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<p>Hello,</p>
<p>I have analyzed in Mathematica the remaining RICH mirrors 2C, 3C,
and 5C. When I was looking at mirror 3C, I noticed that the CMM
measurement file had an error where the right side measurement
points were a repeat of the left side points. The Excel file
attached is the correct data file from Survey Group. <br>
</p>
<p>Attached are the following for each mirror:</p>
<ol>
<li>NX 9.0 plot for the edges.</li>
<li>NX 9 plot for the mirror back surface and back surface- the
mirror back surface is plotted in green, the back surface in
red.<br>
</li>
<li>Mathematica plot for the edges - the back edges are plotted in
blue, the mirror edges in red.<br>
</li>
</ol>
<p style="">Calculated mean thickness and standard deviation of each
side and the difference in mean thickness for each side and the
error of the difference are below for each mirror.</p>
<p style="">From the results below, I think all mirrors are uniform
in thickness. All mirrors (except 5C) are ~1 [mm] of the specified
thicknesses.</p>
<p style=""> I am in the process of debugging my code for mirror 5C
to ensure that the results below are correct. Looking at the plot
for 5C, the measurement points seem to be less uniformly spaced;
points are in almost a zig-zag pattern rather than lined up in
pairs as with other mirrors. This could be a possible source of
the larger estimated mean thicknesses for 5C.<br>
</p>
<p style="">Again, note the CMM equipment, per Jim Dahlberg, has a
resolution of 60 [um].</p>
<p style="">As mentioned before, I will now determine the radius of
curvature for each mirror using the CMM measurement points.</p>
<p style="">Best regards,</p>
<p style="">Tyler<br>
</p>
<p style=""><font size="+3"><u><b>2C</b></u></font></p>
<table height="151" border="2" cellpadding="2" cellspacing="2"
width="542">
<tbody>
<tr>
<td align="center" valign="top"><b>Side</b><br>
</td>
<td align="center" valign="top"><b>Mean </b><b>Thickness </b><b>[mm]</b><b><br>
</b></td>
<td align="center" valign="top"><b>Standard Deviation [mm]</b><br>
</td>
</tr>
<tr>
<td align="center" valign="top">Right<br>
</td>
<td align="center" valign="top">24.949<br>
</td>
<td align="center" valign="top">0.225<br>
</td>
</tr>
<tr>
<td align="center" valign="top">Left<br>
</td>
<td align="center" valign="top">24.989<br>
</td>
<td align="center" valign="top">0.211<br>
</td>
</tr>
<tr>
<td align="center" valign="top">Top<br>
</td>
<td align="center" valign="top">25.341<br>
</td>
<td align="center" valign="top">0.320<br>
</td>
</tr>
<tr>
<td align="center" valign="top">Bottom<br>
</td>
<td align="center" valign="top">25.434<br>
</td>
<td align="center" valign="top">0.489<br>
</td>
</tr>
</tbody>
</table>
<br>
<table height="207" border="1" cellpadding="2" cellspacing="2"
width="576">
<tbody>
<tr>
<td align="center" valign="top"><b>Sides</b><b><br>
</b></td>
<td align="center" valign="top"><b>Difference in Mean
Thickness [mm]</b><br>
</td>
<td align="center" valign="top"><b>Error [mm]</b><b><br>
</b></td>
</tr>
<tr>
<td align="center" valign="top">Left - Right<br>
</td>
<td align="center" valign="top">0.039<br>
</td>
<td align="center" valign="top">0.308<br>
</td>
</tr>
<tr>
<td align="center" valign="top">Left - Top<br>
</td>
<td align="center" valign="top">0.352<br>
</td>
<td align="center" valign="top">0.391<br>
</td>
</tr>
<tr>
<td align="center" valign="top">Left - Bottom<br>
</td>
<td align="center" valign="top">0.445<br>
</td>
<td align="center" valign="top">0.538<br>
</td>
</tr>
<tr>
<td align="center" valign="top">Right - Top<br>
</td>
<td align="center" valign="top">0.391<br>
</td>
<td align="center" valign="top">0.834<br>
</td>
</tr>
<tr>
<td align="center" valign="top">Right - Bottom<br>
</td>
<td align="center" valign="top">0.484<br>
</td>
<td align="center" valign="top">0.533<br>
</td>
</tr>
<tr>
<td align="center" valign="top">Top - Bottom<br>
</td>
<td align="center" valign="top">0.093<br>
</td>
<td align="center" valign="top">0.585<br>
</td>
</tr>
</tbody>
</table>
<br>
<p style=""><font size="+3"><u><b>3C</b></u></font></p>
<table height="151" border="2" cellpadding="2" cellspacing="2"
width="542">
<tbody>
<tr>
<td align="center" valign="top"><b>Side</b><br>
</td>
<td align="center" valign="top"><b>Mean </b><b>Thickness </b><b>[mm]</b><b><br>
</b></td>
