@@ -72,13 +72,13 @@ Transferred to the temporal domain via an inverse Fourier transform :eq:`ifft`,
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it follows
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.. math ::
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- :label: time -wfs-plane
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+ :label: td -wfs-plane
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d(\x _0 ,t) = 2 a(t) * h(t) * w(\x _0 ) \scalarprod {\n _k}{\n _{\x _0 }}
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\dirac {t - \frac {\scalarprod {\n _k}{\x _0 }}{c}},
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.. math ::
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- :label: time -wfs-plane-25 d
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+ :label: td -wfs-plane-25 d
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\begin {aligned}
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d_\text {2.5 D}(\x _0 ,t) =& 2 a(t) * h_\text {2.5 D}(t) * w(\x _0 )
@@ -90,14 +90,14 @@ it follows
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where
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.. math ::
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- :label: time -wfs-prefilter
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+ :label: td -wfs-prefilter
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h(t) = \mathcal {F}^{-1 }\left \{\i\wc \right \},
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and
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.. math ::
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- :label: time -wfs-prefilter-25 d
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+ :label: td -wfs-prefilter-25 d
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h_\text {2.5 D}(t) = \mathcal {F}^{-1 }\left \{
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\sqrt {\i\wc }\right \}
@@ -228,14 +228,14 @@ The default |WFS| driving functions for a point source in the SFS Toolbox are
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temporal domain via an inverse Fourier transform :eq: `ifft ` it follows
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.. math ::
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- :label: time -wfs-point
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+ :label: td -wfs-point
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d(\x _0 ,t) = \frac {1 }{2 {\pi }} a(t) * h(t) * w(\x _0 )
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\frac {\scalarprod {\x _0 -\xs }{\n _{\x _0 }}}{|\x _0 -\xs |^2 }
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\dirac {t-\frac {|\x _0 -\xs |}{c}},
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.. math ::
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- :label: time -wfs-point-25 d
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+ :label: td -wfs-point-25 d
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\begin {aligned}
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d_\text {2.5 D}(\x _0 ,t) =&
@@ -247,7 +247,7 @@ temporal domain via an inverse Fourier transform :eq:`ifft` it follows
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\end {aligned}
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.. math ::
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- :label: time -wfs-point-25 d-refline
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+ :label: td -wfs-point-25 d-refline
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\begin {aligned}
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d_\text {2.5 D}(\x _0 ,t) =&
@@ -349,14 +349,14 @@ transferred to the temporal domain via an inverse Fourier transform :eq:`ifft`
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it follows
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.. math ::
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- :label: time -wfs-line
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+ :label: td -wfs-line
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d(\x _0 ,t) = \sqrt {\frac {1 }{2 \pi }} a(t) * h(t) * w(\x0 )
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\frac {\scalarprod {\vec {v}}{\n _{\x _0 }}}{|\vec {v}|^{\frac {3 }{2 }}}
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\dirac {t-\frac {|\vec {v}|}{c}},
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.. math ::
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- :label: time -wfs-line-25 d
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+ :label: td -wfs-line-25 d
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d_\text {2.5 D}(\x _0 ,t) =
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g_0 \sqrt {\frac {1 }{2 \pi }} a(t) *
@@ -423,10 +423,10 @@ a diverging one as can be seen in :numref:`fig-wfs-25d-focused-source`. In order
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to choose the active secondary sources, especially for circular or spherical
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geometries, the focused source also needs a direction :math: `\n _\text {s}`.
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- The driving function for a focused source is given by the time -reversed
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+ The driving function for a focused source is given by the td -reversed
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versions of the driving function for a point source
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- :eq: `time -wfs-point ` and
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- :eq: `time -wfs-point-25d ` as
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+ :eq: `td -wfs-point ` and
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+ :eq: `td -wfs-point-25d ` as
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.. math ::
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:label: fd-wfs-focused-3 d
@@ -435,8 +435,8 @@ versions of the driving function for a point source
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\frac {\scalarprod {\x _0 -\xs }{\n _{\x _0 }}}{|\x _0 -\xs |^2 }
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\e {\i\wc |\x _0 -\xs |}.
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- The 2.5D driving functions are given by the time -reversed version of
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- :eq: `time -wfs-point-25d ` for a reference point after
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+ The 2.5D driving functions are given by the td -reversed version of
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+ :eq: `td -wfs-point-25d ` for a reference point after
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:cite: `Verheijen1997 `, eq. (A.14) as
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.. math ::
@@ -452,7 +452,7 @@ The 2.5D driving functions are given by the time-reversed version of
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\end {aligned}
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and the time reversed version of
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- :eq: `time -wfs-point-25d-refline ` for a reference line,
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+ :eq: `td -wfs-point-25d-refline ` for a reference line,
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compare :cite: `Start1997 `, eq. (3.16)
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.. math ::
@@ -475,14 +475,14 @@ Transferred to the temporal domain via an inverse Fourier transform :eq:`ifft`
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it follows
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.. math ::
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- :label: time -wfs-focused-3 d
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+ :label: td -wfs-focused-3 d
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d(\x _0 ,t) = \frac {1 }{2 {\pi }} a(t) * h(t) * w(\x _0 )
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\frac {\scalarprod {\x _0 -\xs }{\n _{\x _0 }}}{|\x _0 -\xs |^2 }
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\dirac {t+\frac {|\x _0 -\xs |}{c}},
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.. math ::
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- :label: time -wfs-focused-25 d
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+ :label: td -wfs-focused-25 d
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\begin {aligned}
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d_\text {2.5 D}(\x _0 ,t) =&
@@ -494,7 +494,7 @@ it follows
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\end {aligned}
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.. math ::
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- :label: time -wfs-focused-25 d-refline
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+ :label: td -wfs-focused-25 d-refline
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\begin {aligned}
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d_\text {2.5 D}(\x _0 ,t) =&
@@ -505,7 +505,7 @@ it follows
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\dirac {t+\frac {|\x _0 -\xs |}{c}}.
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\end {aligned}
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- In this document a focused source always refers to the time -reversed version of a
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+ In this document a focused source always refers to the td -reversed version of a
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point source, but a focused line source can be defined in the same way starting
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from :eq: `fd-wfs-line `
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@@ -520,7 +520,7 @@ Transferred to the temporal domain via an inverse Fourier transform :eq:`ifft`
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it follows
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.. math ::
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- :label: time -wfs-focused-2 d
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+ :label: td -wfs-focused-2 d
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d(\x _0 ,t) = \sqrt {\frac {1 }{2 \pi }} a(t) * h(t) * w(\x0 )
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\frac {\scalarprod {\x _0 -\xs }{\n _{\x _0 }}}{|\x _0 -\xs |^{\frac {3 }{2 }}}
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