135
edits
Changes
Jump to navigation
Jump to search
Line 57:
Line 57: − + + + + + + + + + + +
Target Diamond Structural Analysis (view source)
Revision as of 15:48, 5 March 2009
, 15:48, 5 March 2009→Calculating the Shape
<math>A^2 _{recieved} = A^2 + A^2 _t + 2 A A _t \cos ( d _t ) </math>
<math>A^2 _{recieved} = A^2 + A^2 _t + 2 A A _t \cos ( d _t ) </math>
Because we have values for A and <math> A _t </math>, we can almost find <math>A _{recieved} </math>. Unfortunately, we lack values for the new phase-shift term, which is a function of the phase-shifts of <math> \Psi _1 and \Psi _2 </math>.
Because we have values for A and <math> A _t </math>, we can almost find <math>A _{recieved} </math>. Unfortunately, we lack values for the new phase-shift term, which is a function of the phase-shifts of <math> \Psi _1 </math> and <math> \Psi _2 </math>. This can be easily expressed as
<math>\tan { d _f } = ( sin d _1 + sin d _2 ) / ( cos d _1 + cos d _2 ) </math>
Unfortunately, this term is not simple to calculate. Worse yet, the shape is represented by
<math> d _1 c / 2 </math>
As long as this term, which represents the phase-shift between the mirror and the front of the diamond, remains constant, the diamond is a constant shape. Any variation in the diamond's shape (and therefore distance from the apparatus) will cause a greater phase-shift.
We can use small-angle approximations to estimate <math> d _f </math>, but that approach seems invalid when all numbers are extremely small. A solution to this problem is necessary to proceed.
== Future Updates ==
== Future Updates ==