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</style><article id="node-405019" class="node node-logentry article ia-n clearfix" role="article"><header class="node-header"><h1 class="node-title">
<a href="https://logbooks.jlab.org/entry/3332229" rel="bookmark">BCAL time-walk corrections</a>
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<p class="author-datetime">
Lognumber <a href="https://logbooks.jlab.org/entry/3332229" class="lognumber" data-lognumber="3332229">3332229</a>. Submitted by <a href="https://logbooks.jlab.org/user/elton">elton</a> on <time datetime="2015-04-14T11:35:08-0400" pubdate="pubdate">Tue, 04/14/2015 - 11:35</time>. </p>
<table class="field-vitals"><tr><th>Logbooks: </th><td><a href="https://logbooks.jlab.org/book/hdrun">HDRUN</a> <a href="https://logbooks.jlab.org/book/hdbcal">HDBCAL</a></td></tr></table></div>
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<p>I have started thinking again about functional forms for the time-walk, in particular comparing your functional form from Shaun Krueger's thesis (6.2) with my eq. 5 in GlueX-doc-2618.</p>
<p>From GlueX-doc-2618, Eq, 5 and 6:</p>
<p>t^w = t - f^w(P/T) + f^w(P_0/T), where<br />
t^w is the walk-corrected time,<br />
t is the time-over threshold for a fixed discriminator threshold T (in units of ADC counts)<br />
P is the pulse height<br />
P_0 is the reference pulse height that determines the time reference.</p>
<p>f^w(P/T) = c1/(P/T)^c2</p>
<p>Note that I am using the pulse height P instead of area A. If the pulse height is available, we should use it, as we know reflected pulses distort the pulse shape as a function of the position z along the module. Of course, we can always use A~15P, but this is an approximation which could be avoided.</p>
<p>From Shaun Krueger's thesis, we have</p>
<p>F(P) = a + (b/(P+c))^d.</p>
<p>If we make the following identifications:</p>
<p>a = -(b/P_0+c))^d</p>
<p>c1 = -b^d</p>
<p>c2 = d</p>
<p>With these definitions, we see that the two formulas are the same, except for the following:<br />
1. The function f^w is a function of f^w(P/T), and F is a function of F(P+c) -- that is scale vs offset adjustments. f^w gives the explicit dependence of the time-walk relative to thresholds, so it can easily be applied to different threshold conditions. This function is also only valid for P/T > 1, so the range of validity is clear. The parameter T has a well-defined physical interpretation, which c does not.<br />
2. We also need to define the time reference, i.e. the time when the time-walk correction is zero. The reference chosen for the FADCs is the time at half-height. This corresponds to setting P_0=2T in t^w. It is not so clear to me how to set this offset in F(P). </p>
<p>It is likely that in practice the two forms will yield similar performance, but for the reasons given I think we should use Eqs 5 and 6 from GlueX-doc-2618 as we proceed to determine these constants.</p>
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