Lens Models

The lens can be defined either as a function in two variables $(x,y)$ or as a sampled signal in two dimensions.

1. PsiFunctionLens uses a function.

2. SampledFunctionLens uses a sampled function (pixmap).

   • The only operational implementation is the SampledPsiFunctionLens subclass which wraps a PsiFunctionLens object, sampling its function.

   • More generic subclasses could be added.

• Common [Lens API](../Lens API)

The Lens superclass¶

The toplevel Lens class implements only one function, namely getXi which determines the apparent source position by fix-point iteration. This is intended to be shared by SampledLens and ClusterLens, but currently SampledLens implements its own fix-point iteration, and some work is needed to replace it.

Other functions raise a NotImplemented exception. We avoid abstract classes to make python binding easier.

Algebraic Lens Functions¶

The PsiFunctionLens defines the functions psiValue(), psiXvalue(), and psiYvalue() to compute $\psi$, $\partial \psi/\partial x$, and $\partial \psi/\partial y$ respectively. These functions are hardcoded, and subclasses have to be defined for each parametric lens model. Currently SIS and SIE is provided. There is also a PointMassLens class, but this has not been tested.

Sampled Lenses¶

The SampledLens class defines the lens potential $\psi$ as a 2D sampled array. The only operational subclass is SampledPsiFunctionLens which takes a constituent PsiFunctionLens object lens and samples $\psi$ by calling lens->psiValue().

The SampledLens class calculates the deflection, i.e. the derivatives of $\psi$, using a differentiation filter. This makes it an alternative approach for lenses where analytic differentiation is difficult, and an independent test where analytic derivatives have been implemented.

Note that SampledPsiFunctionLens relies on the constituent lens to calculate caustic() and criticalXi(). This should probably be changed to use generic sampled calculatation of the caustics and critical curves. (TODO)