Changes

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.

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 model of the beam splitter featured in the Michelson interferometer.  I will start by giving a brief introduction to electromagnetic radiation, then move on to the model itself (including graphs,etc.).

 

==INTERFERENCE AND LIGHT WAVES==

==INTERFERENCE AND LIGHT WAVES==

Interferometry is the splitting of light beams into two or more paths  and the recombining of those different beams to measure difference in optical path length and refractive index [[#References|[1]]] via interference fringes that form as a result of the recombined beams.       

Interferometry is the splitting of light beams into two or more paths  and the recombining of those different beams to measure difference in optical path length and refractive index [[#References|[1]]] via interference fringes that form as a result of the recombined beams.       

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]” [[#References|[2]]].  The findings of Michelson's experiment eventually went on to support Einstein's theory of relativity. <font color="red">Add something here describing the parts of the Michelson interferometer.</font>

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]” [[#References|[2]]].  The findings of Michelson's experiment eventually went on to support Einstein's theory of relativity.

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 one side of a thin piece of optical glass.  When a beam of light is incident on the beam splitter, a fraction of the photons travel through to the other side of the splitter and the remaining photons reflected.  Here we consider wavelengths at which the fraction of the beam absorbed by the mirror is negligible.

The Michelson interferometer consists of a source, a beam splitter, a reference mirror, a target and a detector (see schematic at right).  Light leaves the source and moves towards the beam splitter.  The beam splitter allows half of the incident light to be transmitted and the other half to be reflected.  The reflected light travels a known distance to the reference mirror, while the transmitted light travels towards the target.  Both beams reflect off of their respective targets and travel back towards the beam splitter, where a similar half-half selection process occurs again.  Only this time, the beams that travel back to the source are removed through an optical device, and the beams that travel to the detector "survive".

Using our knowledge of electric and magnetic fields in conductors and [[Maxwell's Equations]], we can create a simple model of the beam splitter with a light wave at normal incidence.  We are interested in finding two main quantities in this model: the thickness of the conducting film and the phase shift that occurs at the mirror surface.  <font color="red">Need more here about the calculations we did.</font>

 

Using our knowledge of electric and magnetic fields in conductors and [[Maxwell's Equations]], we can create a simple model of the beam splitter with a light wave at normal incidence.  We are interested in finding two main quantities in this model: the thickness of the conducting film and the phase shift that occurs at the mirror surface.  <font color="red">Still need more here about the calculations we did.</font>

Using the programming power of Matlab, we can solve our system of equations Mv=b, where M, v, and b are given below.

Using the programming power of Matlab, we can solve our system of equations Mv=b, where M, v, and b are given below.

\end{bmatrix}</math>

\end{bmatrix}</math>

|align="center" width="80"|(4)

|align="center" width="80"|(4)

|},

|}

{|width="80%"

{|width="80%"

|align="right"|

|align="right"|

<math> v = \begin{bmatrix} E_r\\ E_f\\ E_b\\ E_t\end{bmatrix}</math>

<math> v = \begin{bmatrix} E_r\\ E_f\\ E_b\\ E_t\end{bmatrix}</math>

|align="center" width="80"|(5)

|align="center" width="80"|(5)

|},

|}

{|width="80%"

{|width="80%"

|align="right"|

|align="right"|

{|align=center

{|align=center

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

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

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

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

|}

|}

[[Maxwell's Equations]]  

[[Maxwell's Equations]]  

 

<br style="clear:both;"/>

<br style="clear:both;"/>

<div class="references-small">

<div class="references-small">

1. C. Candler, ''Modern Interferometers'', Addison-Wesley, 1982, p.9.

1. C. Candler, ''Modern Interferometers'', Hilger & Watts Ltd., 1951, p.9.

2. ibid, p.110.

2. ibid, p.110.

</div>

</div>