Solar Limb Darkening Function from Baily's Beads Observations
  We introduce a method to measure with high resolution the solar diameter from the ground, through the eclipse observations by reconsidering the definition of the solar edge. The outer part of the Limb Darkening Function (LDF) is recovered using the luminosity evolution of a Baily's Bead and the profile of the lunar limb available from the Kaguya satellite. The method proposed is applied for the videos of the eclipse in January, 15, 2010 recorded by Richard Nugent in Uganda and Andreas Tegtmeier in India. The result shows light from solar limb detected at least 0.65 arcsec beyond the LDF inflection point, and this fact may suggest to reconsider the evaluations of the historical eclipses made with naked eye. 
Andrea Raponi, Costantino Sigismondi
astro-ph.SR