## 2. Basics of multiple lensingWe shall study a system of n point-lenses placed at positions in coordinates normalized to the Einstein radius where is a reference mass (it can be chosen to be the total mass, the typical mass of a single object or anything else). The source coordinates are normalized to the scaled Einstein radius . The masses of the lenses are measured in terms of . We introduce the complex coordinate in the lens plane and the complex source coordinate . The positions of the masses will be denoted by . We also introduce the functions The lens equation for our system of n masses reads (Witt 1990) Given a source at position This map is locally invertible where the determinant of the Jacobian matrix is different from zero. The points where the Jacobian determinant vanishes are arranged in smooth closed curves called critical curves. The images of these points through the lens map (3) in the source plane are called caustics. When a source crosses a caustic, creation or destruction of pairs of images occurs and the magnification diverges (Schneider et al. 1992). This is all we need to start our search for secondary caustics in close multiple systems. The fundamental hypothesis we make is where © European Southern Observatory (ESO) 2000 Online publication: June 30, 2000 |