The Effects of Amplification Bias in Gravitational Microlensing   Experiments
  Although a source star is fainter than the detection limit imposed by crowding, it is still possible to detect an event if the star is located in the seeing disk of a bright star is and gravitationally amplified: amplification bias. Using a well-constrained luminosity function, I show that $\sim 40\%$ of events detected toward the Galactic bulge are affected by amplification bias and the optical depth might be overestimated by a factor $\sim 1.7$. In addition, I show that if one takes amplification bias into consideration, the observed time scale distribution matches significantly better, especially in the short time-scale region, with the distribution expected from a mass-spectrum model in which lenses are composed of the known stellar population plus an additional population of brown dwarfs than it is without the effect of the amplification bias. 
Cheongho Han