add function dipbackground

StollLab · May 17, 2024 · bd7d606 · bd7d606
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diff --git a/docsrc/dipbackground.html b/docsrc/dipbackground.html
@@ -0,0 +1,85 @@
+<!DOCTYPE html>
+<html>
+<head>
+   <meta charset="utf-8">
+   <link rel="icon" href="img/eslogo196.png">
+   <link rel="stylesheet" type="text/css" href="style.css">
+   <link rel="stylesheet" href="highlight/matlab.css">
+   <script src="highlight/highlight.min.js"></script>
+   <script src="highlight/do_highlight.js"></script>
+   <title>dipkernel</title>
+</head>
+
+<body>
+
+<header>
+<ul>
+<li><img src="img/eslogo42.png">
+<li class="header-title">EasySpin
+<li><a href="index.html">Documentation</a>
+<li><a href="references.html">Publications</a>
+<li><a href="http://easyspin.org" target="_blank">Website</a>
+<li><a href="http://easyspin.org/academy" target="_blank">Academy</a>
+<li><a href="http://easyspin.org/forum" target="_blank">Forum</a>
+</ul>
+</header>
+
+<section>
+
+<div class="functitle">dipbackground</div>
+
+<p>
+Calculate dipolar EPR (DEER) background signal.
+</p>
+
+<!-- =================================================================== -->
+<div class="subtitle">Syntax</div>
+
+<pre class="matlab">
+Vinter = dipbackground(t,conc,lambda)
+dipbackground(...)
+</pre>
+
+<!-- =================================================================== -->
+<div class="subtitle">Description</div>W
+
+<p>
+<code>dipbackground</code> calculates the inter-molecular DEER signal for a homogeneous three-dimensional distribution of spins.
+</p>
+
+<p>
+<code>t</code> is the time vector, in microseconds. <code>conc</code> is the spin concentration, in micromolar (µM). <code>lambda</code> is the modulation depth, between 0 and 1.
+</p>
+
+<p>
+The output <code>Vinter</code> is the inter-molecular dipolar background decay function, scaled such that it is equal to 1 at time zero.
+</p>
+
+<!-- ========================================================== -->
+<div class="subtitle">Examples</div>
+
+<p>
+Here is a typical application, for a 50 µM spin concentration and a modulation depth of 0.3:
+</p>
+
+<pre class="matlab">
+t = -0.2:0.020:5;  % µs
+Vinter = dipbackground(t,100,0.3);
+plot(t,Vinter)
+</pre>
+
+<!-- =================================================================== -->
+<div class="subtitle">See also</div>
+<p>
+<a class="esf" href="dipkernel.html">dipkernel</a>,
+<a class="esf" href="diptensor.html">diptensor</a>,
+<a class="esf" href="ham_ee.html">ham_ee</a>
+</p>
+
+<hr>
+</section>
+
+<footer></footer>
+
+</body>
+</html>
diff --git a/docsrc/funcsalphabet.html b/docsrc/funcsalphabet.html
@@ -55,8 +55,9 @@
 <tr><td><a href="datasmooth.html">datasmooth</a></td><td>Moving averages: smoothing and differentiation</td></tr>
 <tr><td><a href="degree.html">degree</a></td><td>Conversion between radians and degrees</td></tr>
 <tr><td><a href="deriv.html">deriv</a></td><td>Numerical differentiation</td></tr>
+<tr><td><a href="dipbackground.html">dipbackground</a></td><td>Dipolar EPR background signal (DEER)</td></tr>
 <tr><td><a href="dipkernel.html">dipkernel</a></td><td>Dipolar EPR signal (DEER)</td></tr>
-<tr><td><a href="diptensor.html">diptensor</a></td><td>Dipolar tensors</td></tr>
+<tr><td><a href="diptensor.html">diptensor</a></td><td>Dipolar interaction tensor</td></tr>
 <tr><td><a href="easyspin.html">easyspin</a></td><td>Information and tasks regarding EasySpin</td></tr>
 <tr><td><a href="echarge.html">echarge</a></td><td>Elementary electric charge</td></tr>
 <tr><td><a href="emass.html">emass</a></td><td>Mass of electron</td></tr>

diff --git a/docsrc/funcscategory.html b/docsrc/funcscategory.html
@@ -57,6 +57,12 @@
 <tr><td><a href="dipkernel.html">dipkernel</a></td><td>Dipolar EPR signal (DEER)</td></tr>
 <tr><td><a href="photoselect.html">photoselect</a></td><td>Photoselection weights</td></tr>
 
