Apparent position

Roulette amplitudes are normally calculated in the apparent position $\nu$ of the source. The known parameter is the actual position $\eta$, while $\nu$ has to be computed. There are three approaches.

• The SIS lens has constant deflection, and hence the raytrace equation can be used.

  • $\nu = \chi\eta + \nabla\psi(\chi\eta)$

• The point mass lens gives a quadratic equation whose solution is

  • $\chi\eta/2 + \sqrt{\frac14+R_E^2}\cdot\frac{\chi\eta}{||\chi\eta||}$

• The universal solution is to use fix-point iteration to find the solution numerically