We study microlensing of the faint images that form close to the centers of strong gravitational lens galaxies .
These central images , which have finally begun to yield to observations , naturally appear in dense stellar fields and may be particularly sensitive to fine granularity in the mass distribution .
The microlensing magnification maps for overfocussed ( i.e. , demagnified ) images differ strikingly from those for magnified images .
In particular , the familiar “ fold ” and “ cusp ” features of maps for magnified images are only present for certain values of the fraction f of the surface mass density contained in stars .
For central images , the dispersion in microlensing magnifications is generally larger than for normal ( minimum and saddle ) images , especially when the source is comparable to or larger than the stellar Einstein radius .
The dispersion depends in a complicated way on f ; this behaviour may hold the key to using microlensing as a probe of the relative densities of stars and dark matter in the cores of distant galaxies .
Quantitatively , we predict that the central image C in PMN J1632 - 0033 has a magnification dispersion of 0.6 magnitudes for R _ { src } / R _ { E } \la 1 , or 0.3 mag for R _ { src } / R _ { E } = 10 .
For comparison , the dispersions are 0.5–0.6 mag for image B and 0.05–0.1 mag for image A , if R _ { src } / R _ { E } \la 1 ; and just 0.1 mag for B and 0.008 mag for A if R _ { src } / R _ { E } = 10 .
( The dispersions can be extrapolated to larger sources sizes as \sigma \propto R _ { src } ^ { -1 } . )
Thus , central images are more susceptible than other lensed images to microlensing and hence good probes for measuring source sizes .