135
edits
Changes
Jump to navigation
Jump to search
Target Diamond Structural Analysis (view source)
Revision as of 14:19, 19 March 2009
, 14:19, 19 March 2009→Calculating the Shape
Line 53:
Line 53:
+
<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 ==