Papers Multislice orientation

• ChenDyck1997 paper : Multislice Method for Large Beam Tilt with Application to HOLZ Effects in Triclinic and Monoclinic Crystals
• Ishizuka 1982 : Multislice Formula for Inclined Illumination
• xHREM with manual and p32 for inclined illumination implementation.

Ishizuka1982

Multislice Formula for Inclined Illumination

ChenDyck1997

• MS no-tilt : $\Psi(x,y,z)=\varphi(x,y,z)e^{2\pi ikz}$ where $k=k_z$
• MSSBT : $\Psi(x,y,z)=\varphi(x,y,z)e^{2\pi ik_zz}$ max 3 deg
• MSMBT : mix MSLBT and MSSBT max 6 deg
• MSLBT : $\Psi(x,y,z)=\varphi(x,y,z)e^{2\pi ikz}$ max 12 deg

Kirkland no beam tilt : $$\begin{equation} \frac{\dP\varphi(x,y,z)}{\dP_z} = \Big\{\frac{i\lambda}{4\pi}\grad^2_{xy} + i\sigma V(x,y,z) \Big\} \varphi(x,y,z) \end{equation}$$

with beam-tilt $$\begin{equation} \frac{\dP\varphi(x,y,z)}{\dP_z} = \Big\{\frac{i}{4\pi k_z}\grad^2_{xy} + \frac{k}{k_z}i\sigma V(x,y,z) + \frac{i\pi\bb K_u^2}{k_z} \Big\} \varphi(x,y,z) \end{equation}$$

resulting in solution : $$\begin{equation} \varphi_n^{\bb K_u}(x,y) \approx \exp\Big\{\Delta z\left( \frac{i}{4\pi k_z}\grad^2_{xy} - \lambda\bb K_u\cdot\grad - \frac{i\pi\bb K_u^2}{k} \right)\Big\}e^{i\sigma\nu_{z,n}(x,y)}\varphi^{\bb K_u}_{n-1}(x,y,z) \end{equation}$$ where $\epsilon=$