<td align="center" valign="top"><b>Standard Deviation [mm]</b><br>
</td>
</tr>
<tr>
<td align="center" valign="top">Right<br>
</td>
<td align="center" valign="top">25.193<br>
</td>
<td align="center" valign="top">0.368<br>
</td>
</tr>
<tr>
<td align="center" valign="top">Left<br>
</td>
<td align="center" valign="top">24.935<br>
</td>
<td align="center" valign="top">0.329<br>
</td>
</tr>
<tr>
<td align="center" valign="top">Top<br>
</td>
<td align="center" valign="top">25.609<br>
</td>
<td align="center" valign="top">0.326<br>
</td>
</tr>
<tr>
<td align="center" valign="top">Bottom<br>
</td>
<td align="center" valign="top">25.827<br>
</td>
<td align="center" valign="top">0.953<br>
</td>
</tr>
</tbody>
</table>
<br>
<table height="207" border="1" cellpadding="2" cellspacing="2"
width="576">
<tbody>
<tr>
<td align="center" valign="top"><b>Sides</b><b><br>
</b></td>
<td align="center" valign="top"><b>Difference in Mean
Thickness [mm]</b><br>
</td>
<td align="center" valign="top"><b>Error [mm]</b><b><br>
</b></td>
</tr>
<tr>
<td align="center" valign="top">Left - Right<br>
</td>
<td align="center" valign="top">0.259<br>
</td>
<td align="center" valign="top">0.494<br>
</td>
</tr>
<tr>
<td align="center" valign="top">Left - Top<br>
</td>
<td align="center" valign="top">0.674<br>
</td>
<td align="center" valign="top">0.492<br>
</td>
</tr>
<tr>
<td align="center" valign="top">Left - Bottom<br>
</td>
<td align="center" valign="top">0.892<br>
</td>
<td align="center" valign="top">1.022<br>
</td>
</tr>
<tr>
<td align="center" valign="top">Right - Top<br>
</td>
<td align="center" valign="top">0.415<br>
</td>
<td align="center" valign="top">0.463<br>
</td>
</tr>
<tr>
<td align="center" valign="top">Right - Bottom<br>
</td>
<td align="center" valign="top">0.634<br>
</td>
<td align="center" valign="top">1.001<br>
</td>
</tr>
<tr>
<td align="center" valign="top">Top - Bottom<br>
</td>
<td align="center" valign="top">0.218<br>
</td>
<td align="center" valign="top">1.001<br>
</td>
</tr>
</tbody>
</table>
<br>
<br>
<font size="+3"><u><b>5C</b></u></font><br>
<table height="151" border="2" cellpadding="2" cellspacing="2"
width="542">
<tbody>
<tr>
<td align="center" valign="top"><b>Side</b><br>
</td>
<td align="center" valign="top"><b>Mean </b><b>Thickness </b><b>[mm]</b><b><br>
</b></td>
<td align="center" valign="top"><b>Standard Deviation [mm]</b><br>
</td>
</tr>
<tr>
<td align="center" valign="top">Right<br>
</td>
<td align="center" valign="top">27.453<br>
</td>
<td align="center" valign="top">1.170<br>
</td>
</tr>
<tr>
<td align="center" valign="top">Left<br>
</td>
<td align="center" valign="top">25.231<br>
</td>
<td align="center" valign="top">0.242<br>
</td>
</tr>
<tr>
<td align="center" valign="top">Top<br>
</td>
<td align="center" valign="top">26.596<br>
</td>
<td align="center" valign="top">1.581<br>
</td>
</tr>
<tr>
<td align="center" valign="top">Bottom<br>
</td>
<td align="center" valign="top">27.146<br>
</td>
<td align="center" valign="top">1.243<br>
</td>
</tr>
</tbody>
</table>
<br>
<table height="207" border="1" cellpadding="2" cellspacing="2"
width="576">
<tbody>
<tr>
<td align="center" valign="top"><b>Sides</b><b><br>
</b></td>
<td align="center" valign="top"><b>Difference in Mean
Thickness [mm]</b><br>
</td>
<td align="center" valign="top"><b>Error [mm]</b><b><br>
</b></td>
</tr>
<tr>
<td align="center" valign="top">Left - Right<br>
</td>
<td align="center" valign="top">2.222<br>
</td>
<td align="center" valign="top">1.195<br>
</td>
</tr>
<tr>
<td align="center" valign="top">Left - Top<br>
</td>
<td align="center" valign="top">0.857<br>
</td>
<td align="center" valign="top">1.967<br>
</td>
</tr>
<tr>
<td align="center" valign="top">Left - Bottom<br>
</td>
<td align="center" valign="top">0.307<br>
</td>
<td align="center" valign="top">1.711<br>
</td>
</tr>
<tr>
<td align="center" valign="top">Right - Top<br>
</td>
<td align="center" valign="top">1.365<br>
</td>
<td align="center" valign="top">1.599<br>
</td>
</tr>
<tr>
<td align="center" valign="top">Right - Bottom<br>
</td>
<td align="center" valign="top">1.914<br>
</td>
<td align="center" valign="top">1.272<br>
</td>
</tr>
<tr>
<td align="center" valign="top">Top - Bottom<br>
</td>
<td align="center" valign="top">0.549<br>
</td>
<td align="center" valign="top">2.014<br>
</td>
</tr>
</tbody>
</table>
<br>
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