split ripples pages

hugo/content/ref/sample/particle/ff/ripples/_index.md

++++
+title = "Ripples"
+weight = 20
++++
+
+## Ripples
+
+Elongated particles, or ripples, are typically used to model lamellar cuts or gratings.
+
+As everywhere else in BornAgain
+only single scattering in the DWBA is simulated.
+This can be insufficient for periodic gratings
+that cause noticeable higher-order diffraction.
+But for the foreseeable future, multiple-scattering effects are not in the scope of BornAgain.
+
+We choose ripples to be elongated in $x$ direction.
+Different profiles in the $YZ$ plane can be set, for example, bar, cosine, sawtooth.
+For each of them, different profiles can also be chosen in the $XZ$ plane.
+
+[The approach to setting the ripple profiles will be changed soon]({{% url-issues %}}/60)
+
+#### Implementation
+
+Form factor is computed as 
+
+$$  F(\mathbf{q}) = f_\parallel(q_x) f_\bot(q_y,q_z) $$
+
+The longitudinal factor $ f_\parallel $ is defined in $XZ$ plane for the following shapes:
+
+##### Box
+
+$$ f_\parallel(q_x)=L \space \text{sinc}(q_xL/2) $$
+
+##### Gauss
+
+$$ f_\parallel(q_x)= \space \frac{L}{\sqrt{2 \pi}} \text{e}^{- \frac{{(q_x l)}^{2}}{2}} $$
+
+##### Lorentz
+
+$$ f_\parallel(q_x)= \space \frac{L}{1+{(q_x l)}^{2}} $$
+
+The transversal factor $ f_\bot(q_y,q_z) $ is defined by the ripple type
+
+{{% children %}}
+

hugo/content/ref/sample/particle/ff/ripples/bar.md

++++
+title = "Bar ripple"
+weight = 20
++++
+
+## Bar ripple
+
+A ripple with an asymmetric saw-tooth profile that is uniform in $x$-direction.
+
+<img src="/img/draw/ff/3d/Box.png" width="30%" >
+<img src="/img/draw/ff/2d/Box_xy.svg" width="30%">
+<img src="/img/draw/ff/2d/Box_xz.svg" width="30%">
+
+#### Constructors
+
+```python
+Box(L, W, H)
+BarGauss(L, W, H)
+BarLorentz(L, W, H)
+```
+
+Parameters:
+- L, length
+- W, width
+- H, height
+
+#### Usage
+
+As for any other [Form factor](/ref/sample/particle/ff).
+
+#### Implementation
+
+Class {{% ref-class "Sample/HardParticle" "SawtoothRipple" %}} inherits from the interface class
+{{% ref-class "Sample/Particle" "IFormFactor" %}}.
+
+
+Form factor is computed as
+
+$$  F(\mathbf{q}) = f_\parallel(q_x)
+  i\text{e}^{-i q_y d}
+  \left[
+    \text{e}^{i \alpha_{-}/2} \text{sinc}\left( \frac{\alpha_{+}}{2} \right)
+    - \text{e}^{i \alpha_{+}/2} \text{sinc}\left( \frac{\alpha_{-}}{2} \right)
+  \right], $$
+
+with the notation
+$$  \alpha_{+} = H q_z + \frac{q_y W}{2} + q_y d, \quad
+  \alpha_{-} = H q_z - \frac{q_y W}{2} + q_y d. $$
+
+The longitudinal factor $ f_\parallel $ is defined according to "box shape" in $XZ$ plane:
+
+$$ f_\parallel(q_x)=L \space \text{sinc}(q_xL/2). $$
+
+
+Volume [has been validated]({{% url-src %}}/Tests/Unit/Sample/FormFactorBasicTest.cpp)
+against
+$$ V=\dfrac{LWH}{2}. $$
+
+#### Other shapes
+
+We have already stated that transversal $YZ$ and longitudinal $XZ$ profiles are set separately.
+For other longitudinal shapes use
+
+```python
+SawtoothRippleGauss(L, W, H, d)
+SawtoothRippleLorentz(L, W, H, d)
+```
+
+with the corresponding factor $ f_\parallel(q_x) $ inside.
+
+Other transversal profiles are also available:
+
+cosine profile
+```python
+CosineRippleBox(L, W, H)
+CosineRippleGauss(L, W, H)
+CosineRippleLorentz(L, W, H)
+```
+
+and rectangular profile
+
+```python
+Box(L, W, H)
+BarGauss(L, W, H)
+BarLorentz(L, W, H)
+```
+
+
+#### Scattering
+
+Scattering by uncorrelated, oriented sawtooth ripples for horizontal incidence. Rotation around $z$ axis:
+
+<img src="/img/auto/ff/SawtoothRippleBox.png">
+
+Generated by {{% ref-ex "ff/SawtoothRippleBox.py" %}}.
+
+#### History
+
+"CosineRippleBox" and "SawtoothRippleBox" replicate "Ripple1" and "Ripple2" from FitGISAXS [[Babonneau 2013](/lit/babonneau2013)].
+
+Full documentation and API support for all ripple form factors appeared in
+BornAgain 1.17. Before that release, the Lorentz factor $ f_\parallel $ had an extra factor of 2.5.
+The Gauss factor  $ f_\parallel $ was completely wrong up through BornAgain 20.

