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Target Diamond Structural Analysis (view source)
Revision as of 18:13, 26 March 2009
, 18:13, 26 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.
We will be neglecting all sources of error during these calculations. They will be reintroduced after we have obtained our basic calculations.
Light is a wave, and can be expressed as
Light is a wave, and can be expressed as
<math>\Psi = A _{laser} \sin ( \omega t + d ) </math>
<math>\Psi = A _{laser} \sin ( \omega t + d ) </math>
where <math> A _{laser} </math> is the amplitude of the initial laser, <math>\omega</math> is the frequency, t is time, d is the phase-shift, and C is a constant dependent on the reflectivity of all surfaces the laser intercepts.
where <math> A _{laser} </math> is the amplitude of the initial laser beam, <math>\omega</math> is the frequency, t is time, d is the phase-shift, and C is a constant dependent on the reflectivity of all surfaces the laser intercepts.
We have a sum of three waves, which can be expressed as
We have a sum of three waves, which 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 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
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.
The mirror has a coefficient of reflection r = 1 (it reflects all the light and does not transmit any), so we are only concerned with the half-silvered mirror. The recorded amplitude will be equal to <math> C _0 A _{laser} </math>. Because all 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>
<math> A = A _{laser} C _0 </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.