spatial-transfer-functions.html

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         title="Permalink to Spatial Transfer Functions">Spatial Transfer Functions</a></h2>
 
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    <abbr class="published" title="2011-07-13T18:54:00-06:00">
      2011/07/13
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    <address class="vcard author">
      By <a class="url fn" href="https://keflavich.github.io/blog/author/adam-adamgginsburggmailcom.html">Adam (adam.g.ginsburg@gmail.com)</a>
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    <p>The majority of the past week has been dedicated to debugging; it looks
like cross-scanned simulations finally work.
The plot below is a derivation of the spatial transfer function for a
number of different intrinsic sky power-law power spectra.</p>
<img alt="" src="http://2.bp.blogspot.com/-JyAPg0u9uQ8/Th3kuQh1fpI/AAAAAAAAGRs/pP7o3n9_wds/s320/Experiment10_AverageRecoveryFunction.png" />
<p>Justifying the above plot is essential.
First, the very steep power-laws [-3 in the example below] show a
recovery fraction &gt;1. This is simply because their S/N was inadequate -
the output power spectrum is nearly flat, but at a level higher than the
sky.</p>
<img alt="" src="http://4.bp.blogspot.com/-JPBjsLDfP5M/Th3lw5n1xTI/AAAAAAAAGR0/aDeOmMv5s8w/s320/exp10_ds2_astrosky_arrang45_atmotest_amp1.0E%252B01_sky00_seed00_peak010.00_nosmooth_compare.png" />
<img alt="" src="http://3.bp.blogspot.com/-LOCDmoLCcZs/Th3lxfnKVzI/AAAAAAAAGR8/9NCM3OroGoM/s320/exp10_ds2_astrosky_arrang45_atmotest_amp1.0E%252B01_sky00_seed00_peak010.00_nosmooth_psds.png" />
<p>Second, the most plausible power-laws [-1.5 in the example below] show
pretty good recovery (90-95% over the relevant range):</p>
<img alt="" src="http://1.bp.blogspot.com/-MTZ8WGl3ZRc/Th3mMkvv2II/AAAAAAAAGSE/0OO4Te39fPI/s320/exp10_ds2_astrosky_arrang45_atmotest_amp1.0E%252B01_sky03_seed00_peak010.00_nosmooth_compare.png" />
<img alt="" src="http://2.bp.blogspot.com/-5IeTZW-ZTAw/Th3mNHPC8gI/AAAAAAAAGSM/WhIWClGWqbo/s320/exp10_ds2_astrosky_arrang45_atmotest_amp1.0E%252B01_sky03_seed00_peak010.00_nosmooth_psds.png" />
<img alt="" src="http://4.bp.blogspot.com/-O6ofm7GaxUI/Th3mNgf29AI/AAAAAAAAGSU/VzQ7aL-yd_E/s320/exp10_ds2_astrosky_arrang45_atmotest_amp1.0E%252B01_sky03_seed00_peak010.00_nosmooth_stf.png" />
<p>There are some &quot;white&quot; power losses, particularly in the flatter
power-spectra. My best guess is that this has something to do with the
relative scales being offset from a mean of 1, but so far all tests to
show that that is the cause have in fact shown no problems at all. What
else could cause a scale-independent power loss?
Also, the flat power spectrum (and inverted) aren't quite flat because I
impose a &quot;galactic scale height&quot; on them. Should I stop doing that?</p>

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