Changes

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.

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>

<math>s = d _1 \frac{v _a}{2}</math>

where <math> v _a </math> is the speed of light in air. We can rewrite this in terms of <math> d _1 </math>:

where <math> v _a </math> is the speed of light in air. We can rewrite this in terms of <math> d _1 </math>:

Simplifying our initial equation, we find that  

Simplifying our initial equation, we find that  

<math>A^2 _{123} / A^2 = C^2 _1 + C^2 _2 + C^2 _3 + 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>

<math>\frac{A^2 _{123}}{A^2} = C^2 _1 + C^2 _2 + C^2 _3 + 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>

Because the cosine is an even function, we can slightly simplify this further.

Because the cosine is an even function, we can slightly simplify this further.

<math>A^2 _{123} / A^2 = C^2 _1 + C^2 _2 + C^2 _3 + 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>

<math>\frac{A^2 _{123}}{A^2} = C^2 _1 + C^2 _2 + C^2 _3 + 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>

This equation, athough complicated, is completely solvable, as the only unknown is the s-term.

This equation, athough complicated, is completely solvable, as the only unknown is the s-term.