+<tr><td>&nbsp;</td></tr>
+<tr><td colspan="2" class="grouptitle">Dipolar EPR</td></tr>
+<tr><td><a href="dipbackground.html">dipbackground</a></td><td>Dipolar EPR background signal (DEER)</td></tr>
+<tr><td><a href="dipkernel.html">dipkernel</a></td><td>Dipolar EPR signal (DEER)</td></tr>
+<tr><td><a href="diptensor.html">diptensor</a></td><td>Dipolar interaction tensor</td></tr>
+
 <tr><td>&nbsp;</td></tr>
 <tr><td colspan="2" class="grouptitle">Stochastic simulations</td></tr>
 

diff --git a/docsrc/releases.html b/docsrc/releases.html
@@ -32,6 +32,23 @@ <h1>Changes from release to release</h1>
 $ReleaseID$
 </div>
 
+<p>Major new features</p>
+<ul>
+<li>New function <a class="esf" href="dipbackground">dipbackground</a> calculates background decays for dipolar EPR (DEER etc.)</li>
+</ul>
+
+<p>Major bug fixes</p>
+<ul>
+</ul>
+
+<p>Incompatible changes</p>
+<ul>
+</ul>
+
+<div class="subtitle">
+6.0
+</div>
+
 <p>Major new features</p>
 <ul>
 <li>Major overhaul of <a class="esf" href="esfit.html">esfit</a>, it now calculates uncertainties of fitted parameters as well as correlations.</li>

diff --git a/easyspin/dipbackground.m b/easyspin/dipbackground.m
@@ -0,0 +1,47 @@
+% dipbackground  Intermolecular dipolar background decay
+%
+%  Vinter = dipbackground(t,conc,lambda)
+%  dipbackground(...)
+%
+%  Calculates the intermolecular dipolar background decay over the time axis,
+%  for spin concentration conc (in µM) and modulation depth lambda (between 0 and 1).
+%
+%  Input:
+%    t       time axis (µs)
+%    conc    spin concentration (µM)
+%    lambda  modulation depth
+%
+%  Output:
+%    Vinter  intermolecular background decay function
+%
+%  Example:
+%    t = linspace(-0.2,5);  % µs
+%    Vinter = dipbackground(t,100,0.3);
+%    plot(t,Vinter);
+
+function Vinter = dipbackground(t,conc_uM,lambda)
+
+if nargin==0
+  help(mfilename);
+  return
+end
+
+g1 = gfree;
+g2 = gfree;
+
+D = mu0/(4*pi)*g1*g2*bmagn^2/hbar;  % rad/s
+conc_mM = conc_uM/1e3;  % µM -> mM=mol/m^3
+conc = conc_mM*avogadro;  % mM=mol/m^3 -> m^-3
+t = t*1e-6;  % µs -> s
+k = 8*pi^2/(9*sqrt(3))*D*conc*lambda;
+Vinter = exp(-k*abs(t));
+
+% Plotting
+if nargout==0
+  plot(t/1e-6,Vinter)
+  xlabel('time (µs)')
+  ylabel('{\it{V}}_{inter}')
+  grid on
+end
+
+end
diff --git a/tests/dipbackground_explicit.m b/tests/dipbackground_explicit.m
@@ -0,0 +1,18 @@
+function ok = test()
+
+t_us = 1.1;  % µs
+conc_uM = 100;  % µM
+lambda = 0.7;
+
+c_mM = conc_uM/1e3;  % µM -> mM=mol/m^3
+c = c_mM*avogadro;  % mol/m^3 -> m^-3
+
+g = gfree;
+D = mu0/(4*pi)*g^2*bmagn^2/hbar;  % rad/s
+k = 8*pi^2/(9*sqrt(3))*D*lambda*c;
+Vinter_ref = exp(-k*t_us*1e-6);
+Vinter = dipbackground(t_us,conc_uM,lambda);
+
+ok = areequal(Vinter,Vinter_ref,1e-10,'rel');
+
+end