We study three high magnification microlensing events , generally recognized as probable caustic crossings , in the optical light curves of the multiply imaged quasar Q 2237+0305 . We model the light curve of each event as the convolution of a standard thin disk luminosity profile with a straight fold caustic . We also allow for a linear gradient that can account for an additional varying background effect of microlensing . This model not only matches noticeably well the global shape of each of the three independent microlensing events but also gives remarkably similar estimates for the disk size parameter . The measured average half-light radius , R _ { 1 / 2 } = ( 3.0 \pm 1.5 ) \sqrt { M / 0.3 M \odot } light-days , agrees with previous estimates . In the three events , the core of the magnification profile exhibits “ fine structure ” related to the innermost region of the accretion disk ( located at a radial distance of 2.7 \pm 1.4 Schwarzschild radii according to our measurement ) . Relativistic beaming at the internal rim of the accretion disk can explain the shape and size of the fine structure , although alternative explanations are also possible . This is the first direct measurement of the size of a structure , likely the innermost stable circular orbit , at \sim 3 Schwarzschild radii in a quasar accretion disk . The monitoring of thousands of lensed quasars with future telescopes will allow the study of the event horizon environment of black holes in hundreds of quasars in a wide range of redshifts ( 0.5 < z < 5 ) .