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Target Diamond Structural Analysis (view source)
Revision as of 17:32, 25 March 2009
, 17:32, 25 March 2009→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.
We will be neglecting all sources of error during these calculations.
Light is a wave, and can be expressed as
Light is a wave, and can be expressed as
(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 amplitude and frequency. However, the processes of reflection and transmission will modify the amplitudes 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. The mirror has a coefficient of reflection r = 100, so we are only concerned with that of the half-silvered mirror. The recorded amplitude will be equal to <math> C _0 A _{laser} </math>.
Because all three waves are reflections of the same original wave, they all have the same amplitude and frequency. However, the processes of reflection and transmission will modify the amplitudes 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. The mirror has a coefficient of reflection r = 100, so we are only concerned with that of the half-silvered mirror. The recorded amplitude will be equal to <math> C _0 A _{laser} </math>. Because all reflected beams that the detector will recieve will reflect off of and pass through the splitter once, we can create a new amplitude variable A such that
<math> A = A _{laser} C _0 </math>
To find the thickness of the diamond, we only need the first two waves. To remove the third wave, which reflects from the mirror, we can simply obscure the mirror with something that absorbs light, like a black cloth.
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.
The combined wave equation is unimportant, since we only record its amplitude, which is
The combined wave equation is unimportant, since we only record its amplitude, which is