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.

== Thickness Calculation ==

== Ideal Thickness Calculation ==

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.

<math>A^2 _{12} / A^2 = C _1 + C _2 + 2 C _1 C _2 \cos ( d _2 - d _1 ) </math>

<math>A^2 _{12} / A^2 = C _1 + C _2 + 2 C _1 C _2 \cos ( d _2 - d _1 ) </math>

Because the wave reflecting off the back of the diamond travels through the diamond twice, the term <math> d _2 - d _1 </math> is twice the thickness of the diamond, in seconds. Because this measurement is in unhelpful units, we can multiply it by the speed of light in a diamond and divide by two for the thickness <math> \tau </math>.

Because the wave reflecting off the back of the diamond travels through the diamond twice, the term <math> d _2 - d _1 </math> is twice the thickness of the diamond, in radians. Because this measurement is in unhelpful units, we can multiply it by the frequency <math> \gamma </math> and divide by <math> 2 \pi </math> for the thickness <math> \tau </math> in meters.

<math>( d _2 - d _1 ) V _d / 2 = \tau </math>

<math>( d _2 - d _1 ) \gamma / 2 \pi = \tau </math>

Therefore, we can rewrite the earlier equation in terms of <math> \tau </math>:

Therefore, we can rewrite the earlier equation in terms of <math> \tau </math>:

<math>A^2 _{12} / A^2 = C _1 + C _2 + 2 C _1 C _2 \cos ( 2 \tau / V _d ) </math>

<math>A^2 _{12} / A^2 = C _1 + C _2 + 2 C _1 C _2 \cos ( 4 \pi \tau / \gamma ) </math>

== Calculating the Shape ==

== Calculating the Shape ==