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Target Diamond Structural Analysis (view source)
Revision as of 14:19, 19 March 2009
, 14:19, 19 March 2009→Calculating the Shape
<math>A^2 _{123} = A^2 + C^2 _1 A^2 + C^2 _2 A^2 + 2 C _1 C _2 \cos ( d _2 - d _1 ) + 2 C _1 \cos ( - d _1 ) + 2 C _2 \cos ( - d _2 ) </math>
<math>A^2 _{123} = A^2 + C^2 _1 A^2 + C^2 _2 A^2 + 2 C _1 C _2 \cos ( d _2 - d _1 ) + 2 C _1 \cos ( - d _1 ) + 2 C _2 \cos ( - d _2 ) </math>
Although this equation looks very complicated, we know that
<math>( d _2 - d _1 ) = 2 \tau / V _d </math>
and
<math>d _2 = 2 \tau / v _d + d _1</math>
To further simplify, we need a "shape term". This term will represent the difference in the distance traveled by waves 1 and 3. If the phase-shift between 1 and 3 is constant, the diamond is flat; otherwise, it is deformed by some distance expressed by s.
<math>s = d _1 v _a / 2</math>
where <math> v _a </math> is the speed of light in air.
<math>d _1 = 2 s / v _a</math>
Simplifying our initial equation, we find that
<math>A^2 _{123} = A^2 + C^2 _1 A^2 + C^2 _2 A^2 + 2 C _1 C _2 \cos ( 2 \tau / V _d ) + 2 C _1 \cos ( - 2 s / v _a ) + 2 C _2 \cos ( - 2 \tau / v _d - 2 s / v _a ) </math>
== Future Updates ==
== Future Updates ==