  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.
