Changes

== Surface Resolution Approximation ==

== Surface Resolution Approximation ==

An important part of topological interferometry is that the surface be ''retained'' in the reflected image.  Plane wave solutions are most effective when the surface gradually curves and no sharp peaks are present.

An important part of topological interferometry is that the surface be ''retained'' in the reflected image.  Plane wave solutions can be used when the surface gradually curves and no sharp peaks are present.  Using Huygen's principle and knowledge of the surface, the forward distance for image loss can be calculated.

== Huygen's Principle ==

== Huygen's Principle ==

In our model of the diamond surface, Huygen's principle can be used to determine the forward distance from the surface when the reflected light will no longer contain a ''valid'' image of the surface.  Using the diagram at right, [[Image:ResDiagram1.jpg|thumb|Surface Schematic]] and some knowledge of the experimental setup, a rought estimate for the forward distance ''L'' can be calculated using a small angle approximation for the angle.

In our model of the diamond surface, Huygen's principle can be used to determine the forward distance from the surface when the reflected light will no longer contain a ''valid'' image of the surface.  Using the diagram at right, [[Image:ResDiagram1.jpg|thumb|Surface Schematic]] and some knowledge of the experimental setup, a rought estimate for the forward distance ''L'' can be calculated using a small angle approximation for the angle. Using the the diamond surface is about <math>5 \cross 10^{-3} m</math> and the thickness is <math>5 \cross 10^{-6} m</math>, the forward distance for image loss can then be deduced to be 5m.  Since this is much longer than the feature length.  Our experimental setup can be considered effective.

 

 

 

<math>\boldsymbol{E} = \boldsymbol{E_0} e^{i \left( \boldsymbol{k \cdot x} - \omega t \right)}</math>