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EllipsoidalCylinder

An upright cylinder whose cross section is an ellipse.

Constructor

EllipsoidalCylinder(R_a, R_b, H)

Parameters:

  • R_a, radius $R_{a}$ in $x$ direction
  • R_b, radius $R_{b}$ in $y$ direction
  • H, height

Usage

As for any other Form factor.

Implementation

Class EllipsoidalCylinder inherits from the interface class IFormFactor .

Form factor is computed as

$$ F(\mathbf{q})=2\pi R_aR_b H \space \exp\Big(iq_z\dfrac{H}{2}\Big) \text{sinc}\Big(q_z\dfrac{H}{2}\Big) \dfrac{J_1(\gamma)}{\gamma} , $$ with the notation $$ \gamma := \sqrt{(q_xR_a)^2 + (q_yR_b)^2}. $$

Volume has been validated against $$V=\pi R_aR_bH.$$

More special:

Example

Scattering by uncorrelated, oriented cylinders for horizontal incidence. Rotation around $z$ axis:

Generated by Examples/ff/EllipsoidalCylinder.py .

History

Agrees with “Ellipsoid” form factor of IsGISAXS [manual, Eq. 2.40, wrongly labeled in Fig. 2.4] and “Ellipsoidal Cylinder” [Renaud 2009, Eq. 224]