Unbiased reconstruction of the mass function using microlensing survey   data
  The large number of microlensing events discovered towards the Galactic Bulge bears the promise to reconstruct the stellar mass function. The more interesting issue concerning the mass function is certainly to probe its low mass end. However due to the source confusion, even if the distribution and the kinematics of the lenses are known, the estimation of the mass function is extremely biased at low masses. The blending due to the source confusion biases the duration of the event, which in turn dramatically biases the estimation of the mass of the lens. To overcome this problem we propose to use differential photometry of the microlensing events obtained using the image subtraction method. Differential photometry is free of any bias due to blending, however the drawback of differential photometry is that the baseline flux is unknown. In this paper we will show that even without knowing the baseline flux, purely differential photometry allow to estimate the mass function without any biases. The basis of the method is that taking the scalar product of the microlensing light curves with a given function and taking its sum over all the microlensing events is equivalent to project the mass function on another function. This method demonstrates that there is a direct correspondancy between the space of the observations and the space of the mass function. Concerning the function to use in order to project the observations, we show that the principal components of the light curves are an optimal set. To illustrate the method we simulate sets consistent with the microlensing experiments. By using 1000 of these simulations, we show that for instance the exponent of the mass function can be reconstructed without any biases. 
C. Alard