Changes

We must be able to determine the precise thickness and shape of the diamond chip. Because it is tiny (on the order of 50 microns thick), conventional measurements are impossible. Instead, we will use a modified [http://en.wikipedia.org/wiki/Michelson_interferometer Michelson interferometer]. In our design, we will replace one of the mirrors with the target diamond chip. In this modified design, the plane wave returned to the detector will be a combination of three waves (neglecting internal reflection): one reflected off the front of the diamond, one reflected off the back of the diamond, and one reflected off the remaining mirror. However, all that the detector can record is the wave's amplitude. From this, we need to extract thickness and shape.

We must be able to determine the precise thickness and shape of the diamond chip. Because it is tiny (on the order of 50 microns thick), conventional measurements are impossible. Instead, we will use a modified [http://en.wikipedia.org/wiki/Michelson_interferometer Michelson interferometer]. In our design, we will replace one of the mirrors with the target diamond chip. In this modified design, the plane wave returned to the detector will be a combination of three waves (neglecting internal reflection): one reflected off the front of the diamond, one reflected off the back of the diamond, and one reflected off the remaining mirror. However, all that the detector can record is the wave's amplitude. From this, we need to extract thickness and shape.

== Ideal Thickness Calculation ==

== The Diamond and Light Waves ==

Both the front and back planes of the diamond are two-dimensional surfaces in three-dimensional space. The recorded amplitudes will form a two-dimensional graph and record amplitude at points across the diamond's surface. Basically, the light wave can be treated as a massive grid of one-dimensional waves normal to the diamond. All of the following calculations are applied to the recorded amplitude of one of these waves, which is the amplitude at one specific point on the diamond.

Both the front and back planes of the diamond are two-dimensional surfaces in three-dimensional space. The recorded amplitudes will form a two-dimensional graph and record amplitude at points across the diamond's surface. Basically, the light wave can be treated as a massive grid of one-dimensional waves normal to the diamond. All of the following calculations are applied to the recorded amplitude of one of these waves, which is the amplitude at one specific point on the diamond.

(For simplicity, we will say that the wave leaving the mirror has not been phase-shifted, as above.)

(For simplicity, we will say that the wave leaving the mirror has not been phase-shifted, as above.)

Because all three waves are reflections of the same original wave, they all have the same wavelength. However, the processes of reflection and transmission will modify the ''amplitude'' of each wave. By removing the diamond and reflecting the laser solely off of the mirror, we will be able to calculate the amplitude of the initial light after it has reflected off the mirror and beam splitter once and been transmitted through the splitter once.  

Because all three waves are reflections of the same original wave, they all have the same wavelength. However, the processes of reflection and transmission will modify the ''amplitude'' of each wave. By removing the diamond and reflecting the laser solely off of the mirror, we will be able to calculate the amplitude of the initial light after it has reflected off the mirror and beam splitter once and been transmitted through the splitter once.  

Because of this, we will never be dealing with the amplitude of the original laser. This will have no effect on the calculations, but it is important to remember that our value <math> A </math> is ''not'' the same as <math> A _{laser} </math>.

Because of this, we will never be dealing with the amplitude of the original laser. This will have no effect on the calculations, but it is important to remember that our value <math> A </math> is ''not'' the same as <math> A _{laser} </math>.

To find the thickness of the diamond, we ideally only need the first two waves. To remove the third wave, which reflects from the mirror, we can simply remove the mirror.

To find the thickness of the diamond, we ideally only need the first two waves. To remove the third wave, which reflects from the mirror, we can simply remove the mirror.