Changes

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 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 programming power of Matlab, we can solve our system of equations

<math>\left(\begin{bmatrix}

<math>M = \begin{bmatrix}

-1 & 1 & 1 & 0\\

-1 & 1 & 1 & 0\\

Z_1^-1 & Z_2^-1 & -Z_2^-1 & 0\\

Z_1^{-1} & Z_2^{-1} & -Z_2^{-1} & 0\\

0 & e^{ik_2a} & e^{-ik_2a} & -e^{-ik_1a}\\

0 & e^{ik_2a} & e^{-ik_2a} & -e^{-ik_1a}\\

0 & Z_2^-1 e^{ik_2a} & Z_2^-1 e^{-ik_2a} & -Z_1^-1 e^{-ik_1a}

0 & Z_2^{-1} e^{ik_2a} & Z_2^{-1} e^{-ik_2a} & -Z_1^{-1} e^{-ik_1a}

\end{bmatrix}\right)</math>

\end{bmatrix}</math>

[[Image:fig2.jpg|thumb|A Graph of the Phase shift]]

[[Image:fig2.jpg|thumb|A Graph of the Phase shift]]

[[Image:fig1.jpg|thumb|A Graph of Amplitude versus Width]]

[[Image:fig1.jpg|thumb|A Graph of Amplitude versus Width]]