Mass sheet¶

In set_lens.c:set_dynamics(), the impact parameter is computed as such:

$b_0 = \frac{1}{2} \frac{\Sigma_0}{\Sigma_{\rm crit}}$

with $\Sigma_0$ in g/cm ², and $\Sigma_{\rm crit} = \frac{c^2}{4 \pi G}$ $\frac{D_{\rm OS}}{D_{\rm OL} D_{\rm LS}}$ g/cm ².

Note that the factor 1/2 makes the estimated density to be half the true value.

In file e_grad2.c, the 2nd derivatives of the potential are computed as such:

$\partial_{xx} \phi = \partial_{yy} \phi = b_0$

$\partial_{xy} \phi = \partial_{yx} \phi = 0$

In file e_grad.c, the 1st derivates of the potential are computed as such:

$\partial_x \phi = b_0 (x_{\rm img} -x_{\rm lens})$

$\partial_y \phi = b_0 (y_{\rm img} -y_{\rm lens}) $

This profile is not well tested.