3.1.3 Three-Dimensional Point Response Functions

There-dimensional point response functions are modeled as the two-dimensional ones except that the lateral function does not just depend on $x$ but on the distance from the $z$-axis ( $\sqrt{x^2+y^2}$). The $z$-axis is aligned to the ion beam direction.

$$p(x,y,z) = p_v(z)\cdot p_l(\sqrt{x^2+y^2},\sigma_l(z),\gamma_l(z), \beta_l(z))$$ (3.43)