Update WFS 2.5D fs driving functions

index.txt

@@ -1440,6 +1440,15 @@ domain via an inverse Fourier transform :eq:`ifft` it follows
         \frac{1}{\sqrt{2\pi}} a(t) * h_\text{2.5D}(t) * w(\x_0)
         \sqrt{\frac{|\xref-\x_0|}{|\x_0-\xs|+|\xref-\x_0|}} \\
         \cdot \frac{\scalarprod{\x_0-\xs}{\n_{\x_0}}}{|\x_0-\xs|^{\frac{3}{2}}}
+        \dirac{t-\frac{|\x_0-\xs|}{c}},
+
+.. math::
+    :label: d.wfs.ps.2.5D.refline
+
+    d_\text{2.5D}(\x_0,t) =
+        \frac{1}{\sqrt{2\pi}} a(t) * h_\text{2.5D}(t) * w(\x_0)
+        \sqrt{\frac{d_\text{ref}}{d_\text{ref}+d_\text{s}}}
+        \cdot \frac{\scalarprod{\x_0-\xs}{\n_{\x_0}}}{|\x_0-\xs|^{\frac{3}{2}}}
         \dirac{t-\frac{|\x_0-\xs|}{c}}.
 
 The window function :math:`w(\x_0)` for a point source as source model can be
@@ -1590,25 +1599,44 @@ a diverging one as can be seen in :numref:`fig-wfs-25d-focused-source`. In order
 to choose the active secondary sources, especially for circular or spherical
 geometries, the focused source also needs a direction :math:`\n_\text{s}`.
 
-The driving function for a focused source are given by the time-reversed
-versions of the driving functions for a point source :eq:`d.wfs.ps` and
+The driving function for a focused source is given by the time-reversed
+versions of the driving function for a point source :eq:`d.wfs.ps` and
 :eq:`d.wfs.ps.2.5D` as
 
 .. math::
     :label: D.wfs.fs
 
     D(\x_0,\w) = \frac{1}{2\pi} A(\w) w(\x_0) \i\wc
         \frac{\scalarprod{\x_0-\xs}{\n_{\x_0}}}{|\x_0-\xs|^2}
-        \e{\i\wc |\x_0-\xs|},
+        \e{\i\wc |\x_0-\xs|}.
+
+The 2.5D driving functions are given by the time-reversed version of
+:eq:`d.wfs.ps.2.5D` for a reference point [Verheijen1997]_, eq. (A.14)
 
 .. math::
     :label: D.wfs.fs.2.5D
 
     D_\text{2.5D}(\x_0,\w) =
         \frac{1}{\sqrt{2\pi}} A(\w) w(\x_0) \sqrt{\i\wc}
-        \sqrt{\frac{|\xref-\x_0|}{|\x_0-\xs|+|\xref-\x_0|}}
+        \sqrt{\frac{|\xref-\x_0|}{| |\x_0-\xs|-|\xref-\x_0| |}}
         \frac{\scalarprod{\x_0-\xs}{\n_{\x_0}}}{|\x_0-\xs|^{\frac{3}{2}}}
-        \e{\i\wc |\x_0-\xs|}.
+        \e{\i\wc |\x_0-\xs|},
+
+and the time reversed version of :eq:`d.wfs.ps.2.5D.refline` for a reference
+line, compare [Start1997]_, eq. (3.16)
+
+.. math::
+    :label: D.wfs.fs.2.5D.refline
+
+    D_\text{2.5D}(\x_0,\w) =
+        \frac{1}{\sqrt{2\pi}} A(\w) w(\x_0) \sqrt{\i\wc}
+        \sqrt{\frac{d_\text{ref}}{d_\text{ref}-d_\text{s}}}
+        \frac{\scalarprod{\x_0-\xs}{\n_{\x_0}}}{|\x_0-\xs|^{\frac{3}{2}}}
+        \e{\i\wc |\x_0-\xs|},
+
+where :math:`d_\text{ref}` is the distance of a line parallel to the secondary
+source distribution and :math:`d_\text{s}` the shortest possible distance from
+the focused source to the linear secondary source distribution.
 
 Transferred to the temporal domain via an inverse Fourier transform :eq:`ifft` it
 follows
@@ -1627,6 +1655,15 @@ follows
         \frac{1}{\sqrt{2\pi}} a(t) * h_\text{2.5D}(t) * w(\x_0)
         \sqrt{\frac{|\xref-\x_0|}{|\x_0-\xs|+|\xref-\x_0|}} \\
         \cdot \frac{\scalarprod{\x_0-\xs}{\n_{\x_0}}}{|\x_0-\xs|^{\frac{3}{2}}}
+        \dirac{t+\frac{|\x_0-\xs|}{c}},
+
+.. math::
+    :label: d.wfs.fs.2.5D.refline
+
+    d_\text{2.5D}(\x_0,t) =
+        \frac{1}{\sqrt{2\pi}} a(t) * h_\text{2.5D}(t) * w(\x_0)
+        \sqrt{\frac{d_\text{ref}}{d_\text{ref}-d_\text{s}}}
+        \cdot \frac{\scalarprod{\x_0-\xs}{\n_{\x_0}}}{|\x_0-\xs|^{\frac{3}{2}}}
         \dirac{t+\frac{|\x_0-\xs|}{c}}.
 
 In this document a focused source always refers to the time-reversed version of a