Changes

The Michelson interferometer [[Image:MIint.gif|thumb|A Michelson Interferometer! (courtesy of [http://scienceworld.wolfram.com/physics/MichelsonInterferometer.html])]] was invented by Albert Michelson in 1882 “to detect a change in the velocity of light due to the motion of the [ether]” (110).  The findings of Michelson's experiment eventually went on to support Einstein's theory of relativity.  Add something here describing the parts of the Michelson interferometer.

The Michelson interferometer [[Image:MIint.gif|thumb|A Michelson Interferometer! (courtesy of [http://scienceworld.wolfram.com/physics/MichelsonInterferometer.html])]] was invented by Albert Michelson in 1882 “to detect a change in the velocity of light due to the motion of the [ether]” (110).  The findings of Michelson's experiment eventually went on to support Einstein's theory of relativity.  Add something here describing the parts of the Michelson interferometer.

For our experiment we will be utilizing the fringes of the Michelson interferometer to gather information about the topology of synthetic diamond wafers.  In order to be able to utilize a computer program to analyze the data gathered from the Michelson interferometer, we start with an approximation of the beam splitter present at the center of the interferometer.  We know that the beam splitter is comprised of a thin layer of a conducting substance present on two sides of a thin piece of optical glass.  When a beam of light is directed towards the beam splitter, half of the light travels through to the other side of the splitter and the other half is reflected.

For our experiment we will be utilizing the fringes of the Michelson interferometer to gather information about the topology of synthetic diamond wafers.  In order to be able to utilize a computer program to analyze the data gathered from the Michelson interferometer, we start with an approximation of the beam splitter present at the center of the interferometer.  We know that the beam splitter is comprised of a thin layer of a conducting substance present on two sides of a thin piece of optical glass.  When a beam of light is directed towards the beam splitter, half of the light travels through to the other side of the splitter and the other half is reflected.

Using our knowledge of electric and magnetic fields in conductors and [[Maxwell's Equations]], we can create a simple approximation of the beam splitter with a light wave at normal incidence.  We are interested in finding two main quantities in this approximation:  the width of the conducting film and the phase shift that occurs in the conducting film.  Need more here about the calculations we did.  Using the programming power of Matlab, we can solve our system of equations

Using our knowledge of electric and magnetic fields in conductors and [[Maxwell's Equations]], we can create a simple approximation of the beam splitter with a light wave at normal incidence.  We are interested in finding two main quantities in this approximation:  the width of the conducting film and the phase shift that occurs in the conducting film.  Need more here about the calculations we did.  Using the programming power of Matlab, we can solve our system of equations Mv=b, where M, v, and b are given below.

 

<math>M = \begin{bmatrix}

<math>M = \begin{bmatrix}

-1 & 1 & 1 & 0\\

-1 & 1 & 1 & 0\\

<math>b = \begin{bmatrix} 1\\ Z_1^{-1}\\ 0\\ 0\end{bmatrix}</math>

<math>b = \begin{bmatrix} 1\\ Z_1^{-1}\\ 0\\ 0\end{bmatrix}</math>

Our graphs dislpaying phase shift versus depth [[Image:fig2.jpg|thumb|A Graph of the Phase shift versus Depth]] and amplitude versus depth [[Image:fig1.jpg|thumb|A Graph of Amplitude versus Depth]]

Our graphs dislpaying phase shift versus depth [[Image:fig2.jpg|thumb|A Graph of the Phase shift versus Depth]] and amplitude versus depth [[Image:fig1.jpg|thumb|A Graph of Amplitude versus Depth]]

[[Maxwell's Equations]]  

[[Maxwell's Equations]]  

Steel "Interferometry"

Steel "Interferometry"