surfaces using interference

This page represents a ongoing project dealing with using interference patterns to map the surface of a diamond wafer. Since this is my first page, you'll have to excuse any blatant errors that I do not pick up on immediately. Currently this page will represent my work with Dr. Richard Jones on an approximation to the beam splitter featured in the Michelson interferometer. I will start by giving a brief introduction to electromagnetic radiation, then move on to the approximation itself (including graphs,etc.). I will hopefully have this up and running by next Wednesday.

Electromagnetic Radiation

Using Maxwell's Equations we can find solutions for a travelling wave comprised of two perpindicular oscillating electric and magnetic fields, whose direction can be giving by the Poynting vector. [image of EM wave here]

An Electromagnetic Wave! (courtesy of [1])

What is light?

Interference from a Michelson Interferometer (courtesy of [2])

The Michelson Interferometer

A Michelson Interferometer! (courtesy of [3])

What is a Michelson interferometer?

A simplistic approximation

A Graph of the Phase shift

A Graph of Amplitude versus Width

Maxwell's Equations

But, what if I need to make formulas? Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \frac{1}{\sqrt{2\pi\sigma^2}}e^{-\frac{1}{2}\frac{(x-x_0)^2}{\sigma^2}}} I have no idea what that will look like, but let's try it. We can also do vector equations, such as Gauss's Law

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \vec{\nabla}\times\vec{D}=\frac{\rho_{ext}}{\epsilon_0}}

(1)

Next let's make some chapter headings.

Chapter 1

Chapter 2

Chapter 3

Chapter 4