Impact parameter sign degeneracy

This degeneracy arises from symmetries in the caustic structure. The caustic is defined in lens-centered coordinates, such that the impact parameter, u, can take positive and negative values.

For the binary-lens case shown below, the lens-source relative trajectory means that the source intersects the caustic in two places where the magnification is identical, producing an identical lightcurve. These points occur at u and -u.

In point-source, point-lens models, the caustic is a point. Since this is symmetrical from all directions, the models do not have an α parameter, but the same impact parameter degeneracy exists.

Caustic structure with source trajectory intersecting with negative impact parameter [R.A.Street]

Caustic structure with source trajectory intersecting with positive impact parameter [R.A.Street]

Lightcurve of source trajectory intersecting caustic with negative impact parameter [R.A.Street]

Lightcurve of source trajectory intersecting caustic with positive impact parameter [R.A.Street]