hugo/content/ref/sample/particle/ff/ripples/cosine.md

++++
+title = "Cosine ripple"
+weight = 20
++++
+
+## Cosine ripple
+
+A ripple with an asymmetric saw-tooth profile that is uniform in $x$-direction.
+
+<img src="/img/draw/ff/3d/CosineRipple.png" width="30%" >
+<img src="/img/draw/ff/2d/CosineRipple_xy.svg" width="30%">
+<img src="/img/draw/ff/2d/CosineRipple_yz.svg" width="30%">
+
+#### Constructor
+
+```python
+SawtoothRippleBox(L, W, H, d)
+```
+
+Parameters:
+- L, length
+- W, width
+- H, height
+- d, asymmetry
+
+Constraint:
+
+$ |d| \le W/2 $
+
+#### Usage
+
+As for any other [Form factor](/ref/sample/particle/ff).
+
+#### Implementation
+
+Class {{% ref-class "Sample/HardParticle" "SawtoothRipple" %}} inherits from the interface class
+{{% ref-class "Sample/Particle" "IFormFactor" %}}.
+
+
+Form factor is computed as
+
+$$  F(\mathbf{q}) = f_\parallel(q_x)
+  i\text{e}^{-i q_y d}
+  \left[
+    \text{e}^{i \alpha_{-}/2} \text{sinc}\left( \frac{\alpha_{+}}{2} \right)
+    - \text{e}^{i \alpha_{+}/2} \text{sinc}\left( \frac{\alpha_{-}}{2} \right)
+  \right], $$
+
+with the notation
+$$  \alpha_{+} = H q_z + \frac{q_y W}{2} + q_y d, \quad
+  \alpha_{-} = H q_z - \frac{q_y W}{2} + q_y d. $$
+
+The longitudinal factor $ f_\parallel $ is defined according to "box shape" in $XZ$ plane:
+
+$$ f_\parallel(q_x)=L \space \text{sinc}(q_xL/2). $$
+
+
+Volume [has been validated]({{% url-src %}}/Tests/Unit/Sample/FormFactorBasicTest.cpp)
+against
+$$ V=\dfrac{LWH}{2}. $$
+
+#### Other shapes
+
+We have already stated that transversal $YZ$ and longitudinal $XZ$ profiles are set separately.
+For other longitudinal shapes use
+
+```python
+SawtoothRippleGauss(L, W, H, d)
+SawtoothRippleLorentz(L, W, H, d)
+```
+
+with the corresponding factor $ f_\parallel(q_x) $ inside.
+
+Other transversal profiles are also available:
+
+cosine profile
+```python
+CosineRippleBox(L, W, H)
+CosineRippleGauss(L, W, H)
+CosineRippleLorentz(L, W, H)
+```
+
+and rectangular profile
+
+```python
+Box(L, W, H)
+BarGauss(L, W, H)
+BarLorentz(L, W, H)
+```
+
+
+#### Scattering
+
+Scattering by uncorrelated, oriented sawtooth ripples for horizontal incidence. Rotation around $z$ axis:
+
+<img src="/img/auto/ff/SawtoothRippleBox.png">
+
+Generated by {{% ref-ex "ff/SawtoothRippleBox.py" %}}.
+
+#### History
+
+"CosineRippleBox" and "SawtoothRippleBox" replicate "Ripple1" and "Ripple2" from FitGISAXS [[Babonneau 2013](/lit/babonneau2013)].
+
+Full documentation and API support for all ripple form factors appeared in
+BornAgain 1.17. Before that release, the Lorentz factor $ f_\parallel $ had an extra factor of 2.5.
+The Gauss factor  $ f_\parallel $ was completely wrong up through BornAgain 20.

hugo/content/ref/sample/particle/ff/ripples/index.md → hugo/content/ref/sample/particle/ff/ripples/sawtooth.md

 +++
-title = "Ripples"
+title = "Sawtooth ripple"
 weight = 20
 +++
 
-## Ripples
-
-Elongated particles, or ripples, are typically used to model lamellar cuts or gratings.
-
-As everywhere else in BornAgain
-only single scattering in the DWBA is simulated.
-This can be insufficient for periodic gratings
-that cause noticeable higher-order diffraction.
-But for the foreseeable future, multiple-scattering effects are not in the scope of BornAgain.
-
-We choose ripples to be elongated in $x$ direction.
-Different profiles in the $YZ$ plane can be set, for example, bar, cosine, sawtooth.
-For each of them, different profiles can also be chosen in the $XZ$ plane.
-
-[The approach to setting the ripple profiles will be changed soon]({{% url-issues %}}/60)
-
-### Example
+## Sawtooth ripple
 
 A ripple with an asymmetric saw-tooth profile that is uniform in $x$-direction.
 
@@ -119,4 +103,4 @@ Generated by {{% ref-ex "ff/SawtoothRippleBox.py" %}}.
 
 Full documentation and API support for all ripple form factors appeared in
 BornAgain 1.17. Before that release, the Lorentz factor $ f_\parallel $ had an extra factor of 2.5.
-The Gauss factor  $ f_\parallel $ was completely wrong up through BornAgain 20.
+The Gauss factor  $ f_\parallel $ was completely wrong up through BornAgain 20.
\ No newline at end of file