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<p class="MsoNormal"><span style="font-size:11.0pt">I probably should have made it clear, by the way, that the parameter S below is an intermediate coordinate, prior to applying the WCS projection, which would be TAN in this case.<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal" style="margin-left:.5in"><b><span style="color:black">From: </span>
</b><span style="color:black">fitswcs <fitswcs-bounces@listmgr.nrao.edu> on behalf of "Thompson, William T. (GSFC-671.0)[ADNET SYSTEMS INC]" <william.t.thompson@nasa.gov><br>
<b>Date: </b>Wednesday, May 8, 2019 at 10:54 AM<br>
<b>To: </b>FITSWCS <fitswcs@nrao.edu><br>
<b>Subject: </b>[non-nasa source] [fitswcs] Distortions<o:p></o:p></span></p>
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<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:11.0pt"><o:p> </o:p></span></p>
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<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:11.0pt">Folks:</span><o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:11.0pt"> </span><o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:11.0pt">It’s been a while since I’ve heard any chatter about WCS. What’s the status of Paper IV on distortions? Are distortions handled in any of the software packages, such as WCSLIB?</span><o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:11.0pt"> </span><o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:11.0pt">It appears that we may need to use distortions for an upcoming mission. Ray tracing for a spectrometer for the Solar Orbiter mission shows that the relationship between the pixel
positions I,J and the real-world coordinates have significant second-order terms. Our plans are to provide data in two formats, one in the original detector pixel space, and one where the data have been interpolated to linearize and rectify the data. The
latter is no problem, but I would like to accurately describe the coordinates in the former.</span><o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:11.0pt"> </span><o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:11.0pt">Second order effects show up in two places. The most significant is that the plate scale in arc seconds increases linearly with wavelength. In other words</span><o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:11.0pt"> </span><o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in;text-indent:.5in"><span style="font-size:11.0pt">S = a0 + a1 * J * (1 + a2*I)</span><o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:11.0pt"> </span><o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:11.0pt">where S is the spatial dimension along the slit, J is the pixel dimension associated with the spatial dimension, and I is the pixel dimension associated with the spectral dimension.
Here, the second order effect comes from the J*I term.</span><o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:11.0pt"> </span><o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:11.0pt">The other second order effect comes from the fact that the slit images are slightly bowed, so that the wavelength has a dependence on J^2.</span><o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:11.0pt"> </span><o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:11.0pt">Thanks,</span><o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:11.0pt"> </span><o:p></o:p></p>
<p class="MsoNormal" style="margin-left:.5in"><span style="font-size:11.0pt">Bill Thompson</span><o:p></o:p></p>
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