Eric Agol JHU Imaging a Quasar Accretion Disk with Microlensing The Einstein Cross is a gravitationally lensed quasar which undergoes variations due to microlensing by stars in the lens galaxy. Microlensing constrains the size of the optical emission region to be less than $2x10^{15}$ cm. Future IR/optical/UV monitoring will allow us to map out the surface brightness of the quasar by inversion of the lightcurve during a high amplification microlensing event. If the quasar is powered by geometrically thin, azimuthally symmetric accretion onto a black hole, then the lightcurve can also be inverted to obtain the surface brightness at the accretion disk. We perform the inversion using a regularization constraint, and find that we can reproduce the surface brightness quite well (to 30\% near the peak) for accretion disk models which are consistent with the dereddened data, assuming that we have 1\% photometry from K band to near UV at 40 points during a clean high amplification event. We will also be able to constrain the inclination angle of the disk, the spin of the black hole, and size of the black hole (if the caustic velocity is known).