“…The extended source effects in gravitational microlensing enable studying the stellar atmospheres through their limb-darkening profiles and by modelling their microlensed spectra, see Loeb & Sasselov (1995); Sasselov (1996) Pixel-lensing towards M31 may provide an efficient tool to search for exoplanets in that galaxy (Chung et al, 2006;Kim et al, 2007;Ingrosso et al, 2009), and indeed an exoplanet might be already discovered in the PA-N2-99 event (Ingrosso et al, 2009). Since source stars for pixel-lensing towards M31 are basically red giants (and therefore, their typical diameters are comparable to Einstein diameters and the caustic sizes) one has to take into account the source finiteness effect, similarly to microlensing in quasars (Agol & Krolik, 1999;Popović et al, 2006;Jovanović et al, 2008;Zakharov, 2009). As it is well known the amplifications for a finite source and for a point-like source are different because there is a gradient of amplification in respect of a source area.…”